# Band Nonlinearity-Enabled Manipulation of Dirac Nodes, Weyl Cones, and Valleytronics with Intense Linearly Polarized LightClick to copy article linkArticle link copied!

- Ofer Neufeld
*****Ofer NeufeldCenter for Free-electron Laser Science, Max Planck Institute for the Structure and Dynamics of Matter, Hamburg 22761, Germany*****E-mail: [email protected]More by Ofer Neufeld - Hannes HübenerHannes HübenerCenter for Free-electron Laser Science, Max Planck Institute for the Structure and Dynamics of Matter, Hamburg 22761, GermanyMore by Hannes Hübener
- Gregor JotzuGregor JotzuCenter for Free-electron Laser Science, Max Planck Institute for the Structure and Dynamics of Matter, Hamburg 22761, GermanyMore by Gregor Jotzu
- Umberto De GiovanniniUmberto De GiovanniniDipartimento di Fisica e Chimica─Emilio Segrè, Università degli Studi di Palermo, Palermo I-90123, ItalyMore by Umberto De Giovannini
- Angel Rubio
*****Angel RubioCenter for Computational Quantum Physics (CCQ), The Flatiron Institute, New York, New York 10010, United States*****E-mail: [email protected]More by Angel Rubio

## Abstract

We study low-frequency linearly polarized laser-dressing in materials with valley (graphene and hexagonal-Boron-Nitride) and topological (Dirac- and Weyl-semimetals) properties. In Dirac-like linearly dispersing bands, the laser substantially moves the Dirac nodes away from their original position, and the movement direction can be fully controlled by rotating the laser polarization. We prove that this effect originates from band nonlinearities away from the Dirac nodes. We further demonstrate that this physical mechanism is widely applicable and can move the positions of the valley minima in hexagonal materials to tune valley selectivity, split and move Weyl cones in higher-order Weyl semimetals, and merge Dirac nodes in three-dimensional Dirac semimetals. The model results are validated with ab initio calculations. Our results directly affect efforts for exploring light-dressed electronic structure, suggesting that one can benefit from band nonlinearity for tailoring material properties, and highlight the importance of the full band structure in nonlinear optical phenomena in solids.

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Light-induced band structure and optoelectronic device engineering has gained considerable attention in recent years due to its potential to revolutionize electronics. (1−21) Within this paradigm, a system is irradiated by a coherent laser pulse that dresses the electronic states, potentially changing their properties. The process allows modifying band dispersions, turning insulators into conductors and vice versa, altering the crystal symmetry, and tuning the system’s topology. (2,3,9,15,20−32)

One of the most-studied materials for light-induced band engineering is graphene, which in the absence of driving is a two-dimensional (2D) Dirac semimetal with the band touching at the K and K′ points in the Brillouin zone (BZ). The degeneracies can be lifted when driving the system with circularly polarized light, generating diverse topological phases. (15,18,22,23,26) The effect is attributed to the breaking of time-reversal symmetry (TRS). The gap opening in light-driven graphene has not yet been observed in angle-resolved photoemission spectroscopy (ARPES) due to various possible experimental limitations, (32−34) but hybridization gaps have been seen in other systems. (2,35) On the other hand, topologically trivial gap opening in graphene also occurs without breaking TRS if inversion symmetry is lifted (36,37) or strain is introduced (moving the Dirac nodes until oppositely charged nodes annihilate to open a gap). (38,39) It was also shown in optical lattices that by shaking the lattice, one can move the Dirac nodes along high-symmetry axes until they merge, (40,41) with analogous phenomena occurring in the very intense high frequency driven regimes. (42)

Here we show that with strong-field and low frequency laser driving, a linearly polarized monochromatic field can move the Dirac nodes in the BZ by a substantial amount, and the movement’s direction is fully controlled by the laser polarization. Effectively, this opens a large pseudogap at the original position of the Dirac nodes. We analytically show that the physical mechanism for the effect relies on band nonlinearities and therefore does not appear in the simplest linearized low-energy model of Dirac bands. We validate these results with time-dependent density functional theory (TDDFT) calculations of ARPES spectra. Lastly, we show that this physical mechanism is general and allows versatile control of the band engineering in a wide range of materials. As examples, we demonstrate control over the position of the valley minima and valleytronics in hexagonal-Boron-Nitride (hBN, allowing valleytronics control in transition-metal-dichalcogenides), (43−46) splitting and moving charge-II Weyl cones, (47) and merging Dirac nodes in three-dimensional (3D) Dirac semimetals. (48,49)

We begin by analyzing a graphene system with a two-band tight-binding (TB) model with fifth-order nearest-neighbor (NN) terms. (50) In the basis of creation/annihilation operators on the A/B sublattice sites of the honeycomb lattice, the field-free Hamiltonian is

*t*

_{i}are hopping amplitudes to the

*i*th NN site, and

*f*

_{i}(

**k**) are structure factors (see Supporting Information (SI) section I). The second term in eq 1 conveniently sets the top of the valence band to zero energy, while the first term represents the various hopping processes. Note that $\hat{{H}_{0}\phantom{\rule{0em}{0ex}}}$ inherently does not include $\hat{{\sigma}_{z}\phantom{\rule{0em}{0ex}}}$, setting the gap to zero and resulting in Dirac cones with local linear dispersion in the K/K′ points. The eigenvalues of $\hat{{H}_{0}\phantom{\rule{0em}{0ex}}}$, denoted as ϵ

_{±}(

**k**), are obtained analytically. The hopping amplitudes are fitted through least-squares such that ϵ

_{±}(

**k**) match bands obtained from density functional theory (DFT) calculations performed using octopus code (51−53) within the local density approximation (see SI sections II and III). Notably, the TB model provides very good bands around the K/K′ valleys (the main region of interest) but fails around the Γ-point.

$\hat{{H}_{0}\phantom{\rule{0em}{0ex}}}$ is coupled to an external laser by Peierls substitution, yielding

*E*

_{0}is the field amplitude, ω is the driving frequency,

*c*is the speed of light, and

**ê**is a polarization vector. From this time-periodic Hamiltonian we obtain the Floquet Hamiltonian in the basis of harmonic functions of ω with the sub-blocks:

*n*–

*m*| is the photon channel order, and the integrals in eq 2 are solved numerically. ${\hat{H}}_{\mathrm{F}}(\mathbf{k})$ is then exactly diagonalized, and the eigen-energies are corrected by their photon-channel index. The resulting Floquet quasi-energy valence and conduction bands, ϵ

_{±}

^{F}(

**k**), are taken as the bands that converge to the field-free bands for

*E*

_{0}→ 0.

Our main interest is the position of the Dirac nodes in the driven system. Since in graphene the Dirac nodes host a nonzero Berry phase, (54−56) they cannot be removed by a linearly polarized laser field (that does not break inversion or TRS (57)) unless oppositely charged nodes merge. (58) However, we can still track the nodes’ movements with respect to laser driving. In order to simplify the analysis, we initially ask whether a Floquet quasi-energy gap can open in the original positions of the Dirac nodes at K/K′, defined as *E*_{g}^{F} = ϵ_{+}^{F}(**K**) – ϵ_{–}^{F}(**K**). If a gap opens, the linearly dispersing nodes have moved (note that we will later analyze directly the movement of the nodes). We analyze the Floquet propagator, ${\hat{U}}_{\mathrm{F}}(\mathbf{k})=\mathrm{exp}(-i{\int}_{0}^{2\pi /\omega}\hat{H}(\mathbf{k},t))$, and use atomic units unless stated otherwise. ${\hat{U}}_{\mathrm{F}}$ describes time propagation over one laser cycle, and taking the logarithm of its eigenvalues is formally equivalent to diagonalizing the Floquet Hamiltonian. (27) The propagator can be represented by a time-independent effective Hamiltonian, (26,59) ${\hat{U}}_{\mathrm{F}}(\mathbf{k})=\mathrm{exp}(-i\frac{2\pi}{\omega}{\hat{H}}_{\mathrm{eff}}(\mathbf{k}))$, where ${\hat{H}}_{\mathrm{eff}}$ comprises a Magnus series expansion:

The main question of interest is under which conditions do the even-order terms vanish. Let us first prove that for the perfectly linear low-energy Dirac Hamiltonian, fields that do not break TRS cannot open a gap at K. For this, we take the first-order expansion of $\hat{H}(\mathbf{k},t)$ around K, ${\hat{H}}_{\mathrm{D}}(\mathbf{k})=$ ${v}_{\mathrm{f}}({\mathrm{\Delta}k}_{x}\hat{{\sigma}_{x}\phantom{\rule{0em}{0ex}}}+{\mathrm{\Delta}k}_{y}\hat{{\sigma}_{y}\phantom{\rule{0em}{0ex}}})$, where Δ**k** is the momenta away from K and *v*_{f} is the Fermi velocity. Coupling ${\hat{H}}_{\mathrm{D}}(\mathbf{k})$ to an external laser field provides a time-periodic Hamiltonian that is inserted in the Magnus expansion. Due to the linearity of the Dirac Hamiltonian, we obtain $\hat{{H}_{1}\phantom{\rule{0em}{0ex}}}={\hat{H}}_{\mathrm{D}}$ (because ∫_{0}^{2π/ω}**A**(*t*) = 0). Thus, for the Dirac Hamiltonian, only higher order terms can alter the band structure. For $\hat{{H}_{2}\phantom{\rule{0em}{0ex}}}$, we find

There are three main terms inside the integral in eq 4: the first two in the top row vanish at K (Δ**k** = 0). The third term is *k*-independent, and the only one that survives at K. This term clearly vanishes for linear driving since then one of the laser polarization components is zero. We now show that it also vanishes for any TRS field. First, we separate the double integral in the third term in eq 4:

**A**(

*t*) with a pure harmonic sine series,

**A**(

*t*) = ∑

**a**

_{m}sin (

*mωt*), such that the electric field is given by a pure cosine series,

**E**(

*t*) = $-\frac{1}{c}{\partial}_{t}\mathbf{A}(t)=-\omega /c\sum {\mathbf{a}}_{m}m\phantom{\rule{.25em}{0ex}}\mathrm{cos}\phantom{\rule{.1em}{0ex}}(m\omega t)$, inherently respecting TRS (

**E**(

*t*) =

**E**(−

*t*)). Plugging these into eq 5, we note that one polarization component of

**A**(

*t*) is always integrated over in the

*t*′ integral, giving a time-even function, while the other component remains time-odd. The second temporal integral over

*t*then vanishes since it integrates a time-odd function. Thus, $\hat{{H}_{2}\phantom{\rule{0em}{0ex}}}=0$ in the Dirac Hamiltonian for any TRS drive. In the SI (section VI), we generalize this proof to all even orders of the Magnus expansion. Overall, a Floquet pseudogap cannot open in the low-energy Dirac Hamiltonian driven by a TRS field. This is a well-established result that has been shown with other methodologies. It is, however, potentially misleading because it seemingly pinpoints the physical reason a gap does not open at K to the presence of TRS. Contrarily, we argue that the physical origin of the effect is the linearity of the Hamiltonian (and similarly, Weyl (13) or other linearly dispersing systems (7)). Indeed, if one repeats the analysis for a field-free parabolic Hamiltonian of the form $H(\mathbf{k})=v({\mathrm{\Delta}k}_{x}^{2}\hat{{\sigma}_{x}\phantom{\rule{0em}{0ex}}}+{\mathrm{\Delta}k}_{y}^{2}\hat{{\sigma}_{y}\phantom{\rule{0em}{0ex}}})$, the proof no longer holds regardless of TRS. One can verify that in that case, a Floquet gap does open, even though the Hamiltonian is spherically symmetric and in a low-energy continuum form.

For completeness, we repeat the analysis for the TB Hamiltonian at K, keeping only up to second-order NN terms and employing a linearly polarized drive along *k*_{y} (respecting TRS). $\hat{{H}_{2}\phantom{\rule{0em}{0ex}}}(\mathbf{K})$ takes the form:

*t*

_{1}and be independent of

*t*

_{2}(as well as

*t*

_{5}) because they only couple to $\hat{{\sigma}_{0}\phantom{\rule{0em}{0ex}}}$ terms that commute. However, the size of the gap and its scaling with the laser parameters is not expected to correspond well with the size of ${\hat{H}}_{2}(\mathbf{K})$ because in practical conditions, higher order terms in the magnus expansion cannot be neglected. (60,61) Moreover, in the fifth-NN TB Hamiltonian, the

*t*

_{1}hopping term interferes with higher-order terms, leading to more complex dynamics (see SI section VI). Nonetheless, even if not quantitative, this analysis establishes the gap opening at K and its physical origin─if ${\hat{H}}_{2}(\mathbf{K})\ne 0$, higher order terms will also be nonzero, and there is no general symmetry constraint that causes their summation to vanish. In the SI (section VI), we provide thorough exact numerical investigations of the size of the pseudogap; it indeed scales parabolically with

*t*

_{1}and does not scale with

*t*

_{2}, corroborating the analytical analysis. We generally found that the gap at K can be very substantial (up to 0.5 eV). Practically, we recall that this pseudogap means that the Dirac nodes moved elsewhere, where a larger gap suggests the positions have moved further away from K/K′.

Before moving further, it is worth highlighting some noteworthy points: (i) If *E*_{0}/ω ∼ 1, the Magnus series can converge very slowly, or even diverge, but it is still valid for determining if a gap opens at K. (ii) The gap at K (and Dirac nodes movement) arises from band nonlinearity in the field-free Hamiltonian away from K, and it vanishes in the limit where the low-energy Dirac Hamiltonian becomes valid. However, simply evaluating the Hamiltonian in the vicinity of K does not guarantee that the low-energy expansion around it is valid; rather, *E*_{0}/ω must be sufficiently small. This condition breaks if *E*_{0} is large, or ω is small, as obtained in the strong-field limit, and it is already broken in often-employed conditions for observing Floquet sidebands (powers of ∼10^{11} W/cm^{2} and wavelengths ∼1600 nm open a pseudogap of ∼50 meV and move the Dirac node ∼0.3% of the BZ along *k*_{x}). (iii) The Dirac node motion strongly depends on the laser orientation, since that greatly changes the Magnus expansion. For instance, for a laser polarized along *k*_{x}, we obtain *g*(*t*,*t*^{′}) = 0, and only even terms beyond the fourth-order in the Magnus expansion are nonzero.

Having established this result, we numerically investigated its dependence on the laser parameters. When graphene is driven along high symmetry axes (along Γ–*M* or Γ–*K*), we find that the Dirac nodes only move along the *k*_{x} axis (similarly to shaken optical lattices (40)). Figure 1(a,b) presents the distance of the out-of-equilibrium Dirac nodes from K (Δ*K*) vs laser power and wavelength, which can be quite substantial, and up to ∼10% of the BZ in reasonable experimental conditions. In more extreme cases, oppositely charged Dirac nodes can even merge. We determined that this process requires laser powers of ∼10^{13} W/cm^{2} (at 1600 nm driving wavelength along the *x*-axis), although this value is qualitative because it depends on the details of the TB model around Γ, where it fails. This critical power is slightly higher than graphene’s damage threshold, implying that linearly polarized driving cannot open a proper gap.

Slightly different results are observed for *y*-polarized driving, where the Dirac nodes move in the opposite direction (Figure 1(a,b)). Interestingly, here, the Dirac node at K(K′) interacts with the hybridized Floquet sidebands (replicas of K′(K)) until they gradually merge and open a gap for a certain critical pump wavelength and power. At that point, another gapless sideband enters the region. Such dynamics continue for longer wavelengths (or higher intensities), where more sidebands enter the region around K/K′. The effect is similar to phenomena observed in other driving conditions with Dirac point spawning, (26,36) but seems distinct to very long wavelength driving at which it also becomes difficult to distinguish between Floquet replicas and the original Dirac points (see SI section VI). Thus, measuring the position of the Dirac nodes with respect to the driving parameters could potentially probe additional information about the system such as band hybridization.

Figure 1(c,d) plots the position of the Dirac nodes in the driven system vs the laser polarization axis (both angle, θ_{K}─the angle of the shifted Dirac point around its original position, and distance, *R*_{K}─the distances of the shifted Dirac point from its original position; see illustrated trajectories in the inset of Figure 1(d)). As the laser polarization rotates, the Dirac nodes smoothly rotate (with a trigonal pattern) around their equilibrium positions in correspondence. This verifies that a single monochromatic linearly polarized laser can arbitrarily place the Dirac nodes in the BZ.

We next show that these results are not specific to graphene, or even to linearly dispersing systems; band nonlinearity inherently exists in all periodic systems regardless of their low-energy local structure. First, we perform similar calculations in monolayer hBN (see SI section V and ref (62) for details). Figure 2(a,b) shows that the position of the valley minima (defined as the minimal optical gap points in the BZ) moves around with the laser drive and rotates around their equilibrium position by few percent. This provides a potential path to optically tune valley selectivity (also in transition-metal-dichalcogenides) without circular driving, because the local orbital character around the minima point differs from that at K/K′, and the valley minima can be arbitrarily shifted away (whereas with circular driving, it is fixed due to rotational symmetry). This is especially clear if one considers that valley optical selection rules can be explicitly derived only at K/K′ points, while the Bloch states have mixed character in their vicinity. (45,46) Second, we perform similar calculations in the 3D Dirac semimetal, Na_{3}Bi (48,49) (see SI section V). Crucially, in Na_{3}Bi even the low-energy Hamiltonian contains large nonlinearities at the Dirac nodes because they arise from a crossing of two parabolic bands. Figure 2(c) shows that linearly polarized laser driving can move the Dirac nodes just as in graphene. The two nodes merge at laser powers of ∼10^{11} W/cm^{2} (at 1600 nm), which is within experimental feasibility. Physically, this merging is possible in Na_{3}Bi because the nodes are initially relatively close to each other. However, this predicted critical power might slightly differ in the realistic system due to the validity of the low energy Hamiltonian around Γ. Third, we calculate the Floquet quasi-energy bands for linearly polarized driven SrSi_{2}, which is a Charge-II Weyl semimetal with parabolically dispersing Weyl cones. (47) Due to the parabolic dispersion, the system is inherently nonlinear (see SI section V). We find that the laser splits the Charge-II Weyl cone into two Charge-I linearly dispersing cones. Figure 2(d) shows that as the driving power increases, the new charge-I cones move further apart. We have found that their motion can be fully controlled within the *xy*-plane, in which the field-free bands are parabolic (following the laser polarization). Along the *k*_{z}-axis on the other hand, the electronic bands are linearly dispersing and no driving parameters can move the Weyl cones. This highlights that the physical mechanism relies on band nonlinearity.

Lastly, to further establish the model results, we performed ab initio TDDFT calculations of ARPES in light-driven graphene. The methodology follows ref (63), but with artificially doping the conduction band to make the ARPES signals from it more visible. All details of these calculations are delegated to the SI section IV (see also refs (51−53), (64−67)). Figure 3 presents the resulting spectra along *k*_{x}- and *k*_{y}-axes overlaid with the quasi-energy bands obtained from the model, which agree remarkably well; a large gap of ∼0.18 eV opens at the original K point (seen when plotting along *k*_{y}), and the Dirac nodes shifts by ∼1.15% of the BZ along *k*_{x}. Note that the use of the Dirac Hamiltonian in this case completely fails in describing the spectra because it fixes the Dirac nodes to K/K′. We further emphasize that even though intense pumping is required to observe these phenomena in ARPES, intensities of up to 4 × 10^{10} W/cm^{2} are already achievable, (68) and work is underway to allow even more intense pumping. (69) Moreover, by utilizing longer wavelength pumps (e.g., in the THz regime (70)), weaker peak powers can be used to observe similar phenomena (see SI section VI). Regardless, even weaker signals of Dirac point motion could be extracted from experimental spectra by subtracting the field-free backgrounds or utilizing only their asymmetric part. Furthermore, as the motion is polarization-dependent, spectra obtained at different polarizations will help distill the signal. Therefore, these predictions should be experimentally accessible with the current technology.

To conclude, we investigated several material systems irradiated by intense low-frequency linearly polarized lasers. For Dirac linearly dispersing systems, we showed that the laser moves the Dirac nodes away from their initial position. This motion is substantial and can be fully controlled by changing the laser parameters (intensity, wavelength, polarization). The effect was analytically shown to originate from band nonlinearities, highlighting the importance of the employed model. Consequently, our results emphasize the obvious yet sometimes overlooked feature that low-energy Hamiltonians fail when driven by sufficiently intense or long-wavelength lasers. We further validated the generality of the physical mechanism with extensive additional calculations, showing that linearly polarized driving can: (i) control the positions of valley minima in valley-selective materials (tuning valleytronics), (ii) merge Dirac nodes in 3D Dirac semimetals, and (iii) split high-order Weyl cones and control the positions of the resulting linearly dispersing cones. We confirmed the model results with ab initio TDDFT calculations and outlined an ARPES setup able to test our predictions.

The present findings should help guide future experiments and theory of Floquet band engineering; and in particular, to benefit from electronic band structure nonlinearities to tailor material properties. Our results also emphasize the importance of the full BZ and band structure away from the minimal gap points in strong-field physics processes in solids, such as high harmonic generation, (71−73) photogalvanic effects, (74−76) magneto-optical effects, (77,78) and more. This is especially relevant in quantum materials and systems with topological or linearly dispersing bands, (70,79−83) motivating development of ab initio methodologies. We expect that the movement of the high-symmetry points in the BZ will imprint additional characteristics not only directly in ARPES, but also for linear and nonlinear optical responses such as transient absorption spectra and high harmonic generation, which should motivate future work.

## Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.3c02139.

Technical details of the tight-binding model. Technical details about the DFT calculations and fitting procedures of the tight binding hopping amplitudes. Technical details of the TDDFT calculations and ARPES calculations. Technical details of the Floquet calculations in material systems other than graphene. Extended proof that all higher-order even Magnus expansion terms vanish in the Dirac Hamiltonian driven by time-reversal symmetric light. Extended numerical investigation of the pseudogap opening in graphene and its scaling with laser parameters and tight-binding parameters. Additional results of tr-ARPES in graphene for other laser parameters. (PDF)

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Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

## Acknowledgments

This work was supported by the Cluster of Excellence Advanced Imaging of Matter (AIM) – EXC 2056 – project ID 390715994, SFB-925 “Light induced dynamics and control of correlated quantum systems”, project 170620586 of the Deutsche Forschungsgemeinschaft (DFG), Grupos Consolidados (IT1453-22), and the Max Planck–New York City Center for Non-Equilibrium Quantum Phenomena. The Flatiron Institute is a division of the Simons Foundation. O.N. gratefully acknowledges the generous support of a Schmidt Science Fellowship.

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Phys.*2021,*17*(10), 1087– 1092, DOI: 10.1038/s41567-021-01366-1Google Scholar4https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitF2nsLzF&md5=2e012e8596e698decdeb4cd29ed2255bEngineering crystal structures with lightDisa, Ankit S.; Nova, Tobia F.; Cavalleri, AndreaNature Physics (2021), 17 (10), 1087-1092CODEN: NPAHAX; ISSN:1745-2473. (Nature Portfolio)Abstr.: The crystal structure of a solid largely dictates its electronic, optical and mech. properties. Indeed, much of the exploration of quantum materials in recent years including the discovery of new phases and phenomena in correlated, topol. and two-dimensional materials-has been based on the ability to rationally control crystal structures through materials synthesis, strain engineering or heterostructuring of van der Waals bonded materials. These static approaches, while enormously powerful, are limited by thermodn. and elastic constraints. An emerging avenue of study has focused on extending such structural control to the dynamical regime by using resonant laser pulses to drive vibrational modes in a crystal. This paradigm of 'nonlinear phononics' provides a basis for rationally designing the structure and symmetry of crystals with light, allowing for the manipulation of functional properties at high speed and, in many instances, beyond what may be possible in equil. Here we provide an overview of the developments in this field, discussing the theory, applications and future prospects of optical crystal structure engineering.**5**Castro, A.; De Giovannini, U.; Sato, S. A.; Hübener, H.; Rubio, A. Floquet Engineering the Band Structure of Materials with Optimal Control Theory.*Phys. Rev. Res.*2022,*4*(3), 33213, DOI: 10.1103/PhysRevResearch.4.033213Google Scholar5https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38Xis1yls77F&md5=c41cc847f94d308796b5dedad0c5225fFloquet engineering the band structure of materials with optimal control theoryCastro, Alberto; De Giovannini, Umberto; Sato, Shunsuke A.; Hubener, Hannes; Rubio, AngelPhysical Review Research (2022), 4 (3), 033213CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)We demonstrate that the electronic structure of a material can be deformed into Floquet pseudobands with arbitrarily tailored shapes. We achieve this goal with a combination of quantum optimal control theory and Floquet engineering. The power and versatility of this framework is demonstrated here by utilizing the independent-electron tight-binding description of the π electronic system of graphene. We show several prototype examples focusing on the region around the K (Dirac) point of the Brillouin zone: creation of a gap with opposing flat valence and conduction bands, creation of a gap with opposing concave sym. valence and conduction bands (which would correspond to a material with an effective neg. electron-hole mass), and closure of the gap when departing from a modified graphene model with a nonzero field-free gap. We employ time-periodic drives with several frequency components and polarizations, in contrast to the usual monochromatic fields, and use control theory to find the amplitudes of each component that optimize the shape of the bands as desired. In addn., we use quantum control methods to find realistic switch-on pulses that bring the material into the predefined stationary Floquet band structure, i.e., into a state in which the desired Floquet modes of the target bands are fully occupied, so that they should remain stroboscopically stationary, with long lifetimes, when the weak periodic drives are started. Finally, we note that although we have focused on solid state materials, the technique that we propose could be equally used for the Floquet engineering of ultracold atoms in optical lattices and for other nonequil. dynamical and correlated systems.**6**Lu, M.; Reid, G. H.; Fritsch, A. R.; Piñeiro, A. M.; Spielman, I. B. Floquet Engineering Topological Dirac Bands.*Phys. Rev. Lett.*2022,*129*(4), 40402, DOI: 10.1103/PhysRevLett.129.040402Google Scholar6https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitFSgtL%252FO&md5=b7bd00c888495a56e5e47c356e71e23bFloquet Engineering Topological Dirac BandsLu, Mingwu; Reid, G. H.; Fritsch, A. R.; Pineiro, A. M.; Spielman, I. B.Physical Review Letters (2022), 129 (4), 040402CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We exptl. realized a time-periodically modulated 1D lattice for ultracold atoms featuring a pair of linear bands, each with a Floquet winding no. These bands are spin-momentum locked and almost perfectly linear everywhere in the Brillouin zone: a near-ideal realization of the 1D Dirac Hamiltonian. We characterized the Floquet winding no. using a form of quantum state tomog., covering the Brillouin zone and following the micromotion through one Floquet period. Last, we altered the modulation timing to lift the topol. protection, opening a gap at the Dirac point that grew in proportion to the deviation from the topol. configuration.**7**Trevisan, T. V.; Arribi, P. V.; Heinonen, O.; Slager, R.-J.; Orth, P. P. Bicircular Light Floquet Engineering of Magnetic Symmetry and Topology and Its Application to the Dirac Semimetal Cd3As2.*Phys. Rev. Lett.*2022,*128*(6), 66602, DOI: 10.1103/PhysRevLett.128.066602Google Scholar7https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XkvVansro%253D&md5=a75b471ab3f985b9a7b65aba42970014Bicircular Light Floquet Engineering of Magnetic Symmetry and Topology and Its Application to the Dirac Semimetal Cd3As2Trevisan, Thais V.; Arribi, Pablo Villar; Heinonen, Olle; Slager, Robert-Jan; Orth, Peter P.Physical Review Letters (2022), 128 (6), 066602CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We show that bicircular light (BCL) is a versatile way to control magnetic symmetries and topol. in materials. The elec. field of BCL, which is a superposition of two circularly polarized light waves with frequencies that are integer multiples of each other, traces out a rose pattern in the polarization plane that can be chosen to break selective symmetries, including spatial inversion. Using a realistic low-energy model, we theor. demonstrate that the three-dimensional Dirac semimetal Cd3As2 is a promising platform for BCL Floquet engineering. Without strain, BCL irradn. induces a transition to a noncentrosym. magnetic Weyl semimetal phase with tunable energy sepn. between the Weyl nodes. In the presence of strain, we predict the emergence of a magnetic topol. cryst. insulator with exotic unpinned surface Dirac states that are protected by a combination of twofold rotation and time reversal (2') and can be controlled by light.**8**Bhattacharya, U.; Chaudhary, S.; Grass, T.; Johnson, A. S.; Wall, S.; Lewenstein, M. Fermionic Chern Insulator from Twisted Light with Linear Polarization.*Phys. Rev. B*2022,*105*(8), L081406, DOI: 10.1103/PhysRevB.105.L081406Google Scholar8https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XntlCitrk%253D&md5=ed1e99024ca533b4f5e1751334570df8Fermionic Chern insulator from twisted light with linear polarizationBhattacharya, Utso; Chaudhary, Swati; Grass, Tobias; Johnson, Allan S.; Wall, Simon; Lewenstein, MaciejPhysical Review B (2022), 105 (8), L081406CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)The breaking of time-reversal symmetry is a crucial ingredient to topol. bands. It can occur intrinsically in materials with magnetic order, or be induced by external fields, such as magnetic fields in quantum Hall systems or circularly polarized light fields in Floquet Chern insulators. Apart from polarization, photons can carry another degree of freedom, orbital angular momentum, through which time-reversal symmetry can be broken. In this Letter we pose the question of whether this property allows for inducing topol. bands via a linearly polarized but twisted light beam. To this end we study a graphenelike model of electrons on a honeycomb lattice interacting with a twisted light field. To identify the topol. behavior of the electrons, we calc. their local markers of Chern no. and monitor the presence of in-gap edge states. Our results are shown to be fully analogous to the behavior found in paradigmatic models for static and driven Chern insulators, and realizing the state is exptl. straightforward. With this, our work establishes a mechanism for generating fermionic topol. phases of matter that can harness the central phase singularity of an optical vortex beam.**9**Uzan-Narovlansky, A. J.; Jimenez-Galan, A.; Orenstein, G.; Silva, R. E. F.; Arusi-Parpar, T.; Shames, S.; Bruner, B. D.; Yan, B.; Smirnova, O.; Ivanov, M.; Dudovich, N. Observation of Light-Driven Band Structure via Multiband High-Harmonic Spectroscopy.*Nat. Photonics*2022,*16*, 428– 432, DOI: 10.1038/s41566-022-01010-1Google Scholar9https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsFKgtLzE&md5=38996d61df8f9395e3a638e25842da91Observation of light-driven band structure via multiband high-harmonic spectroscopyUzan-Narovlansky, Ayelet J.; Jimenez-Galan, Alvaro; Orenstein, Gal; Silva, Rui E. F.; Arusi-Parpar, Talya; Shames, Sergei; Bruner, Barry D.; Yan, Binghai; Smirnova, Olga; Ivanov, Misha; Dudovich, NiritNature Photonics (2022), 16 (6), 428-432CODEN: NPAHBY; ISSN:1749-4885. (Nature Portfolio)Intense light-matter interactions have revolutionized our ability to probe and manipulate quantum systems at sub-femtosecond timescales1, opening routes to the all-optical control of electronic currents in solids at petahertz rates2-7. Such control typically requires elec.-field amplitudes in the range of almost volts per angstrom, when the voltage drop across a lattice site becomes comparable to the characteristic bandgap energies. In this regime, intense light-matter interaction induces notable modifications to the electronic and optical properties8-10, dramatically modifying the crystal band structure. Yet, identifying and characterizing such modifications remain an outstanding problem. As the oscillating elec. field changes within the driving field's cycle, does the band structure follow and how can it be defined. Here we address this fundamental question, proposing all-optical spectroscopy to probe the laser-induced closing of the bandgap between adjacent conduction bands. Our work reveals the link between nonlinear light-matter interactions in strongly driven crystals and the sub-cycle modifications in their effective band structure.**10**Bloch, J.; Cavalleri, A.; Galitski, V.; Hafezi, M.; Rubio, A. Strongly Correlated Electron–Photon Systems.*Nature*2022,*606*(7912), 41– 48, DOI: 10.1038/s41586-022-04726-wGoogle Scholar10https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhtlyjurfO&md5=6d0f03a30e70b06b578199d5bca0eb35Strongly correlated electron-photon systemsBloch, Jacqueline; Cavalleri, Andrea; Galitski, Victor; Hafezi, Mohammad; Rubio, AngelNature (London, United Kingdom) (2022), 606 (7912), 41-48CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Abstr.: An important goal of modern condensed-matter physics involves the search for states of matter with emergent properties and desirable functionalities. Although the tools for material design remain relatively limited, notable advances have been recently achieved by controlling interactions at heterointerfaces, precise alignment of low-dimensional materials and the use of extreme pressures. Here we highlight a paradigm based on controlling light-matter interactions, which provides a way to manipulate and synthesize strongly correlated quantum matter. We consider the case in which both electron-electron and electron-photon interactions are strong and give rise to a variety of phenomena. Photon-mediated supercond., cavity fractional quantum Hall physics and optically driven topol. phenomena in low dimensions are among the frontiers discussed in this Perspective, which highlights a field that we term here 'strongly correlated electron-photon science'.**11**Esin, I.; Rudner, M. S.; Lindner, N. H. Floquet Metal-to-Insulator Phase Transitions in Semiconductor Nanowires.*Sci. Adv.*2020,*6*(35), eaay4922 DOI: 10.1126/sciadv.aay4922Google ScholarThere is no corresponding record for this reference.**12**Topp, G. E.; Jotzu, G.; McIver, J. W.; Xian, L.; Rubio, A.; Sentef, M. A. Topological Floquet Engineering of Twisted Bilayer Graphene.*Phys. Rev. Res.*2019,*1*(2), 023031, DOI: 10.1103/PhysRevResearch.1.023031Google Scholar12https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhvVOhtrnL&md5=1e7134e69316bd9efcaf8348bb607130Topological floquet engineering of twisted bilayer grapheneTopp, Gabriel E.; Jotzu, Gregor; McIver, James W.; Xian, Lede; Rubio, Angel; Sentef, Michael A.Physical Review Research (2019), 1 (2), 023031CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)We investigate the topol. properties of Floquet-engineered twisted bilayer graphene above the so-called magic angle driven by circularly polarized laser pulses. Employing a full Moire-unit-cell tight-binding Hamiltonian based on first-principles electronic structure, we show that the band topol. in the bilayer, at twisting angles above 1.05°, essentially corresponds to the one of single-layer graphene. However, the ability to open topol. trivial gaps in this system by a bias voltage between the layers enables the full topol. phase diagram to be explored, which is not possible in single-layer graphene. Circularly polarized light induces a transition to a topol. nontrivial Floquet band structure with the Berry curvature analogus to a Chern insulator. Importantly, the twisting allows for tuning electronic energy scales, which implies that the electronic bandwidth can be tailored to match realistic driving frequencies in the UV or midinfrared photon-energy regimes. This implies that Moire superlattices are an ideal playground for combining twistronics, Floquet engineering, and strongly interacting regimes out of thermal equil.**13**Hübener, H.; Sentef, M. A.; De Giovannini, U.; Kemper, A. F.; Rubio, A. Creating Stable Floquet-Weyl Semimetals by Laser-Driving of 3D Dirac Materials.*Nat. Commun.*2017,*8*, 13940, DOI: 10.1038/ncomms13940Google ScholarThere is no corresponding record for this reference.**14**Nag, T.; Slager, R.-J.; Higuchi, T.; Oka, T. Dynamical Synchronization Transition in Interacting Electron Systems.*Phys. Rev. B*2019,*100*(13), 134301, DOI: 10.1103/PhysRevB.100.134301Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXit1ygt7fL&md5=5a14fcbd33acf3b0dc2c0372198ed387Dynamical synchronization transition in interacting electron systemsNag, Tanay; Slager, Robert-Jan; Higuchi, Takuya; Oka, TakashiPhysical Review B (2019), 100 (13), 134301CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)A review. Synchronization is a ubiquitous phenomenon in nature and we propose its new perspective in ultrafast dynamics in interacting electron systems. In particular, using graphene irradiated by an intense bicircular pulse laser as a prototypical and exptl. viable example, we theor. investigate how to selectively generate a coherent oscillation of electronic order such as charge d. orders (CDOs). The key is to use tailored fields that match the cryst. symmetry broken by the target order. After the pump, a macroscopic no. of electrons start oscillating and coherence is built up through a transition. The resulting physics is detectable as a coherent light emission at the synchronizion frequency and may be used as a purely electronic way of realizing Floquet states respecting exotic space-time cryst. symmetries. In the process, we also explore possible flipping of existing static CDOs and generation of higher harmonics. The general framework for the coherent electronic order is found to be analogous with the celebrated Kuramoto model, describing the classical synchronization of coupled pendulums.**15**Oka, T.; Kitamura, S. Floquet Engineering of Quantum Materials.*Annu. Rev. Condens. Matter Phys.*2019,*10*(1), 387– 408, DOI: 10.1146/annurev-conmatphys-031218-013423Google ScholarThere is no corresponding record for this reference.**16**Nathan, F.; Abanin, D.; Berg, E.; Lindner, N. H.; Rudner, M. S. Anomalous Floquet Insulators.*Phys. Rev. B*2019,*99*(19), 195133, DOI: 10.1103/PhysRevB.99.195133Google Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhsVOju7rL&md5=af5ea40c5eeed0455783f2f2668ce3e9Anomalous Floquet insulatorsNathan, Frederik; Abanin, Dmitry; Berg, Erez; Lindner, Netanel H.; Rudner, Mark S.Physical Review B (2019), 99 (19), 195133CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)Landau's theory of phase transitions provides a framework for describing phases of matter in thermodn. equil. Recently, an intriguing new class of quantum many-body localized (MBL) systems that do not reach thermodn. equil. was discovered. The possibility of MBL systems to not heat up under periodic driving, which drastically changes the nature of dynamics in the system, opens the door for new, truly nonequil. phases of matter. In this paper we find a two-dimensional nonequil. topol. phase, the anomalous Floquet insulator (AFI), which arises from the combination of periodic driving and MBL. Having no counterpart in equil., the AFI is characterized by an MBL bulk, and topol. protected delocalized (thermalizing) chiral states at its boundaries. After establishing the regime of stability of the AFI phase in a simple yet exptl. realistic model, we investigate the interplay between the thermalizing edge and the localized bulk via numerical simulations of an AFI in a geometry with edges. We find that nonuniform particle d. profiles remain stable in the bulk up to the longest timescales that we can access, while the propagating edge states persist and thermalize. These findings open the possibility of observing quantized edge transport in interacting systems at high temp.**17**Frisk Kockum, A.; Miranowicz, A.; De Liberato, S.; Savasta, S.; Nori, F. Ultrastrong Coupling between Light and Matter.*Nat. Rev. Phys.*2019,*1*(1), 19– 40, DOI: 10.1038/s42254-018-0006-2Google ScholarThere is no corresponding record for this reference.**18**Rudner, M. S.; Lindner, N. H. Band Structure Engineering and Non-Equilibrium Dynamics in Floquet Topological Insulators.*Nat. Rev. Phys.*2020,*2*(5), 229– 244, DOI: 10.1038/s42254-020-0170-zGoogle Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXosVyrtbo%253D&md5=6ad0b274d105cc77c9f4045bcf822e1cBand structure engineering and non-equilibrium dynamics in Floquet topological insulatorsRudner, Mark S.; Lindner, Netanel H.Nature Reviews Physics (2020), 2 (5), 229-244CODEN: NRPACZ; ISSN:2522-5820. (Nature Research)Abstr.: Non-equil. topol. phenomena can be induced in quantum many-body systems using time-periodic fields (for example, by laser or microwave illumination). This Review begins with the key principles underlying Floquet band engineering, wherein such fields are used to change the topol. properties of a system's single-particle spectrum. In contrast to equil. systems, non-trivial band structure topol. in a driven many-body system does not guarantee that robust topol. behavior will be obsd. In particular, periodically driven many-body systems tend to absorb energy from their driving fields and thereby tend to heat up. We survey various strategies for overcoming this challenge of heating and for obtaining new topol. phenomena in this non-equil. setting. We describe how drive-induced topol. edge states can be probed in the regime of mesoscopic transport, and three routes for observing topol. phenomena beyond the mesoscopic regime: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of the regimes covered, and their exptl. realizations in solid-state, cold at., and photonic systems.**19**Rodriguez-Vega, M.; Vogl, M.; Fiete, G. A. Floquet Engineering of Twisted Double Bilayer Graphene.*Phys. Rev. Res.*2020,*2*(3), 33494, DOI: 10.1103/PhysRevResearch.2.033494Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitV2gsL7O&md5=f157c4f131a83c97e107e7dce3ac4065Floquet engineering of twisted double bilayer grapheneRodriguez-Vega, Martin; Vogl, Michael; Fiete, Gregory A.Physical Review Research (2020), 2 (3), 033494CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)Motivated by the recent exptl. realization of twisted double bilayer graphene (TDBG) samples, we study, both anal. and numerically, the effects of circularly polarized light propagating in free space and confined in a waveguide on the band structure and topol. properties of these systems. These two complementary Floquet protocols allow us to selectively tune different parameters of the system by varying the intensity and light frequency. For the drive protocol in free space, in the high-frequency regime, we find that in TDBG with AB/BA stacking, we can selectively close the zone-center quasienergy gaps around one valley while increasing the gaps near the opposite valley by tuning the parameters of the drive. In TDBG with AB/AB stacking, a similar effect can be obtained upon the application of a perpendicular static elec. field. Furthermore, we study the topol. properties of the driven system in different settings, provide accurate effective Floquet Hamiltonians, and show that relatively strong drives can generate flat bands. On the other hand, longitudinal light confined in a waveguide couples to the components of the interlayer hopping that are perpendicular to the TDBG sheet, allowing for selective engineering of the bandwidth of Floquet zone-center quasienergy bands without breaking the symmetries of the static system.**20**Jiménez-Galán, Á.; Silva, R. E. F.; Smirnova, O.; Ivanov, M. Lightwave Control of Topological Properties in 2D Materials for Sub-Cycle and Non-Resonant Valley Manipulation.*Nat. Photonics*2020,*14*(12), 728– 732, DOI: 10.1038/s41566-020-00717-3Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitlGrs7rN&md5=3fb5017b99030a16460b371a46acc5c6Lightwave control of topological properties in 2D materials for sub-cycle and non-resonant valley manipulationJimenez-Galan, A.; Silva, R. E. F.; Smirnova, O.; Ivanov, M.Nature Photonics (2020), 14 (12), 728-732CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)Modern light generation technol. offers extraordinary capabilities for sculpting light pulses, with full control over individual elec. field oscillations within each laser cycle1-3. These capabilities are at the core of lightwave electronics-the dream of ultrafast lightwave control over electron dynamics in solids on a sub-cycle timescale, aiming at information processing at petahertz rates4-8. Here, bringing the frequency-domain concept of topol. Floquet systems9,10 to the few-femtosecond time domain, we develop a theor. method that can be implemented with existing technol., to control the topol. properties of two-dimensional materials on few-femtosecond timescales by controlling the sub-cycle structure of non-resonant driving fields. We use this method to propose an all-optical, non-element-specific technique, phys. transparent in real space, to coherently write, manipulate and read selective valley excitation using fields carried in a wide range of frequencies and on timescales that are orders of magnitude shorter than the valley lifetime, crucial for the implementation of valleytronic devices11,12.**21**Shan, J.-Y.; Ye, M.; Chu, H.; Lee, S.; Park, J.-G.; Balents, L.; Hsieh, D. Giant Modulation of Optical Nonlinearity by Floquet Engineering.*Nature*2021,*600*(7888), 235– 239, DOI: 10.1038/s41586-021-04051-8Google Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXis12qtrnP&md5=3ef6f175f80d7f6bf66176e30418e1ddGiant modulation of optical nonlinearity by Floquet engineeringShan, Jun-Yi; Ye, M.; Chu, H.; Lee, Sungmin; Park, Je-Geun; Balents, L.; Hsieh, D.Nature (London, United Kingdom) (2021), 600 (7888), 235-239CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Strong periodic driving with light offers the potential to coherently manipulate the properties of quantum materials on ultrafast timescales. Recently, strategies have emerged to drastically alter electronic and magnetic properties by optically inducing non-trivial band topologies1-6, emergent spin interactions7-11 and even supercond.12. However, the prospects and methods of coherently engineering optical properties on demand are far less understood13. Here we demonstrate coherent control and giant modulation of optical nonlinearity in a van der Waals layered magnetic insulator, manganese phosphorus trisulfide (MnPS3). By driving far off-resonance from the lowest on-site manganese d-d transition, we observe a coherent on-off switching of its optical second harmonic generation efficiency on the timescale of 100 fs with no measurable dissipation. At driving elec. fields of the order of 109 V per m, the on-off ratio exceeds 10, which is limited only by the sample damage threshold. Floquet theory calcns.14 based on a single-ion model of MnPS3 are able to reproduce the measured driving field amplitude and polarization dependence of the effect. Our approach can be applied to a broad range of insulating materials and could lead to dynamically designed nonlinear optical elements.**22**Lindner, N. H.; Refael, G.; Galitski, V. Floquet Topological Insulator in Semiconductor Quantum Wells.*Nat. Phys.*2011,*7*(6), 490– 495, DOI: 10.1038/nphys1926Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmvVartro%253D&md5=fe24c43703ca957d00a378f792ee7fb4Floquet topological insulator in semiconductor quantum wellsLindner, Netanel H.; Refael, Gil; Galitski, VictorNature Physics (2011), 7 (6), 490-495CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)Topol. phases of matter have captured our imagination over the past few years, with tantalizing properties such as robust edge modes and exotic non-Abelian excitations, and potential applications ranging from semiconductor spintronics to topol. quantum computation. Despite recent advancements in the field, our ability to control topol. transitions remains limited, and usually requires changing material or structural properties. We show, using Floquet theory, that a topol. state can be induced in a semiconductor quantum well, initially in the trivial phase. This can be achieved by irradn. with microwave frequencies, without changing the well structure, closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. We discuss the necessary exptl. parameters for our proposal. This proposal provides an example and a proof of principle of a new non-equil. topol. state, the Floquet topol. insulator, introduced in this paper.**23**Kitagawa, T.; Oka, T.; Brataas, A.; Fu, L.; Demler, E. Transport Properties of Nonequilibrium Systems under the Application of Light: Photoinduced Quantum Hall Insulators without Landau Levels.*Phys. Rev. B*2011,*84*(23), 235108, DOI: 10.1103/PhysRevB.84.235108Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XisVKjtg%253D%253D&md5=297e145524f14ba9f4511adc2e5944b6Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levelsKitagawa, Takuya; Oka, Takashi; Brataas, Arne; Fu, Liang; Demler, EugenePhysical Review B: Condensed Matter and Materials Physics (2011), 84 (23), 235108/1-235108/13CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)In this paper, we study transport properties of nonequil. systems under the application of light in many-terminal measurements, using the Floquet picture. We propose and demonstrate that the quantum transport properties can be controlled in materials such as graphene and topol. insulators, via the application of light. Remarkably, under the application of off-resonant light, topol. transport properties can be induced; these systems exhibit quantum Hall effects in the absence of a magnetic field with a near quantization of the Hall conductance, realizing so-called quantum Hall systems without Landau levels first proposed by Haldane.**24**Usaj, G.; Perez-Piskunow, P. M.; Foa Torres, L. E. F.; Balseiro, C. A. Irradiated Graphene as a Tunable Floquet Topological Insulator.*Phys. Rev. B*2014,*90*(11), 115423, DOI: 10.1103/PhysRevB.90.115423Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitFOltrrF&md5=24bc9f58440c9a75fef3a611b67d7681Irradiated graphene as a tunable Floquet topological insulatorUsaj, Gonzalo; Perez-Piskunow, P. M.; Foa Torres, L. E. F.; Balseiro, C. A.Physical Review B: Condensed Matter and Materials Physics (2014), 90 (11), 115423/1-115423/12, 12 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)In the presence of a circularly polarized mid-IR radiation graphene develops dynamical band gaps in its quasienergy band structure and becomes a Floquet insulator. Here, we analyze how topol. protected edge states arise inside these gaps in the presence of an edge. Our results show that the gap appearing at ℏΩ/2, where ℏΩ is the photon energy, is bridged by two chiral edge states whose propagation direction is set by the direction of the polarization of the radiation field. Therefore, both the propagation direction and the energy window where the states appear can be controlled externally. We present both anal. and numerical calcns. that fully characterize these states. This is complemented by simple topol. arguments that account for them and by numerical calcns. for the case of the semi-infinite sample, thereby eliminating finite-size effects.**25**Titum, P.; Lindner, N. H.; Rechtsman, M. C.; Refael, G. Disorder-Induced Floquet Topological Insulators.*Phys. Rev. Lett.*2015,*114*(5), 056801, DOI: 10.1103/PhysRevLett.114.056801Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXktlaku7g%253D&md5=b1b69aa2d51f6cd5caf59f156d628404Disorder-induced Floquet topological insulatorTitum, Paraj; Lindner, Netanel H.; Rechtsman, Mikael C.; Refael, GilPhysical Review Letters (2015), 114 (5), 056801CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We investigate the possibility of realizing a disorder-induced topol. Floquet spectrum in two-dimensional periodically driven systems. Such a state would be a dynamical realization of the topol. Anderson insulator. We establish that a disorder-induced trivial-to-topol. transition indeed occurs, and characterize it by computing the disorder averaged Bott index, suitably defined for the time-dependent system. The presence of edge states in the topol. state is confirmed by exact numerical time evolution of wave packets on the edge of the system. We consider the optimal driving regime for exptl. observing the Floquet topol. Anderson insulator, and discuss its possible realization in photonic lattices.**26**Mikami, T.; Kitamura, S.; Yasuda, K.; Tsuji, N.; Oka, T.; Aoki, H. Brillouin-Wigner Theory for High-Frequency Expansion in Periodically Driven Systems: Application to Floquet Topological Insulators.*Phys. Rev. B*2016,*93*(14), 144307, DOI: 10.1103/PhysRevB.93.144307Google Scholar26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsF2ks7fK&md5=7a8329e5dd5971b0d1310662dc040eb6Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: application to Floquet topological insulatorsMikami, Takahiro; Kitamura, Sota; Yasuda, Kenji; Tsuji, Naoto; Oka, Takashi; Aoki, HideoPhysical Review B (2016), 93 (14), 144307/1-144307/25CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in 1/ω, with ω being the frequency of the drive. The advantage of the BW method is that it is not only efficient in deriving higher-order terms, but even enables us to write down the whole infinite series expansion, as compared to the van Vleck degenerate perturbation theory. The expansion is also free from a spurious dependence on the driving phase, which has been an obstacle in the Floquet-Magnus expansion. We apply the BW expansion to various models of noninteracting electrons driven by circularly polarized light. As the amplitude of the light is increased, the system undergoes a series of Floquet topol.-to-topol. phase transitions, whose phase boundary in the high-frequency regime is well explained by the BW expansion. As the frequency is lowered, the high-frequency expansion breaks down at some point due to band touching with nonzero-photon sectors, where we find numerically even more intricate and richer Floquet topol. phases spring out. We have then analyzed, with the Floquet dynamical mean-field theory, the effects of electron-electron interaction and energy dissipation. We have specifically revealed that phase transitions from Floquet-topol. to Mott insulators emerge, where the phase boundaries can again be captured with the high-frequency expansion.**27**Holthaus, M. Floquet Engineering with Quasienergy Bands of Periodically Driven Optical Lattices.*J. Phys. B At. Mol. Opt. Phys.*2016,*49*(1), 13001, DOI: 10.1088/0953-4075/49/1/013001Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XksVemsb8%253D&md5=2c53a9ad94a7ca3337e1326a303358c4Floquet engineering with quasienergy bands of periodically driven optical latticesHolthaus, MartinJournal of Physics B: Atomic, Molecular and Optical Physics (2016), 49 (1), 013001/1-013001/26CODEN: JPAPEH; ISSN:0953-4075. (IOP Publishing Ltd.)A primer on the Floquet theory of periodically time-dependent quantum systems is provided, and it is shown how to apply this framework for computing the quasienergy band structure governing the dynamics of ultracold atoms in driven optical cosine lattices. Such systems are viewed here as spatially and temporally periodic structures living in an extended Hilbert space, giving rise to spatio-temporal Bloch waves whose dispersion relations can be manipulated at will by exploiting ac-Stark shifts and multiphoton resonances. The elements required for numerical calcns. are introduced in a tutorial manner, and some example calcns. are discussed in detail, thereby illustrating future prospects of Floquet engineering.**28**Sato, S. A.; McIver, J. W.; Nuske, M.; Tang, P.; Jotzu, G.; Schulte, B.; Hübener, H.; De Giovannini, U.; Mathey, L.; Sentef, M. A.; Cavalleri, A.; Rubio, A. Microscopic Theory for the Light-Induced Anomalous Hall Effect in Graphene.*Phys. Rev. B*2019,*99*(21), 214302, DOI: 10.1103/PhysRevB.99.214302Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhslWltLvJ&md5=c726c54e327336a7c1c5b474f7b5d2d5Microscopic theory for the light-induced anomalous Hall effect in grapheneSato, S. A.; McIver, J. W.; Nuske, M.; Tang, P.; Jotzu, G.; Schulte, B.; Hubener, H.; De Giovannini, U.; Mathey, L.; Sentef, M. A.; Cavalleri, A.; Rubio, A.Physical Review B (2019), 99 (21), 214302CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)We employ a quantum Liouville equation with relaxation to model the recently obsd anomalous Hall effect in graphene irradiated by an ultrafast pulse of circularly polarized light. In the weak-field regime, we demonstrate that the Hall effect originates from an asym population of photocarriers in the Dirac bands. By contrast, in the strong-field regime, the system is driven into a nonequil. steady state that is well described by topol nontrivial Floquet-Bloch bands. Here, the anomalous Hall current originates from the combination of a population imbalance in these dressed bands together with a smaller anomalous velocity contribution arising from their Berry curvature. This robust and general finding enables the simulation of elec transport from light-induced Floquet-Bloch bands in an exptl relevant parameter regime and creates a pathway to designing ultrafast quantum devices with Floquet-engineered transport properties.**29**McIver, J. W.; Schulte, B.; Stein, F.-U.; Matsuyama, T.; Jotzu, G.; Meier, G.; Cavalleri, A. Light-Induced Anomalous Hall Effect in Graphene.*Nat. Phys.*2020,*16*(1), 38– 41, DOI: 10.1038/s41567-019-0698-yGoogle Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXitV2msbzL&md5=57bf09d294b4c31eb11c03aa8a18ecd1Light-induced anomalous Hall effect in grapheneMcIver, J. W.; Schulte, B.; Stein, F.-U.; Matsuyama, T.; Jotzu, G.; Meier, G.; Cavalleri, A.Nature Physics (2020), 16 (1), 38-41CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)Many non-equil. phenomena have been discovered or predicted in optically driven quantum solids1. Examples include light-induced supercond.2,3 and Floquet-engineered topol. phases4-8. These are short-lived effects that should lead to measurable changes in elec. transport, which can be characterized using an ultrafast device architecture based on photoconductive switches9. Here, we report the observation of a light-induced anomalous Hall effect in monolayer graphene driven by a femtosecond pulse of circularly polarized light. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect a Floquet-engineered topol. band structure4,5, similar to the band structure originally proposed by Haldane10. This includes an approx. 60 meV wide conductance plateau centered at the Dirac point, where a gap of equal magnitude is predicted to open. We find that when the Fermi level lies within this plateau the estd. anomalous Hall conductance sats. around 1.8 ± 0.4 e2/h.**30**Schüler, M.; De Giovannini, U.; Hübener, H.; Rubio, A.; Sentef, M. A.; Devereaux, T. P.; Werner, P. How Circular Dichroism in Time- and Angle-Resolved Photoemission Can Be Used to Spectroscopically Detect Transient Topological States in Graphene.*Phys. Rev. X*2020,*10*(4), 41013, DOI: 10.1103/PhysRevX.10.041013Google ScholarThere is no corresponding record for this reference.**31**Broers, L.; Mathey, L. Observing Light-Induced Floquet Band Gaps in the Longitudinal Conductivity of Graphene.*Commun. Phys.*2021,*4*(1), 248, DOI: 10.1038/s42005-021-00746-6Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXisFyhs77L&md5=099b2e9634b5457be791a6a3007fe800Observing light-induced Floquet band gaps in the longitudinal conductivity of grapheneBroers, Lukas; Mathey, LudwigCommunications Physics (2021), 4 (1), 248CODEN: CPOHDJ; ISSN:2399-3650. (Nature Research)Floquet engineering presents a versatile method of dynamically controlling material properties. The light-induced Floquet-Bloch bands of graphene feature band gaps, which have not yet been obsd. directly. We propose optical longitudinal cond. as a realistic observable to detect light-induced Floquet band gaps in graphene. These gaps manifest as resonant features in the cond., when resolved with respect to the probing frequency and the driving field strength. The electron distribution follows the light-induced Floquet-Bloch bands, resulting in a natural interpretation as occupations of these bands. Furthermore, we show that there are population inversions of the Floquet-Bloch bands at the band gaps for sufficiently strong driving field strengths. This strongly reduces the cond. at the corresponding frequencies. Therefore our proposal puts forth not only an unambiguous demonstration of light-induced Floquet-Bloch bands, which advances the field of Floquet engineering in solids, but also points out the control of transport properties via light, that derives from the electron distribution on these bands.**32**Aeschlimann, S.; Sato, S. A.; Krause, R.; Chávez-Cervantes, M.; De Giovannini, U.; Hübener, H.; Forti, S.; Coletti, C.; Hanff, K.; Rossnagel, K.; Rubio, A.; Gierz, I. Survival of Floquet–Bloch States in the Presence of Scattering.*Nano Lett.*2021,*21*(12), 5028– 5035, DOI: 10.1021/acs.nanolett.1c00801Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXht1WnsLfI&md5=11719ccf347a3cb579a5d9baee235838Survival of Floquet-Bloch States in the Presence of ScatteringAeschlimann, Sven; Sato, Shunsuke A.; Krause, Razvan; Chavez-Cervantes, Mariana; De Giovannini, Umberto; Huebener, Hannes; Forti, Stiven; Coletti, Camilla; Hanff, Kerstin; Rossnagel, Kai; Rubio, Angel; Gierz, IsabellaNano Letters (2021), 21 (12), 5028-5035CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)Floquet theory has spawned many exciting possibilities for electronic structure control with light, with enormous potential for future applications. The exptl. demonstration in solids, however, remains largely unrealized. In particular, the influence of scattering on the formation of Floquet-Bloch states remains poorly understood. Here, we combine time- and angle-resolved photoemission spectroscopy with time-dependent d. functional theory and a two-level model with relaxation to investigate the survival of Floquet-Bloch states in the presence of scattering. We find that Floquet-Bloch states will be destroyed if scattering - activated by electronic excitations - prevents the Bloch electrons from following the driving field coherently. The two-level model also shows that Floquet-Bloch states reappear at high field intensities where energy exchange with the driving field dominates over energy dissipation to the bath. Our results clearly indicate the importance of long scattering times combined with strong driving fields for the successful realization of various Floquet phenomena.**33**Broers, L.; Mathey, L. Detecting Light-Induced Floquet Band Gaps of Graphene via TrARPES.*Phys. Rev. Res.*2022,*4*(1), 13057, DOI: 10.1103/PhysRevResearch.4.013057Google Scholar33https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XpsFOrtLg%253D&md5=85a8b3d961ac780a3cd7938b38306686Detecting light-induced Floquet band gaps of graphene via trARPESBroers, Lukas; Mathey, LudwigPhysical Review Research (2022), 4 (1), 013057CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)We propose a realistic regime to detect the light-induced topol. band gap in graphene via time-resolved angle-resolved photoelectron spectroscopy (trARPES), which can be achieved with current technol. The direct observation of Floquet-Bloch bands in graphene is limited by low-mobility, Fourier-broadening, laser-assisted photoemission (LAPE), probe-pulse energy-resoln. bounds, space-charge effects, and more. We characterize a regime of low driving frequency and high amplitude of the circularly polarized light that induces an effective band gap at the Dirac point that exceeds the Floquet zone. This circumvents limitations due to energy resolns. and band broadening. The electron distribution across the Floquet replicas in this limit allows for distinguishing LAPE replicas from Floquet replicas. We derive our results from a dissipative master equation approach that gives access to two-point correlation functions and the electron distribution relevant for trARPES measurements.**34**Broers, L.; Mathey, L. Observing Light-Induced Floquet Band Gaps in the Longitudinal Conductivity of Graphene.*Commun. Phys.*2021,*4*(1), 248, DOI: 10.1038/s42005-021-00746-6Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXisFyhs77L&md5=099b2e9634b5457be791a6a3007fe800Observing light-induced Floquet band gaps in the longitudinal conductivity of grapheneBroers, Lukas; Mathey, LudwigCommunications Physics (2021), 4 (1), 248CODEN: CPOHDJ; ISSN:2399-3650. (Nature Research)Floquet engineering presents a versatile method of dynamically controlling material properties. The light-induced Floquet-Bloch bands of graphene feature band gaps, which have not yet been obsd. directly. We propose optical longitudinal cond. as a realistic observable to detect light-induced Floquet band gaps in graphene. These gaps manifest as resonant features in the cond., when resolved with respect to the probing frequency and the driving field strength. The electron distribution follows the light-induced Floquet-Bloch bands, resulting in a natural interpretation as occupations of these bands. Furthermore, we show that there are population inversions of the Floquet-Bloch bands at the band gaps for sufficiently strong driving field strengths. This strongly reduces the cond. at the corresponding frequencies. Therefore our proposal puts forth not only an unambiguous demonstration of light-induced Floquet-Bloch bands, which advances the field of Floquet engineering in solids, but also points out the control of transport properties via light, that derives from the electron distribution on these bands.**35**Zhou, S.; Bao, C.; Fan, B.; Zhou, H.; Gao, Q.; Zhong, H.; Lin, T.; Liu, H.; Yu, P.; Tang, P.; Meng, S.; Duan, W.; Zhou, S. Pseudospin-Selective Floquet Band Engineering in Black Phosphorus.*Nature*2023,*614*(7946), 75– 80, DOI: 10.1038/s41586-022-05610-3Google Scholar36https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXis1Siu78%253D&md5=dfeae9aaf904cc04c9f55b3097c5c15ePseudospin-selective Floquet band engineering in black phosphorusZhou, Shaohua; Bao, Changhua; Fan, Benshu; Zhou, Hui; Gao, Qixuan; Zhong, Haoyuan; Lin, Tianyun; Liu, Hang; Yu, Pu; Tang, Peizhe; Meng, Sheng; Duan, Wenhui; Zhou, ShuyunNature (London, United Kingdom) (2023), 614 (7946), 75-80CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Time-periodic light field has emerged as a control knob for manipulating quantum states in solid-state materials1-3, cold atoms4 and photonic systems5 through hybridization with photon-dressed Floquet states6 in the strong-coupling limit, dubbed Floquet engineering. Such interaction leads to tailored properties of quantum materials7-11, for example, modifications of the topol. properties of Dirac materials12,13 and modulation of the optical response14-16. Despite extensive research interests over the past decade3,8,17-20, there is no exptl. evidence of momentum-resolved Floquet band engineering of semiconductors, which is a crucial step to extend Floquet engineering to a wide range of solid-state materials. Here, on the basis of time and angle-resolved photoemission spectroscopy measurements, we report exptl. signatures of Floquet band engineering in a model semiconductor, black phosphorus. On near-resonance pumping at a photon energy of 340-440 meV, a strong band renormalization is obsd. near the band edges. In particular, light-induced dynamical gap opening is resolved at the resonance points, which emerges simultaneously with the Floquet sidebands. Moreover, the band renormalization shows a strong selection rule favoring pump polarization along the armchair direction, suggesting pseudospin selectivity for the Floquetband engineering as enforced by the lattice symmetry. Our work demonstrates pseudospin-selective Floquet band engineering in black phosphorus and provides important guiding principles for Floquet engineering of semiconductors.**36**Rodriguez-Lopez, P.; Betouras, J. J.; Savel’ev, S. E. Dirac Fermion Time-Floquet Crystal: Manipulating Dirac Points.*Phys. Rev. B*2014,*89*(15), 155132, DOI: 10.1103/PhysRevB.89.155132Google Scholar37https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtVSns7zK&md5=61aedfd34d447346c994a34051424f32Dirac fermion time-Floquet crystal: manipulating Dirac pointsRodriguez-Lopez, Pablo; Betouras, Joseph J.; Savel'ev, Sergey E.Physical Review B: Condensed Matter and Materials Physics (2014), 89 (15), 155132/1-155132/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We demonstrate how to control the spectra and current flow of Dirac electrons in both a graphene sheet and a topol. insulator (TI) by applying either two linearly polarized laser fields with frequencies ω and 2ω or a monochromatic (one-frequency) laser field together with a spatially periodic static potential (graphene/TI superlattice). Using the Floquet theory and the resonance approxn., we show that a Dirac point in the electron spectrum can be split into several Dirac points whose relative location in momentum space can be efficiently manipulated by changing the characteristics of the laser fields. In addn., the laser-field-controlled Dirac fermion band structure-a Dirac fermion time-Floquet crystal-allows the manipulation of the electron currents in graphene and topol. insulators. Furthermore, the generation of dc currents of desirable intensity in a chosen direction occurs when the biharmonic laser field is applied, which can provide a straightforward exptl. test of the predicted phenomena.**37**Wang, Y.; Walter, A.-S.; Jotzu, G.; Viebahn, K. Topological Floquet Engineering Using Two Frequencies in Two Dimensions.*Phys. Rev. A*2023,*107*, 043309, DOI: 10.1103/PhysRevA.107.043309Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXhtVeku7vM&md5=925a18a07f2ef0f3a092b790e71eb4dbTopological Floquet engineering using two frequencies in two dimensionsWang, Yixiao; Walter, Anne-Sophie; Jotzu, Gregor; Viebahn, KonradPhysical Review A (2023), 107 (4), 043309CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)Using two-frequency driving in two dimensions opens up new possibilities for Floquet engineering, which range from controlling specific symmetries to tuning the properties of resonant gaps. In this work, we study two-band lattice models subject to two-tone Floquet driving and analyze the resulting effective Floquet band structures both numerically and anal. On the one hand, we extend the methodol. of Sandholzer et al. [Phys.Rev.Res.4, 013056 (2022)2643-156410.1103/PhysRevResearch.4.013056] from one to two dimensions and find competing topol. phases in a simple Bravais lattice when the two resonant drives at 1ω and 2ω interfere. On the other hand, we explore driving-induced symmetry breaking in the hexagonal lattice, in which the breaking of either inversion or time-reversal symmetry can be tuned independently via the Floquet modulation. Possible applications of our work include a simpler generation of topol. bands for ultracold atoms and the realization of nonlinear Hall effects as well as Haldane's parity anomaly in inversion-sym. parent lattices.**38**Gui, G.; Li, J.; Zhong, J. Band Structure Engineering of Graphene by Strain: First-Principles Calculations.*Phys. Rev. B*2008,*78*(7), 75435, DOI: 10.1103/PhysRevB.78.075435Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXhtVKitLzM&md5=eefa8bc2bb38eca389cb08286edb4357Band structure engineering of graphene by strain: First-principles calculationsGui, Gui; Li, Jin; Zhong, JianxinPhysical Review B: Condensed Matter and Materials Physics (2008), 78 (7), 075435/1-075435/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We have investigated the electronic structure of graphene under different planar strain distributions using the first-principles pseudopotential plane-wave method and the tight-binding approach. We found that graphene with a sym. strain distribution is always a zero band-gap semiconductor and its pseudogap decreases linearly with the strain strength in the elastic regime. However, asym. strain distributions in graphene result in opening of band gaps at the Fermi level. For the graphene with a strain distribution parallel to C-C bonds, its band gap continuously increases to its max. width of 0.486 eV as the strain increases up to 12.2%. For the graphene with a strain distribution perpendicular to C-C bonds, its band gap continuously increases only to its max. width of 0.170 eV as the strain increases up to 7.3%. The anisotropic nature of graphene is also reflected by different Poisson ratios under large strains in different directions. We found that the Poisson ratio approaches to a const. of 0.1732 under small strains but decreases differently under large strains along different directions.**39**Cocco, G.; Cadelano, E.; Colombo, L. Gap Opening in Graphene by Shear Strain.*Phys. Rev. B*2010,*81*(24), 241412, DOI: 10.1103/PhysRevB.81.241412Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXosVyiurY%253D&md5=a18172c411810ff9d65fdeb6e9a233b2Gap opening in graphene by shear strainCocco, Giulio; Cadelano, Emiliano; Colombo, LucianoPhysical Review B: Condensed Matter and Materials Physics (2010), 81 (24), 241412/1-241412/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We exploit the concept of strain-induced band-structure engineering in graphene through the calcn. of its electronic properties under uniaxial, shear, and combined uniaxial-shear deformations. We show that by combining shear deformations to uniaxial strains it is possible modulate the graphene energy-gap value from zero up to 0.9 eV. Interestingly enough, the use of a shear component allows for a gap opening at moderate abs. deformation, safely smaller than the graphene failure strain.**40**Koghee, S.; Lim, L.-K.; Goerbig, M. O.; Smith, C. M. Merging and Alignment of Dirac Points in a Shaken Honeycomb Optical Lattice.*Phys. Rev. A*2012,*85*(2), 23637, DOI: 10.1103/PhysRevA.85.023637Google Scholar40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XjvFyhtLk%253D&md5=3f42312573e66ce0ab3cc09a4c6005e4Merging and alignment of Dirac points in a shaken honeycomb optical latticeKoghee, Selma; Lim, Lih-King; Goerbig, M. O.; Smith, C. MoraisPhysical Review A: Atomic, Molecular, and Optical Physics (2012), 85 (2-B), 023637/1-023637/11CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)Inspired by the recent creation of a honeycomb optical lattice and the realization of a Mott-insulating state in a square lattice by shaking, we study here the shaken honeycomb optical lattice. For a periodic shaking of the lattice, Floquet theory may be applied to derive a time-independent Hamiltonian. In this effective description, the hopping parameters are renormalized by a Bessel function, which depends on the shaking direction, amplitude, and frequency. Consequently, the hopping parameters can vanish and even change sign, in an anisotropic manner, thus yielding different band structures. Here, we study the merging and the alignment of Dirac points and dimensional crossovers from the two-dimensional system to one-dimensional chains and zero-dimensional dimers. We also consider next-nearest-neighbor hopping, which breaks the particle-hole symmetry and leads to a metallic phase when it becomes dominant over the nearest-neighbor hopping. Furthermore, we include weak repulsive on-site interactions and find the d. profiles for different values of the hopping parameters and interactions, both in a homogeneous system and in the presence of a trapping potential. Our results may be exptl. obsd. by use of momentum-resolved Raman spectroscopy.**41**Jotzu, G.; Messer, M.; Desbuquois, R.; Lebrat, M.; Uehlinger, T.; Greif, D.; Esslinger, T. Experimental Realization of the Topological Haldane Model with Ultracold Fermions.*Nature*2014,*515*(7526), 237– 240, DOI: 10.1038/nature13915Google Scholar41https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitVyku77E&md5=84fdb73ca8a11182595106e875745031Experimental realization of the topological Haldane model with ultracold fermionsJotzu, Gregor; Messer, Michael; Desbuquois, Remi; Lebrat, Martin; Uehlinger, Thomas; Greif, Daniel; Esslinger, TilmanNature (London, United Kingdom) (2014), 515 (7526), 237-240CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)The Haldane model on a honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topol. distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band structure, rather than being caused by an external magnetic field. Although phys. implementation has been considered unlikely, the Haldane model has provided the conceptual basis for theor. and exptl. research exploring topol. insulators and superconductors. Here we report the exptl. realization of the Haldane model and the characterization of its topol. band structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The Haldane model is based on breaking both time-reversal symmetry and inversion symmetry. To break time-reversal symmetry, we introduce complex next-nearest-neighbor tunnelling terms, which we induce through circular modulation of the lattice position. To break inversion symmetry, we create an energy offset between neighboring sites. Breaking either of these symmetries opens a gap in the band structure, which we probe using momentum-resolved interband transitions. We explore the resulting Berry curvatures, which characterize the topol. of the lowest band, by applying a const. force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between the two broken symmetries gives rise to a transition between topol. distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line exptl. and quant. compare it to calcns. using Floquet theory without free parameters. We verify that our approach, which allows us to tune the topol. properties dynamically, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realize spin-dependent topol. Hamiltonians.**42**Delplace, P.; Gómez-León, Á.; Platero, G. Merging of Dirac Points and Floquet Topological Transitions in Ac-Driven Graphene.*Phys. Rev. B*2013,*88*(24), 245422, DOI: 10.1103/PhysRevB.88.245422Google Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXisVGktLs%253D&md5=711547e6a7e7ecd70c8b6c1682d3c541Merging of Dirac points and Floquet topological transitions in ac-driven grapheneDelplace, Pierre; Gomez-Leon, Alvaro; Platero, GloriaPhysical Review B: Condensed Matter and Materials Physics (2013), 88 (24), 245422/1-245422/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We investigate the effect of an in-plane ac elec. field coupled to electrons in the honeycomb lattice and show that it can be used to manipulate the Dirac points of the electronic structure. We find that the position of the Dirac points can be controlled by the amplitude and the polarization of the field for high-frequency drivings, providing a new platform to achieve their merging, a topol. transition which has not been obsd. yet in electronic systems. Importantly, for lower frequencies we find that the multiphoton absorptions and emissions processes yield the creation of addnl. pairs of Dirac points. This provides an addnl. method to achieve the merging transition by just tuning the frequency of the driving. Our approach, based on Floquet formalism, is neither restricted to specific choice of amplitude or polarization of the field, nor to a low-energy approxn. for the Hamiltonian.**43**Schaibley, J. R.; Yu, H.; Clark, G.; Rivera, P.; Ross, J. S.; Seyler, K. L.; Yao, W.; Xu, X. Valleytronics in 2D Materials.*Nat. Rev. Mater.*2016,*1*(11), 16055, DOI: 10.1038/natrevmats.2016.55Google Scholar43https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhtVertbw%253D&md5=c8ac26ba3b7f390bb15df8bb643c59cdValleytronics in 2D materialsSchaibley, John R.; Yu, Hongyi; Clark, Genevieve; Rivera, Pasqual; Ross, Jason S.; Seyler, Kyle L.; Yao, Wang; Xu, XiaodongNature Reviews Materials (2016), 1 (11), 16055CODEN: NRMADL; ISSN:2058-8437. (Nature Publishing Group)Semiconductor technol. is currently based on the manipulation of electronic charge; however, electrons have addnl. degrees of freedom, such as spin and valley, that can be used to encode and process information. Over the past several decades, there has been significant progress in manipulating electron spin for semiconductor spintronic devices, motivated by potential spin-based information processing and storage applications. However, exptl. progress towards manipulating the valley degree of freedom for potential valleytronic devices has been limited until very recently. We review the latest advances in valleytronics, which have largely been enabled by the isolation of 2D materials (such as graphene and semiconducting transition metal dichalcogenides) that host an easily accessible electronic valley degree of freedom, allowing for dynamic control.**44**Ye, Z.; Sun, D.; Heinz, T. F. Optical Manipulation of Valley Pseudospin.*Nat. Phys.*2017,*13*(1), 26– 29, DOI: 10.1038/nphys3891Google Scholar44https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsV2rtb%252FO&md5=5b91bd253616b1c3264a1da1d6d4d95fOptical manipulation of valley pseudospinYe, Ziliang; Sun, Dezheng; Heinz, Tony F.Nature Physics (2017), 13 (1), 26-29CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)The coherent manipulation of spin and pseudospin underlies existing and emerging quantum technologies, including quantum communication and quantum computation. Valley polarization, assocd. with the occupancy of degenerate, but quantum mech. distinct valleys in momentum space, closely resembles spin polarization and has been proposed as a pseudospin carrier for the future quantum electronics. Valley exciton polarization has been created in the transition metal dichalcogenide monolayers using excitation by circularly polarized light and has been detected both optically and elec. In addn., the existence of coherence in the valley pseudospin has been identified exptl. The manipulation of such valley coherence has, however, remained out of reach. Here we demonstrate all-optical control of the valley coherence by means of the pseudomagnetic field assocd. with the optical Stark effect. Using below-bandgap circularly polarized light, we rotate the valley exciton pseudospin in monolayer WSe2 on the femtosecond timescale. Both the direction and speed of the rotation can be manipulated optically by tuning the dynamic phase of excitons in opposite valleys.**45**Geondzhian, A.; Rubio, A.; Altarelli, M. Valley Selectivity of Soft X-Ray Excitations of Core Electrons in Two-Dimensional Transition Metal Dichalcogenides.*Phys. Rev. B*2022,*106*(11), 115433, DOI: 10.1103/PhysRevB.106.115433Google Scholar45https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XislaqtL7O&md5=0638eb1eeebb895b6b1c7c47c2ae3242Valley selectivity of soft x-ray excitations of core electrons in two-dimensional transition metal dichalcogenidesGeondzhian, Andrey; Rubio, Angel; Altarelli, MassimoPhysical Review B (2022), 106 (11), 115433CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)Optical properties of semiconducting monolayer transition metal dichalcogenides have received a lot of attention in recent years, following the discovery of the valley selective optical population of either K+ or K- valleys at the direct band gap, depending on the polarization of the incoming light. We use group theor. selection rules, as well as ab initio DFT calcns., to investigate whether this valley selectivity effect is also present in x-ray optical transitions from the flat core level of the transition metal atom to the valence and conduction band K valleys. Valley selectivity is predicted for s, p1/2, and p3/2 edges in transitions to and from the valence band edges with circularly polarized radiation. Possible novel applications to the diagnostics of valleytronic properties and intervalley dynamics are investigated and the feasibility of ultrafast pump-probe and Kerr rotations expts. with suitable soft-x-ray free-electron laser sources is discussed.**46**Cheng, J.; Huang, D.; Jiang, T.; Shan, Y.; Li, Y.; Wu, S.; Liu, W.-T. Chiral Selection Rules for Multi-Photon Processes in Two-Dimensional Honeycomb Materials.*Opt. Lett.*2019,*44*(9), 2141– 2144, DOI: 10.1364/OL.44.002141Google Scholar46https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhvFWnt7nO&md5=e11fa1e9e763f6e298de5514933adceaChiral selection rules for multi-photon processes in two-dimensional honeycomb materialsCheng, Jingxin; Huang, Di; Jiang, Tao; Shan, Yuwei; Li, Yingguo; Wu, Shiwei; Liu, Wei-TaoOptics Letters (2019), 44 (9), 2141-2144CODEN: OPLEDP; ISSN:1539-4794. (Optical Society of America)We examine the chirality-dependent optical selection rules in two-dimensional monolayer materials with honeycomb lattices, and, based on symmetry argument, we generalize these rules to multi-photon transitions of arbitrary orders. We also present the phase relations between incident and outgoing photons in such processes. The results agree nicely with our exptl. observations of second- and third-harmonic generation. In particular, we demonstrate that the phase relation of chiral second-harmonic generation can serve as a handy tool for imaging domains and domain boundaries of these monolayers. Our results can benefit future studies on chirality-related optical phenomena and opto-electronic applications of such materials.**47**Huang, S.-M.; Xu, S.-Y.; Belopolski, I.; Lee, C.-C.; Chang, G.; Chang, T.-R.; Wang, B.; Alidoust, N.; Bian, G.; Neupane, M.; Sanchez, D.; Zheng, H.; Jeng, H.-T.; Bansil, A.; Neupert, T.; Lin, H.; Hasan, M. Z. New Type of Weyl Semimetal with Quadratic Double Weyl Fermions.*Proc. Natl. Acad. Sci. U. S. A.*2016,*113*(5), 1180– 1185, DOI: 10.1073/pnas.1514581113Google Scholar47https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhtFSht7o%253D&md5=c381afb9ba354df495011c64e4c679a5New type of Weyl semimetal with quadratic double Weyl fermionsHuang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. ZahidProceedings of the National Academy of Sciences of the United States of America (2016), 113 (5), 1180-1185CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The exptl. realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theor. interest to the realm of exptl. studies and device applications, it is of crucial importance to identify other robust candidates that are exptl. feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compd. strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topol. Weyl physics that is not possible in TaAs.**48**Wang, Z.; Sun, Y.; Chen, X.-Q.; Franchini, C.; Xu, G.; Weng, H.; Dai, X.; Fang, Z. Dirac Semimetal and Topological Phase Transitions in A3 Bi (A = Na,K,Rb).*Phys. Rev. B*2012,*85*(19), 195320, DOI: 10.1103/PhysRevB.85.195320Google Scholar48https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtVWjur3N&md5=fed822f06a1335d52abcf311ea6ec195Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb)Wang, Zhijun; Sun, Yan; Chen, Xing-Qiu; Franchini, Cesare; Xu, Gang; Weng, Hongming; Dai, Xi; Fang, ZhongPhysical Review B: Condensed Matter and Materials Physics (2012), 85 (19), 195320/1-195320/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Three-dimensional (3D) Dirac point, where two Weyl points overlap in momentum space, is usually unstable and hard to realize. Here we show, based on the first-principles calcns. and effective model anal., that cryst. A3Bi (A = Na, K, Rb) are Dirac semimetals with bulk 3D Dirac points protected by crystal symmetry. They possess nontrivial Fermi arcs on the surfaces and can be driven into various topol. distinct phases by explicit breaking of symmetries. Giant diamagnetism, linear quantum magnetoresistance, and quantum spin Hall effect will be expected for such compds.**49**Liu, Z. K.; Zhou, B.; Zhang, Y.; Wang, Z. J.; Weng, H. M.; Prabhakaran, D.; Mo, S.-K.; Shen, Z. X.; Fang, Z.; Dai, X.; Hussain, Z.; Chen, Y. L. Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi.*Science*2014,*343*(6173), 864– 867, DOI: 10.1126/science.1245085Google Scholar49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXis1Cgsr8%253D&md5=047f0a9c3918d63013604938e88af330Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3BiLiu, Z. K.; Zhou, B.; Zhang, Y.; Wang, Z. J.; Weng, H. M.; Prabhakaran, D.; Mo, S.-K.; Shen, Z. X.; Fang, Z.; Dai, X.; Hussain, Z.; Chen, Y. L.Science (Washington, DC, United States) (2014), 343 (6173), 864-867CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)Three-dimensional (3D) topol. Dirac semimetals (TDSs) represent an unusual state of quantum matter that can be viewed as "3D graphene. "In contrast to 2D Dirac fermions in graphene or on the surface of 3D topol. insulators, TDSs possess 3D Dirac fermions in the bulk. By investigating the electronic structure of Na3Bi with angle-resolved photoemission spectroscopy, we detected 3D Dirac fermions with linear dispersions along all momentum directions. Furthermore, we demonstrated the robustness of 3D Dirac fermions in Na3Bi against in situ surface doping. Our results establish Na3Bi as a model system for 3D TDSs, which can serve as an ideal platform for the systematic study of quantum phase transitions between rich topol. quantum states.**50**Wang, Y.; Huang, C.; Li, D.; Li, P.; Yu, J.; Zhang, Y.; Xu, J. Tight-Binding Model for Electronic Structure of Hexagonal Boron Phosphide Monolayer and Bilayer.*J. Phys.: Condens. Matter*2019,*31*(28), 285501, DOI: 10.1088/1361-648X/ab1528Google Scholar50https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXht12gtrrN&md5=a03350384f2e90a8d22089d9253f845eTight-binding model for electronic structure of hexagonal boron phosphide monolayer and bilayerWang, Ying; Huang, Changbao; Li, Dong; Li, Ping; Yu, Jiangying; Zhang, Yuzhong; Xu, JinrongJournal of Physics: Condensed Matter (2019), 31 (28), 285501CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)Graphene-like hexagonal boron phosphide BP with its moderate band gap and high carrier mobility is considered to be a high potential material for electronics and optoelectronics. In this work, the tight-binding Hamiltonian of hexagonal boron phosphide monolayer and bilayer with two stacking orders are derived in detail. Including up to fifth-nearest-neighbor in plane and next-nearest-neighbor interlayer hoppings, the tight-binding approximated band structure can well reproduce the first-principle calcns. based on the screened Heyd-Scuseria-Ernzerhof hybrid functional level over the entire Brillouin zone. The band gap deviations for monolayer and bilayer between our tight-binding and first-principle results are only 2 meV. The low-energy effective Hamiltonian matrix and band structure are obtained by expanding the full band structure close to the K point. The results show that the isoenergetic lines of max. valence band in the vicinity of K point undergo a pseudo-Lifshitz transition from h-BP monolayer to AB_B-P or AB_B-B bilayer. The mechanism of pseudo-Lifshitz transition can be attributed to two interlayer hoppings rather than one.**51**Castro, A.; Appel, H.; Oliveira, M.; Rozzi, C. A.; Andrade, X.; Lorenzen, F.; Marques, M. A. L.; Gross, E. K. U.; Rubio, A. Octopus: A Tool for the Application of Time-Dependent Density Functional Theory.*Phys. status solidi*2006,*243*(11), 2465– 2488, DOI: 10.1002/pssb.200642067Google Scholar51https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xpsl2msLY%253D&md5=a2fdd76ba81266f00fab34c1ae4e3f53Octopus: a tool for the application of time-dependent density functional theoryCastro, Alberto; Appel, Heiko; Oliveira, Micael; Rozzi, Carlo A.; Andrade, Xavier; Lorenzen, Florian; Marques, M. A. L.; Gross, E. K. U.; Rubio, AngelPhysica Status Solidi B: Basic Solid State Physics (2006), 243 (11), 2465-2488CODEN: PSSBBD; ISSN:0370-1972. (Wiley-VCH Verlag GmbH)A review. We report on the background, current status, and current lines of development of the octopus project. This program materializes the main equations of d.-functional theory in the ground state, and of time-dependent d.-functional theory for dynamical effects. The focus is nowadays placed on the optical (i.e. electronic) linear response properties of nanostructures and biomols., and on the non-linear response to high-intensity fields of finite systems, with particular attention to the coupled ionic-electronic motion (i.e. photo-chem. processes). In addn., we are currently extending the code to the treatment of periodic systems (both to one-dimensional chains, two-dimensional slabs, or fully periodic solids), magnetic properties (ground state properties and excitations), and to the field of quantum-mech. transport or "mol. electronics.". In this communication, we conc. on the development of the methodol.: we review the essential numerical schemes used in the code, and report on the most recent implementations, with special attention to the introduction of adaptive coordinates, to the extension of our real-space technique to tackle periodic systems, and on large-scale parallelization.**52**Andrade, X.; Strubbe, D.; De Giovannini, U.; Larsen, A. H.; Oliveira, M. J. T.; Alberdi-Rodriguez, J.; Varas, A.; Theophilou, I.; Helbig, N.; Verstraete, M. J.; Stella, L.; Nogueira, F.; Aspuru-Guzik, A.; Castro, A.; Marques, M. A. L.; Rubio, A. Real-Space Grids and the Octopus Code as Tools for the Development of New Simulation Approaches for Electronic Systems.*Phys. Chem. Chem. Phys.*2015,*17*(47), 31371– 31396, DOI: 10.1039/C5CP00351BGoogle Scholar52https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXjtVyktLw%253D&md5=2457aa1e92d75da4f45ac2d66297c5caReal-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systemsAndrade, Xavier; Strubbe, David; De Giovannini, Umberto; Larsen, Ask Hjorth; Oliveira, Micael J. T.; Alberdi-Rodriguez, Joseba; Varas, Alejandro; Theophilou, Iris; Helbig, Nicole; Verstraete, Matthieu J.; Stella, Lorenzo; Nogueira, Fernando; Aspuru-Guzik, Alan; Castro, Alberto; Marques, Miguel A. L.; Rubio, AngelPhysical Chemistry Chemical Physics (2015), 17 (47), 31371-31396CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new phys. models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calc. response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact soln. of the Schr.ovrddot.odinger equation for low-dimensionality systems.**53**Tancogne-Dejean, N.; Oliveira, M. J. T.; Andrade, X.; Appel, H.; Borca, C. H.; Le Breton, G.; Buchholz, F.; Castro, A.; Corni, S.; Correa, A. A.; De Giovannini, U.; Delgado, A.; Eich, F. G.; Flick, J.; Gil, G.; Gomez, A.; Helbig, N.; Hübener, H.; Jestädt, R.; Jornet-Somoza, J.; Larsen, A. H.; Lebedeva, I. V.; Lüders, M.; Marques, M. A. L.; Ohlmann, S. T.; Pipolo, S.; Rampp, M.; Rozzi, C. A.; Strubbe, D. A.; Sato, S. A.; Schäfer, C.; Theophilou, I.; Welden, A.; Rubio, A. Octopus, a Computational Framework for Exploring Light-Driven Phenomena and Quantum Dynamics in Extended and Finite Systems.*J. Chem. Phys.*2020,*152*(12), 124119, DOI: 10.1063/1.5142502Google Scholar53https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXmtl2ktbs%253D&md5=2f758c867e416d566cc26a1268ecac68Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systemsTancogne-Dejean, Nicolas; Oliveira, Micael J. T.; Andrade, Xavier; Appel, Heiko; Borca, Carlos H.; Le Breton, Guillaume; Buchholz, Florian; Castro, Alberto; Corni, Stefano; Correa, Alfredo A.; De Giovannini, Umberto; Delgado, Alain; Eich, Florian G.; Flick, Johannes; Gil, Gabriel; Gomez, Adrian; Helbig, Nicole; Huebener, Hannes; Jestaedt, Rene; Jornet-Somoza, Joaquim; Larsen, Ask H.; Lebedeva, Irina V.; Lueders, Martin; Marques, Miguel A. L.; Ohlmann, Sebastian T.; Pipolo, Silvio; Rampp, Markus; Rozzi, Carlo A.; Strubbe, David A.; Sato, Shunsuke A.; Schaefer, Christian; Theophilou, Iris; Welden, Alicia; Rubio, AngelJournal of Chemical Physics (2020), 152 (12), 124119CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)A review. Over the last few years, extraordinary advances in exptl. and theor. tools have allowed one to monitor and control matter at short time and at. scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, esp. at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the phys. and chem. properties of complex systems is of utmost importance. The 1st principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows one to describe nonequil. phenomena in mol. complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mech. effects within a generalized time-dependent d. functional theory. This article aims to present the new features that were implemented over the last few years, including tech. developments related to performance and massive parallelism. The authors also describe the major theor. developments to address ultrafast light-driven processes, such as the new theor. framework of quantum electrodynamics d.-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in mols. and materials, and new emergent states of matter (quantum electrodynamical-materials). (c) 2020 American Institute of Physics.**54**Zhang, Y.; Tan, Y.-W.; Stormer, H. L.; Kim, P. Experimental Observation of the Quantum Hall Effect and Berry’s Phase in Graphene.*Nature*2005,*438*(7065), 201– 204, DOI: 10.1038/nature04235Google Scholar54https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtF2nsrnJ&md5=9e5c67d812c899a4f0ab95df50cd25b7Experimental observation of the quantum Hall effect and Berry's phase in grapheneZhang, Yuanbo; Tan, Yan-Wen; Stormer, Horst L.; Kim, PhilipNature (London, United Kingdom) (2005), 438 (7065), 201-204CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)When electrons are confined in two-dimensional materials, quantum-mech. enhanced transport phenomena such as the quantum Hall effect can be obsd. Graphene, consisting of an isolated single at. layer of graphite, is an ideal realization of such a two-dimensional system. However, its behavior is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron-hole degeneracy and vanishing carrier mass near the point of charge neutrality. Indeed, a distinctive half-integer quantum Hall effect was predicted theor., as has the existence of a nonzero Berry's phase (a geometric quantum phase) of the electron wavefunction-a consequence of the exceptional topol. of the graphene band structure. Recent advances in micromech. extn. and fabrication techniques for graphite structures now permit such exotic two-dimensional electron systems to be probed exptl. Here the authors report an exptl. study of magneto-transport in a high-mobility single layer of graphene. Adjusting the chem. potential using the elec. field effect, the authors observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these expts. is confirmed by magneto-oscillations. In addn. to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.**55**Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Two-Dimensional Gas of Massless Dirac Fermions in Graphene.*Nature*2005,*438*(7065), 197– 200, DOI: 10.1038/nature04233Google Scholar55https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtF2nsrnI&md5=56138229370ff26ece1857a049f00f53Two-dimensional gas of massless Dirac fermions in grapheneNovoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A.Nature (London, United Kingdom) (2005), 438 (7065), 197-200CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmol. and from astrophysics to quantum chem. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known exptl. systems that can be described accurately by the non-relativistic Schroedinger equation. Here we report an exptl. study of a condensed-matter system (graphene, a single at. layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* ≈ 106 m s-1. Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have obsd. the following: first, graphene's cond. never falls below a min. value corresponding to the quantum unit of conductance, even when concns. of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass mc of massless carriers in graphene is described by E = mcc*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top expt.**56**Dutreix, C.; González-Herrero, H.; Brihuega, I.; Katsnelson, M. I.; Chapelier, C.; Renard, V. T. Measuring the Berry Phase of Graphene from Wavefront Dislocations in Friedel Oscillations.*Nature*2019,*574*(7777), 219– 222, DOI: 10.1038/s41586-019-1613-5Google Scholar56https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhvVOqurbK&md5=d8871e70558c9ccb6b0357bb6d2ef8c6Measuring the Berry phase of graphene from wavefront dislocations in Friedel oscillationsDutreix, C.; Gonzalez-Herrero, H.; Brihuega, I.; Katsnelson, M. I.; Chapelier, C.; Renard, V. T.Nature (London, United Kingdom) (2019), 574 (7777), 219-222CODEN: NATUAS; ISSN:0028-0836. (Nature Research)Electronic band structures dictate the mech., optical and elec. properties of cryst. solids. Their exptl. detn. is therefore crucial for technol. applications. Although the spectral distribution in energy bands is routinely measured by various techniques1, it is more difficult to access the topol. properties of band structures such as the quantized Berry phase, γ, which is a gauge-invariant geometrical phase accumulated by the wavefunction along an adiabatic cycle2. In graphene, the quantized Berry phase γ = π accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect4,5. It is usually thought that measuring the Berry phase requires the application of external electromagnetic fields to force the charged particles along closed trajectories3. Contradicting this belief, here we demonstrate that the Berry phase of graphene can be measured in the absence of any external magnetic field. We observe edge dislocations in oscillations of the charge d. ρ (Friedel oscillations) that are formed at hydrogen atoms chemisorbed on graphene. Following Nye and Berry6 in describing these topol. defects as phase singularities of complex fields, we show that the no. of addnl. wavefronts in the dislocation is a real-space measure of the Berry phase of graphene. Because the electronic dispersion relation can also be detd. from Friedel oscillations7, our study establishes the charge d. as a powerful observable with which to det. both the dispersion relation and topol. properties of wavefunctions. This could have profound consequences for the study of the band-structure topol. of relativistic and gapped phases in solids.**57**Neufeld, O.; Podolsky, D.; Cohen, O. Floquet Group Theory and Its Application to Selection Rules in Harmonic Generation.*Nat. Commun.*2019,*10*(1), 405, DOI: 10.1038/s41467-018-07935-yGoogle Scholar57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3cjltVeisw%253D%253D&md5=ebd7778c81f2f0e754968bb0e4181958Floquet group theory and its application to selection rules in harmonic generationNeufeld Ofer; Cohen Oren; Neufeld Ofer; Podolsky Daniel; Cohen OrenNature communications (2019), 10 (1), 405 ISSN:.Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. Here we formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems, and derive their correspondence to observable selection rules. We apply the theory to harmonic generation, deriving closed-form tables linking DSs of the driving laser and medium (gas, liquid, or solid) in (2+1)D and (3+1)D geometries to the allowed and forbidden harmonic orders and their polarizations. We identify symmetries, including time-reversal-based, reflection-based, and elliptical-based DSs, which lead to selection rules that are not explained by currently known conservation laws. We expect the theory to be useful for ultrafast high harmonic symmetry-breaking spectroscopy, as well as in various other systems such as Floquet topological insulators.**58**Tarruell, L.; Greif, D.; Uehlinger, T.; Jotzu, G.; Esslinger, T. Creating, Moving and Merging Dirac Points with a Fermi Gas in a Tunable Honeycomb Lattice.*Nature*2012,*483*(7389), 302– 305, DOI: 10.1038/nature10871Google Scholar58https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XktVaku7k%253D&md5=aadfa8754e07cc2b1b97d1a3a2ccdef7Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb latticeTarruell, Leticia; Greif, Daniel; Uehlinger, Thomas; Jotzu, Gregor; Esslinger, TilmanNature (London, United Kingdom) (2012), 483 (7389), 302-305CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topol. insulators. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material dets. the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a min. bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a crit. limit, the two Dirac points merge and annihilate each other - a situation that has recently attracted considerable theor. interest but that is extremely challenging to observe in solids. We map out this topol. transition in lattice parameter space and find excellent agreement with ab initio calcns. Our results not only pave the way to model materials in which the topol. of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions.**59**Brinkmann, A. Introduction to Average Hamiltonian Theory. I. Basics.*Concepts Magn. Reson. Part A*2016,*45A*(6), e21414 DOI: 10.1002/cmr.a.21414Google ScholarThere is no corresponding record for this reference.**60**Bukov, M.; D’Alessio, L.; Polkovnikov, A. Universal High-Frequency Behavior of Periodically Driven Systems: From Dynamical Stabilization to Floquet Engineering.*Adv. Phys.*2015,*64*(2), 139– 226, DOI: 10.1080/00018732.2015.1055918Google ScholarThere is no corresponding record for this reference.**61**Eckardt, A.; Anisimovas, E. High-Frequency Approximation for Periodically Driven Quantum Systems from a Floquet-Space Perspective.*New J. Phys.*2015,*17*(9), 93039, DOI: 10.1088/1367-2630/17/9/093039Google Scholar61https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XmtlGksLk%253D&md5=9770891cc2ea820d238c904c02b59152High-frequency approximation for periodically driven quantum systems from a Floquet-space perspectiveEckardt, Andre; Anisimovas, EgidijusNew Journal of Physics (2015), 17 (Sept.), 093039/1-093039/35CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)Wederive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the extended Floquet Hilbert space by means of degenerate perturbation theory. The final results are equiv. to those obtained within a different approach and can also be related to the Floquet-Magnus expansion.We discuss that the dependence on the driving phase, which plagues the latter, can lead to artifactual symmetry breaking. The high-frequency approach is illustrated using the example of a periodically driven Hubbard model. Moreover, we discuss the nature of the approxn. and its limitations for systems of many interacting particles.**62**Galler, A.; Rubio, A.; Neufeld, O. Mapping Light-Dressed Floquet Bands by Highly Nonlinear Optical Excitations and Valley Polarization.*arXiv (Optics)*, March 27, 2023, arxiv:2303.15055. DOI: 10.48550/arXiv.2303.15055 . (Accessed 07–28–2023).Google ScholarThere is no corresponding record for this reference.**63**Neufeld, O.; Mao, W.; Hübener, H.; Tancogne-Dejean, N.; Sato, S. A.; De Giovannini, U.; Rubio, A. Time- and Angle-Resolved Photoelectron Spectroscopy of Strong-Field Light-Dressed Solids: Prevalence of the Adiabatic Band Picture.*Phys. Rev. Res.*2022,*4*(3), 033101, DOI: 10.1103/PhysRevResearch.4.033101Google Scholar63https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38Xis1OnsrzK&md5=6cfc4ba43adf3f3d3e7043ae24a392c7Time- and angle-resolved photoelectron spectroscopy of strong-field light-dressed solids: Prevalence of the adiabatic band pictureNeufeld, Ofer; Mao, Wenwen; Huebener, Hannes; Tancogne-Dejean, Nicolas; Sato, Shunsuke A.; De Giovannini, Umberto; Rubio, AngelPhysical Review Research (2022), 4 (3), 033101CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)In recent years, strong-field physics in condensed matter was pioneered as a potential approach for controlling material properties through laser dressing, as well as for ultrafast spectroscopy via nonlinear light-matter interactions (e.g., harmonic generation). A potential controversy arising from these advancements is that it is sometimes vague which band picture should be used to interpret strong-field expts.: The field-free bands, the adiabatic (instantaneous) field-dressed bands, Floquet bands, or some other intermediate picture. Here, we try to resolve this issue by performing theor. expts. of time- and angle-resolved photoelectron spectroscopy (Tr-ARPES) for a strong-field laser-pumped solid, which should give access to the actual observable bands of the irradiated material. To our surprise, we find that the adiabatic band picture survives quite well up to high field intensities (∼1012W/cm2) and in a wide frequency range (driving wavelengths of 4000 to 800 nm, with Keldysh parameters ranging up to ∼7). We conclude that, to first order, the adiabatic instantaneous bands should be the std. blueprint for interpreting ultrafast electron dynamics in solids when the field is highly off resonant with characteristic energy scales of the material. We then discuss weaker effects of modifications of the bands beyond this picture that are nonadiabatic, showing that by using bichromatic fields the deviations from the std. picture can be probed with enhanced sensitivity. In this paper, we outline a clear band picture for the physics of strong-field interactions in solids, which should be useful for designing and analyzing strong-field exptl. observables and to formulate simpler semi-empirical models.**64**Hartwigsen, C.; Goedecker, S.; Hutter, J. Relativistic Separable Dual-Space Gaussian Pseudopotentials from H to Rn.*Phys. Rev. B*1998,*58*(7), 3641– 3662, DOI: 10.1103/PhysRevB.58.3641Google Scholar64https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXltVSktbc%253D&md5=b4cb04039858295984bc02009985d739Relativistic separable dual-space Gaussian pseudopotentials from H to RnHartwigsen, C.; Goedecker, S.; Hutter, J.Physical Review B: Condensed Matter and Materials Physics (1998), 58 (7), 3641-3662CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole Periodic Table, and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real-space grid, it is highly accurate, and, due to its analytic form, it can be specified by a very small no. of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of mol. calcns.**65**Scrinzi, A. Fully Differential Two-Electron Photo-Emission Spectra.*New J. Phys.*2012,*14*(8), 085008, DOI: 10.1088/1367-2630/14/8/085008Google Scholar65https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsF2iu7zP&md5=e85d1dc0947abfcc3a2bd9158a3cfb3ct-SURFF: fully differential two-electron photo-emission spectraScrinzi, ArminNew Journal of Physics (2012), 14 (Aug.), 085008/1-085008/17CODEN: NJOPFM; ISSN:1367-2630. (Institute of Physics Publishing)The time-dependent surface flux (t-SURFF) method is extended to single and double ionization of two-electron systems. Fully differential double emission spectra by strong pulses at extreme UV and IR wavelengths are calcd. using simulation vols. that only accommodate the effective range of the at. binding potential and the quiver radius of free electrons in the external field. For a model system, we found a pronounced dependence of shake-up and non-sequential double ionization on the phase and duration of the laser pulse. The extension to fully three-dimensional calcns. is discussed.**66**De Giovannini, U.; Hübener, H.; Rubio, A. A First-Principles Time-Dependent Density Functional Theory Framework for Spin and Time-Resolved Angular-Resolved Photoelectron Spectroscopy in Periodic Systems.*J. Chem. Theory Comput.*2017,*13*(1), 265– 273, DOI: 10.1021/acs.jctc.6b00897Google Scholar66https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhvFKns77P&md5=d1b1532a9697a3b98356e04595f0f65bA First-Principles Time-Dependent Density Functional Theory Framework for Spin and Time-Resolved Angular-Resolved Photoelectron Spectroscopy in Periodic SystemsDe Giovannini, Umberto; Hubener, Hannes; Rubio, AngelJournal of Chemical Theory and Computation (2017), 13 (1), 265-273CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)The authors present a novel theor. approach to simulate spin-, time-, and angle-resolved photoelectron spectroscopy (ARPES) from 1st principles that is applicable to surfaces, thin films, few layer systems, and low-dimensional nanostructures. The method is based on a general formulation in the framework of time-dependent d. functional theory (TDDFT) to describe the real time-evolution of electrons escaping from a surface under the effect of any external (arbitrary) laser field. By extending the so called t-SURFF method to periodic systems 1 can calc. the final photoelectron spectrum by collecting the flux of the ionization current through an analyzing surface. The resulting approach, named t-SURFFP, allows describing a wide range of irradn. conditions without any assumption on the dynamics of the ionization process allowing for pump-probe simulations on an equal footing. To illustrate the wide scope of applicability of the method, applications to graphene, mono and bilayer WSe2, and hexagonal BN (hBN) under different laser configurations are presented.**67**Neufeld, O.; Cohen, O. Background-Free Measurement of Ring Currents by Symmetry-Breaking High-Harmonic Spectroscopy.*Phys. Rev. Lett.*2019,*123*(10), 103202, DOI: 10.1103/PhysRevLett.123.103202Google Scholar67https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXit1SjtbvL&md5=fa8873e37505b38c76331e9ef993beb6Background-Free Measurement of Ring Currents by Symmetry-Breaking High-Harmonic SpectroscopyNeufeld, Ofer; Cohen, OrenPhysical Review Letters (2019), 123 (10), 103202CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We propose and explore an all-optical technique for ultrafast characterization of electronic ring currents in atoms and mols., based on high-harmonic generation (HHG). In our approach, a medium is irradiated by an intense reflection-sym. laser pulse that leads to HHG, where the polarization of the emitted harmonics is strictly linear if the medium is reflection invariant (e.g., randomly oriented at. or mol. media). The presence of a ring current in the medium breaks this symmetry, causing the emission of elliptically polarized harmonics, where the harmonics' polarization directly maps the ring current, and the signal is background-free. Scanning the delay between the current excitation and the HHG driving pulse provides an attosecond time-resolved signal for the multielectron dynamics in the excited current (including electron-electron interactions). We analyze the responsible phys. mechanism and derive the analytic dependence of the HHG emission on the ring current. The method is numerically demonstrated using quantum models for neon and benzene, as well as through ab initio calcns.**68**Dong, S.; Beaulieu, S.; Selig, M.; Rosenzweig, P.; Christiansen, D.; Pincelli, T.; Dendzik, M.; Ziegler, J. D.; Maklar, J.; Xian, R. P.; Neef, A.; Mohammed, A.; Schulz, A.; Stadler, M.; Jetter, M.; Michler, P.; Taniguchi, T.; Watanabe, K.; Takagi, H.; Starke, U.; Chernikov, A.; Wolf, M.; Nakamura, H.; Knorr, A.; Rettig, L.; Ernstorfer, R. Observation of Ultrafast Interfacial Meitner-Auger Energy Transfer in a van Der Waals Heterostructure.*arXiv (Materials Science)*, August 15, 2021, arxiv:2108.06803, ver. 2. DOI: 10.48550/arXiv.2108.06803 . (Accessed 07–28–2023).Google ScholarThere is no corresponding record for this reference.**69**Schönhense, G.; Kutnyakhov, D.; Pressacco, F.; Heber, M.; Wind, N.; Agustsson, S. Y.; Babenkov, S.; Vasilyev, D.; Fedchenko, O.; Chernov, S.; Rettig, L.; Schönhense, B.; Wenthaus, L.; Brenner, G.; Dziarzhytski, S.; Palutke, S.; Mahatha, S. K.; Schirmel, N.; Redlin, H.; Manschwetus, B.; Hartl, I.; Matveyev, Y.; Gloskovskii, A.; Schlueter, C.; Shokeen, V.; Duerr, H.; Allison, T. K.; Beye, M.; Rossnagel, K.; Elmers, H. J.; Medjanik, K. Suppression of the Vacuum Space-Charge Effect in Fs-Photoemission by a Retarding Electrostatic Front Lens.*Rev. Sci. Instrum.*2021,*92*(5), 53703, DOI: 10.1063/5.0046567Google Scholar69https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB2c3pslCqtw%253D%253D&md5=798974eb1617c1e4ab4fdfa1a0ade61eSuppression of the vacuum space-charge effect in fs-photoemission by a retarding electrostatic front lensSchonhense G; Agustsson S Y; Babenkov S; Vasilyev D; Fedchenko O; Elmers H J; Medjanik K; Kutnyakhov D; Pressacco F; Heber M; Wenthaus L; Brenner G; Dziarzhytski S; Palutke S; Schirmel N; Redlin H; Manschwetus B; Hartl I; Matveyev Yu; Gloskovskii A; Schlueter C; Beye M; Wind N; Chernov S; Allison T K; Rettig L; Schonhense B; Mahatha S K; Rossnagel K; Shokeen V; Duerr HThe Review of scientific instruments (2021), 92 (5), 053703 ISSN:.The performance of time-resolved photoemission experiments at fs-pulsed photon sources is ultimately limited by the e-e Coulomb interaction, downgrading energy and momentum resolution. Here, we present an approach to effectively suppress space-charge artifacts in momentum microscopes and photoemission microscopes. A retarding electrostatic field generated by a special objective lens repels slow electrons, retaining the k-image of the fast photoelectrons. The suppression of space-charge effects scales with the ratio of the photoelectron velocities of fast and slow electrons. Fields in the range from -20 to -1100 V/mm for Ekin = 100 eV to 4 keV direct secondaries and pump-induced slow electrons back to the sample surface. Ray tracing simulations reveal that this happens within the first 40 to 3 μm above the sample surface for Ekin = 100 eV to 4 keV. An optimized front-lens design allows switching between the conventional accelerating and the new retarding mode. Time-resolved experiments at Ekin = 107 eV using fs extreme ultraviolet probe pulses from the free-electron laser FLASH reveal that the width of the Fermi edge increases by just 30 meV at an incident pump fluence of 22 mJ/cm(2) (retarding field -21 V/mm). For an accelerating field of +2 kV/mm and a pump fluence of only 5 mJ/cm(2), it increases by 0.5 eV (pump wavelength 1030 nm). At the given conditions, the suppression mode permits increasing the slow-electron yield by three to four orders of magnitude. The feasibility of the method at high energies is demonstrated without a pump beam at Ekin = 3830 eV using hard x rays from the storage ring PETRA III. The approach opens up a previously inaccessible regime of pump fluences for photoemission experiments.**70**Schmid, C. P.; Weigl, L.; Grössing, P.; Junk, V.; Gorini, C.; Schlauderer, S.; Ito, S.; Meierhofer, M.; Hofmann, N.; Afanasiev, D.; Crewse, J.; Kokh, K. A.; Tereshchenko, O. E.; Güdde, J.; Evers, F.; Wilhelm, J.; Richter, K.; Höfer, U.; Huber, R. Tunable Non-Integer High-Harmonic Generation in a Topological Insulator.*Nature*2021,*593*(7859), 385– 390, DOI: 10.1038/s41586-021-03466-7Google Scholar70https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhtFanurzO&md5=5712be253d0ee22de2d5cf6ed6d85c08Tunable non-integer high-harmonic generation in a topological insulatorSchmid, C. P.; Weigl, L.; Groessing, P.; Junk, V.; Gorini, C.; Schlauderer, S.; Ito, S.; Meierhofer, M.; Hofmann, N.; Afanasiev, D.; Crewse, J.; Kokh, K. A.; Tereshchenko, O. E.; Guedde, J.; Evers, F.; Wilhelm, J.; Richter, K.; Hoefer, U.; Huber, R.Nature (London, United Kingdom) (2021), 593 (7859), 385-390CODEN: NATUAS; ISSN:0028-0836. (Nature Portfolio)Abstr.: When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material1-11. Sub-optical-cycle dynamics-such as dynamical Bloch oscillations2-5, quasiparticle collisions6,12, valley pseudospin switching13 and heating of Dirac gases10-leave fingerprints in the HH spectra of conventional solids. Topol. non-trivial matter14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation16-20. Here we exptl. demonstrate HH generation in a three-dimensional topol. insulator-bismuth telluride. The frequency of the terahertz driving field sharply discriminates between HH generation from the bulk and from the topol. surface, where the unique combination of long scattering times owing to spin-momentum locking17 and the quasi-relativistic dispersion enables unusually efficient HH generation. Intriguingly, all obsd. orders can be continuously shifted to arbitrary non-integer multiples of the driving frequency by varying the carrier-envelope phase of the driving field-in line with quantum theory. The anomalous Berry curvature warranted by the non-trivial topol. enforces meandering ballistic trajectories of the Dirac fermions, causing a hallmark polarization pattern of the HH emission. Our study provides a platform to explore topol. and relativistic quantum physics in strong-field control, and could lead to non-dissipative topol. electronics at IR frequencies.**71**Ghimire, S.; Reis, D. A. High-Harmonic Generation from Solids.*Nat. Phys.*2019,*15*(1), 10– 16, DOI: 10.1038/s41567-018-0315-5Google Scholar71https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXit1Crsb%252FF&md5=f303d68070480de031be39c88dd19d5aHigh-harmonic generation from solidsGhimire, Shambhu; Reis, David A.Nature Physics (2019), 15 (1), 10-16CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)A review. High-harStanford PULSE Institutemonic generation in at. gases has been studied for decades, and has formed the basis of attosecond science. Observation of high-order harmonics from bulk crystals was, however, reported much more recently, in 2010. This Review surveys the subsequent efforts aimed at understanding the microscopic mechanism of solid-state harmonics in terms of what it can tell us about the electronic structure of the source materials, how it can be used to probe driven ultrafast dynamics and its prospects for novel, compact short-wavelength light sources. Although most of this work has focused on bulk materials as the source, recent expts. have investigated high-harmonic generation from engineered structures, which could form flexible platforms for attosecond photonics.**72**Yue, L.; Gaarde, M. B. Introduction to Theory of High-Harmonic Generation in Solids: Tutorial.*J. Opt. Soc. Am. B*2022,*39*(2), 535– 555, DOI: 10.1364/JOSAB.448602Google Scholar72https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XmsFKns7c%253D&md5=051a2f3e5697dfddd9d673ef536f59e4Introduction to theory of high-harmonic generation in solids: tutorialYue, Lun; Gaarde, Mette B.Journal of the Optical Society of America B: Optical Physics (2022), 39 (2), 535-555CODEN: JOBPDE; ISSN:1520-8540. (Optica Publishing Group)A review. High-harmonic generation (HHG) in solids has emerged in recent years as a rapidly expanding and interdisciplinary field, attracting attention from both the condensed-matter and the at., mol., and optics communities. It has exciting prospects for the engineering of new light sources and the probing of ultrafast carrier dynamics in solids, and the theor. understanding of this process is of fundamental importance. This tutorial provides a hands-on introduction to the theor. description of the strong-field laser-matter interactions in a condensed-phase system that give rise to HHG. We provide an overview ranging from a detailed description of different approaches to calcg. the microscopic dynamics and how these are intricately connected to the description of the crystal structure, through the conceptual understanding of HHG in solids as supported by the semiclassical recollision model. Finally, we offer a brief description of how to calc. the macroscopic response. We also give a general introduction to the Berry phase, and we discuss important subtleties in the modeling of HHG, such as the choice of structure and laser gauges, and the construction of a smooth and periodic structure gauge for both nondegenerate and degenerate bands. The advantages and drawbacks of different structure and laser-gauge choices are discussed, both in terms of their ability to address specific questions and in terms of their numerical feasibility.**73**Lakhotia, H.; Kim, H. Y.; Zhan, M.; Hu, S.; Meng, S.; Goulielmakis, E. Laser Picoscopy of Valence Electrons in Solids.*Nature*2020,*583*(7814), 55– 59, DOI: 10.1038/s41586-020-2429-zGoogle Scholar73https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtlShtbvO&md5=ce057e01e0529cbd4eb00703739c5ec6Laser picoscopy of valence electrons in solidsLakhotia, H.; Kim, H. Y.; Zhan, M.; Hu, S.; Meng, S.; Goulielmakis, E.Nature (London, United Kingdom) (2020), 583 (7814), 55-59CODEN: NATUAS; ISSN:0028-0836. (Nature Research)High harmonics were used to reconstruct images of the valence potential and electron d. in cryst. MgF2 and CaF2 with a spatial resoln. of ∼26 pm. The pm-scale imaging of valence electrons could enable direct probing of the chem., electronic, optical and topol. properties of materials.**74**Schiffrin, A.; Paasch-Colberg, T.; Karpowicz, N.; Apalkov, V.; Gerster, D.; Mühlbrandt, S.; Korbman, M.; Reichert, J.; Schultze, M.; Holzner, S.; Barth, J. V.; Kienberger, R.; Ernstorfer, R.; Yakovlev, V. S.; Stockman, M. I.; Krausz, F. Optical-Field-Induced Current in Dielectrics.*Nature*2013,*493*(7430), 70– 74, DOI: 10.1038/nature11567Google Scholar74https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC3s7pvVGhsw%253D%253D&md5=8b0d62e9a60740ae0a3cccc60af75519Optical-field-induced current in dielectricsSchiffrin Agustin; Paasch-Colberg Tim; Karpowicz Nicholas; Apalkov Vadym; Gerster Daniel; Muhlbrandt Sascha; Korbman Michael; Reichert Joachim; Schultze Martin; Holzner Simon; Barth Johannes V; Kienberger Reinhard; Ernstorfer Ralph; Yakovlev Vladislav S; Stockman Mark I; Krausz FerencNature (2013), 493 (7430), 70-4 ISSN:.The time it takes to switch on and off electric current determines the rate at which signals can be processed and sampled in modern information technology. Field-effect transistors are able to control currents at frequencies of the order of or higher than 100 gigahertz, but electric interconnects may hamper progress towards reaching the terahertz (10(12) hertz) range. All-optical injection of currents through interfering photoexcitation pathways or photoconductive switching of terahertz transients has made it possible to control electric current on a subpicosecond timescale in semiconductors. Insulators have been deemed unsuitable for both methods, because of the need for either ultraviolet light or strong fields, which induce slow damage or ultrafast breakdown, respectively. Here we report the feasibility of electric signal manipulation in a dielectric. A few-cycle optical waveform reversibly increases--free from breakdown--the a.c. conductivity of amorphous silicon dioxide (fused silica) by more than 18 orders of magnitude within 1 femtosecond, allowing electric currents to be driven, directed and switched by the instantaneous light field. Our work opens the way to extending electronic signal processing and high-speed metrology into the petahertz (10(15) hertz) domain.**75**Higuchi, T.; Heide, C.; Ullmann, K.; Weber, H. B.; Hommelhoff, P. Light-Field-Driven Currents in Graphene.*Nature*2017,*550*(7675), 224– 228, DOI: 10.1038/nature23900Google Scholar75https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1M%252FivV2ltw%253D%253D&md5=1d61c91141d83548e9b9c571d1673365Light-field-driven currents in grapheneHiguchi Takuya; Heide Christian; Hommelhoff Peter; Ullmann Konrad; Weber Heiko BNature (2017), 550 (7675), 224-228 ISSN:.The ability to steer electrons using the strong electromagnetic field of light has opened up the possibility of controlling electron dynamics on the sub-femtosecond (less than 10(-15) seconds) timescale. In dielectrics and semiconductors, various light-field-driven effects have been explored, including high-harmonic generation, sub-optical-cycle interband population transfer and the non-perturbative change of the transient polarizability. In contrast, much less is known about light-field-driven electron dynamics in narrow-bandgap systems or in conductors, in which screening due to free carriers or light absorption hinders the application of strong optical fields. Graphene is a promising platform with which to achieve light-field-driven control of electrons in a conducting material, because of its broadband and ultrafast optical response, weak screening and high damage threshold. Here we show that a current induced in monolayer graphene by two-cycle laser pulses is sensitive to the electric-field waveform, that is, to the exact shape of the optical carrier field of the pulse, which is controlled by the carrier-envelope phase, with a precision on the attosecond (10(-18) seconds) timescale. Such a current, dependent on the carrier-envelope phase, shows a striking reversal of the direction of the current as a function of the driving field amplitude at about two volts per nanometre. This reversal indicates a transition of light-matter interaction from the weak-field (photon-driven) regime to the strong-field (light-field-driven) regime, where the intraband dynamics influence interband transitions. We show that in this strong-field regime the electron dynamics are governed by sub-optical-cycle Landau-Zener-Stuckelberg interference, composed of coherent repeated Landau-Zener transitions on the femtosecond timescale. Furthermore, the influence of this sub-optical-cycle interference can be controlled with the laser polarization state. These coherent electron dynamics in graphene take place on a hitherto unexplored timescale, faster than electron-electron scattering (tens of femtoseconds) and electron-phonon scattering (hundreds of femtoseconds). We expect these results to have direct ramifications for band-structure tomography and light-field-driven petahertz electronics.**76**Neufeld, O.; Tancogne-Dejean, N.; De Giovannini, U.; Hübener, H.; Rubio, A. Light-Driven Extremely Nonlinear Bulk Photogalvanic Currents.*Phys. Rev. Lett.*2021,*127*(12), 126601, DOI: 10.1103/PhysRevLett.127.126601Google Scholar76https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitFGnur7J&md5=e03baa734d3a5945c4bf9b32bba82ceaLight-Driven Extremely Nonlinear Bulk Photogalvanic CurrentsNeufeld, Ofer; Tancogne-Dejean, Nicolas; De Giovannini, Umberto; Huebener, Hannes; Rubio, AngelPhysical Review Letters (2021), 127 (12), 126601CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We predict the generation of bulk photocurrents in materials driven by bichromatic fields that are circularly polarized and corotating. The nonlinear photocurrents have a fully controllable directionality and amplitude without requiring carrier-envelope-phase stabilization or few-cycle pulses, and can be generated with photon energies much smaller than the band gap (reducing heating in the photoconversion process). We demonstrate with ab initio calcns. that the photocurrent generation mechanism is universal and arises in gaped materials (Si, diamond, MgO, hBN), in semimetals (graphene), and in two- and three-dimensional systems. Photocurrents are shown to rely on sub-laser-cycle asymmetries in the nonlinear response that build-up coherently from cycle to cycle as the conduction band is populated. Importantly, the photocurrents are always transverse to the major axis of the co-circular lasers regardless of the material's structure and orientation (analogously to a Hall current), which we find originates from a generalized time-reversal symmetry in the driven system. At high laser powers (~ 1013 W/cm2) this symmetry can be spontaneously broken by vast electronic excitations, which is accompanied by an onset of carrier-envelope-phase sensitivity and ultrafast many-body effects. Our results are directly applicable for efficient light-driven control of electronics, and for enhancing sub-band-gap bulk photogalvanic effects.**77**Okyay, M. S.; Kulahlioglu, A. H.; Kochan, D.; Park, N. Resonant Amplification of the Inverse Faraday Effect Magnetization Dynamics of Time Reversal Symmetric Insulators.*Phys. Rev. B*2020,*102*(10), 104304, DOI: 10.1103/PhysRevB.102.104304Google Scholar77https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitVOitLfI&md5=5c85b158cdfd9cace2442974e4f830d5Resonant amplification of the inverse Faraday effect magnetization dynamics of time reversal symmetric insulatorsOkyay, Mahmut Sait; Kulahlioglu, Adem Halil; Kochan, Denis; Park, NoejungPhysical Review B (2020), 102 (10), 104304CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)All-optical helicity-dependent manipulations of magnetism have attracted broad attention in the context of ultrafast control of magnetic units. Here, we investigate the spin dynamics in time reversal sym. insulators induced by strong circularly polarized light. We perform real-time time-dependent d. functional theory calcns. together with model Hamiltonian analyses for MoS2 and WS2 monolayers, which are exemplary spin-orbit-coupled time reversal sym. insulators. We trace the evolution of dynamical spin states, starting from the Kramers-paired electronic ground state, and find that the induced magnetization exhibits a sharp resonance peak when the applied light frequency is close to half the spin-flipping energy gap. The resonance condition is secondarily affected by the field strength and the pulse width. We suggest that low-energy time reversal broken excitations of insulators can be pursued with a sharp frequency selection as another class of ultrafast phenomena.**78**Neufeld, O.; Tancogne-Dejean, N.; De Giovannini, U.; Hübener, H.; Rubio, A. Attosecond Magnetization Dynamics in Non-Magnetic Materials Driven by Intense Femtosecond Lasers.*npj Comput. Mater.*2023,*9*(1), 39, DOI: 10.1038/s41524-023-00997-7Google Scholar78https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXmtVansrc%253D&md5=b55b4ebb58251a654bdb3470c61cd1fcAttosecond magnetization dynamics in non-magnetic materials driven by intense femtosecond lasersNeufeld, Ofer; Tancogne-Dejean, Nicolas; De Giovannini, Umberto; Huebener, Hannes; Rubio, Angelnpj Computational Materials (2023), 9 (1), 39CODEN: NCMPCS; ISSN:2057-3960. (Nature Portfolio)Irradiating solids with ultrashort laser pulses is known to initiate femtosecond timescale magnetization dynamics. However, sub-femtosecond spin dynamics have not yet been obsd. or predicted. Here, we explore ultrafast light-driven spin dynamics in a highly nonresonant strong-field regime. Through state-of-the-art ab initio calcns., we predict that a nonmagnetic material can transiently transform into a magnetic one via dynamical extremely nonlinear spin-flipping processes, which occur on attosecond timescales and are mediated by cascaded multi-photon and spin-orbit interactions. These are nonperturbative nonresonant analogs to the inverse Faraday effect, allowing the magnetization to evolve in very high harmonics of the laser frequency (e.g. here up to the 42nd, oscillating at ∼100 as), and providing control over the speed of magnetization by tuning the laser power and wavelength. Remarkably, we show that even for linearly polarized driving, where one does not intuitively expect the onset of an induced magnetization, the magnetization transiently oscillates as the system interacts with light. This response is enabled by transverse light-driven currents in the solid, and typically occurs on timescales of ∼500 as (with the slower femtosecond response suppressed). An exptl. setup capable of measuring these dynamics through pump-probe transient absorption spectroscopy is simulated. Our results pave the way for attosecond regimes of manipulation of magnetism.**79**Bai, Y.; Fei, F.; Wang, S.; Li, N.; Li, X.; Song, F.; Li, R.; Xu, Z.; Liu, P. High-Harmonic Generation from Topological Surface States.*Nat. Phys.*2021,*17*(3), 311– 315, DOI: 10.1038/s41567-020-01052-8Google Scholar79https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXisVWjur7L&md5=0a3f1498ebcaf6a31aa294a76fd0bf42High-harmonic generation from topological surface statesBai, Ya; Fei, Fucong; Wang, Shuo; Li, Na; Li, Xiaolu; Song, Fengqi; Li, Ruxin; Xu, Zhizhan; Liu, PengNature Physics (2021), 17 (3), 311-315CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)Abstr.: Three-dimensional topol. insulators are a phase of matter that hosts unique spin-polarized gapless surface states that are protected by time-reversal symmetry. They exhibit unconventional charge and spin transport properties1,2. Intense laser fields can drive ballistic charge dynamics in Dirac bands3,4 or they can coherently steer spin5 and valley pseudospin6. Similarly, high-harmonic generation (HHG) in solids provides insights into the dynamics of the electrons in topol. insulators7-13. Despite several theor. attempts to identify a topol. signature in the high-harmonic spectrum14-16, a unique fingerprint has yet to be found exptl. Here, we observe HHG that arises from topol. surface states in the intrinsic topol. insulator BiSbTeSe2. The components of the even-order harmonics that are polarized along the pump polarization stem from the spin current in helical surface states, whereas the perpendicular components originate from the out-of-plane spin polarization related to the hexagonal wrapping effect17. The dependence of HHG on surface doping in ambient air also suggests the presence of a Rashba-split two-dimensional electron gas, whose strength can be enhanced by an increase in the intensity of the mid-IR pump.**80**Baykusheva, D.; Chacón, A.; Lu, J.; Bailey, T. P.; Sobota, J. A.; Soifer, H.; Kirchmann, P. S.; Rotundu, C.; Uher, C.; Heinz, T. F.; Reis, D. A.; Ghimire, S. All-Optical Probe of Three-Dimensional Topological Insulators Based on High-Harmonic Generation by Circularly Polarized Laser Fields.*Nano Lett.*2021,*21*(21), 8970– 8978, DOI: 10.1021/acs.nanolett.1c02145Google Scholar80https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXit1yhur3N&md5=95f27545bf48679f75cc1469dd901925All-Optical Probe of Three-Dimensional Topological Insulators Based on High-Harmonic Generation by Circularly Polarized Laser FieldsBaykusheva, Denitsa; Chacon, Alexis; Lu, Jian; Bailey, Trevor P.; Sobota, Jonathan A.; Soifer, Hadas; Kirchmann, Patrick S.; Rotundu, Costel; Uher, Ctirad; Heinz, Tony F.; Reis, David A.; Ghimire, ShambhuNano Letters (2021), 21 (21), 8970-8978CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)We report the observation of an anomalous nonlinear optical response of the prototypical three-dimensional topol. insulator bismuth selenide through the process of high-order harmonic generation. We find that the generation efficiency increases as the laser polarization is changed from linear to elliptical, and it becomes max. for circular polarization. With the aid of a microscopic theory and a detailed anal. of the measured spectra, we reveal that such anomalous enhancement encodes the characteristic topol. of the band structure that originates from the interplay of strong spin-orbit coupling and time-reversal symmetry protection. The implications are in ultrafast probing of topol. phase transitions, light-field driven dissipationless electronics, and quantum computation.**81**Lv, Y.-Y.; Xu, J.; Han, S.; Zhang, C.; Han, Y.; Zhou, J.; Yao, S.-H.; Liu, X.-P.; Lu, M.-H.; Weng, H.; Xie, Z.; Chen, Y. B.; Hu, J.; Chen, Y.-F.; Zhu, S. High-Harmonic Generation in Weyl Semimetal β-WP2 Crystals.*Nat. Commun.*2021,*12*(1), 6437, DOI: 10.1038/s41467-021-26766-yGoogle Scholar81https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXisVegtrvO&md5=7433a01378085a7b7b1b7ead8da79e2dHigh-harmonic generation in Weyl semimetal β-WP2 crystalsLv, Yang-Yang; Xu, Jinlong; Han, Shuang; Zhang, Chi; Han, Yadong; Zhou, Jian; Yao, Shu-Hua; Liu, Xiao-Ping; Lu, Ming-Hui; Weng, Hongming; Xie, Zhenda; Chen, Y. B.; Hu, Jianbo; Chen, Yan-Feng; Zhu, ShiningNature Communications (2021), 12 (1), 6437CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)As a quantum material, Weyl semimetal has a series of electronic-band-structure features, including Weyl points with left and right chirality and corresponding Berry curvature, which have been obsd. in expts. These band-structure features also lead to some unique nonlinear properties, esp. high-order harmonic generation (HHG) due to the dynamic process of electrons under strong laser excitation, which has remained unexplored previously. Herein, we obtain effective HHG in type-II Weyl semimetal β-WP2 crystals, where both odd and even orders are obsd., with spectra extending into the vacuum UV region (190 nm, 10th order), even under fairly low femtosecond laser intensity. In-depth studies have interpreted that odd-order harmonics come from the Bloch electron oscillation, while even orders are attributed to Bloch oscillations under the "spike-like" Berry curvature at Weyl points. With crystallog. orientation-dependent HHG spectra, we further quant. retrieved the electronic band structure and Berry curvature of β-WP2. These findings may open the door for exploiting metallic/semimetallic states as solid platforms for deep UV radiation and offer an all-optical and pragmatic soln. to characterize the complicated multiband electronic structure and Berry curvature of quantum topol. materials.**82**Heide, C.; Kobayashi, Y.; Baykusheva, D. R.; Jain, D.; Sobota, J. A.; Hashimoto, M.; Kirchmann, P. S.; Oh, S.; Heinz, T. F.; Reis, D. A.; Ghimire, S. Probing Topological Phase Transitions Using High-Harmonic Generation.*Nat. Photonics*2022,*16*(9), 620– 624, DOI: 10.1038/s41566-022-01050-7Google Scholar82https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitFKgtLjI&md5=370314fe9ff6e6da30c5f99c9a5847b0Probing topological phase transitions using high-harmonic generationHeide, Christian; Kobayashi, Yuki; Baykusheva, Denitsa R.; Jain, Deepti; Sobota, Jonathan A.; Hashimoto, Makoto; Kirchmann, Patrick S.; Oh, Seongshik; Heinz, Tony F.; Reis, David A.; Ghimire, ShambhuNature Photonics (2022), 16 (9), 620-624CODEN: NPAHBY; ISSN:1749-4885. (Nature Portfolio)Abstr.: The prediction and realization of topol. insulators have sparked great interest in exptl. approaches to the classification of materials1-3. The phase transition between non-trivial and trivial topol. states is important, not only for basic materials science but also for next-generation technol., such as dissipation-free electronics4. It is therefore crucial to develop advanced probes that are suitable for a wide range of samples and environments. Here we demonstrate that circularly polarized laser-field-driven high-harmonic generation is distinctly sensitive to the non-trivial and trivial topol. phases in the prototypical three-dimensional topol. insulator bismuth selenide5. The phase transition is chem. initiated by reducing the spin-orbit interaction strength through the substitution of bismuth with indium atoms6,7. We find strikingly different high-harmonic responses of trivial and non-trivial topol. surface states that manifest themselves as a conversion efficiency and elliptical dichroism that depend both on the driving laser ellipticity and the crystal orientation. The origins of the anomalous high-harmonic response are corroborated by calcns. using the semiconductor optical Bloch equations with pairs of surface and bulk bands. As a purely optical approach, this method offers sensitivity to the electronic structure of the material, including its nonlinear response, and is compatible with a wide range of samples and sample environments.**83**Neufeld, O.; Tancogne-Dejean, N.; Hubener, H.; De Giovannini, U.; Rubio, A. Are There Universal Signatures of Topological Phases in High Harmonic Generation? Probably Not.*Phys. Rev. X*2023,*13*(3), 031011, DOI: 10.1103/PhysRevX.13.031011Google ScholarThere is no corresponding record for this reference.

## Cited By

This article is cited by 1 publications.

- Anna Galler, Angel Rubio, Ofer Neufeld. Mapping Light-Dressed Floquet Bands by Highly Nonlinear Optical Excitations and Valley Polarization. The Journal of Physical Chemistry Letters
**2023**,*14*(50) , 11298-11304. https://doi.org/10.1021/acs.jpclett.3c02936

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**1**Dóra, B.; Cayssol, J.; Simon, F.; Moessner, R. Optically Engineering the Topological Properties of a Spin Hall Insulator.*Phys. Rev. Lett.*2012,*108*(5), 56602, DOI: 10.1103/PhysRevLett.108.0566021https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XisFansb0%253D&md5=e851708c763c874a3be638233c7030dbOptically engineering the topological properties of a spin Hall insulatorDora, Balazs; Cayssol, Jerome; Simon, Ferenc; Moessner, RoderichPhysical Review Letters (2012), 108 (5), 056602/1-056602/5CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Time-periodic perturbations can be used to engineer topol. properties of matter by altering the Floquet band structure. This is demonstrated for the helical edge state of a spin Hall insulator in the presence of monochromatic circularly polarized light. The inherent spin structure of the edge state is influenced by the Zeeman coupling and not by the orbital effect. The photocurrent (and the magnetization along the edge) develops a finite, helicity-dependent expectation value and turns from dissipationless to dissipative with increasing radiation frequency, signaling a change in the topol. properties. The connection with Thouless' charge pumping and nonequil. zitterbewegung is discussed, together with possible expts.**2**Wang, Y. H.; Steinberg, H.; Jarillo-Herrero, P.; Gedik, N. Observation of Floquet-Bloch States on the Surface of a Topological Insulator.*Science*2013,*342*(6157), 453– 457, DOI: 10.1126/science.12398342https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhs1Ckt73O&md5=e5e5bdfd4e3f6c09f6deb5d1aecda96cObservation of Floquet-Bloch States on the Surface of a Topological InsulatorWang, Y. H.; Steinberg, H.; Jarillo-Herrero, P.; Gedik, N.Science (Washington, DC, United States) (2013), 342 (6157), 453-457CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)The unique electronic properties of the surface electrons in a topol. insulator are protected by time-reversal symmetry. Circularly polarized light naturally breaks time-reversal symmetry, which may lead to an exotic surface quantum Hall state. Using time- and angle-resolved photoemission spectroscopy, an intense ultrashort mid-IR pulse with energy below the bulk band gap hybridizes with the surface Dirac fermions of a topol. insulator to form Floquet-Bloch bands. These photon-dressed surface bands exhibit polarization-dependent band gaps at avoided crossings. Circularly polarized photons induce an addnl. gap at the Dirac point, which is a signature of broken time-reversal symmetry on the surface. These observations establish the Floquet-Bloch bands in solids and pave the way for optical manipulation of topol. quantum states of matter.**3**Dehghani, H.; Hafezi, M.; Ghaemi, P. Light-Induced Topological Superconductivity via Floquet Interaction Engineering.*Phys. Rev. Res.*2021,*3*(2), 23039, DOI: 10.1103/PhysRevResearch.3.0230393https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhsFSgtLfN&md5=20418c271440d54ad1779a4fd8be9086Light-induced topological superconductivity via Floquet interaction engineeringDehghani, Hossein; Hafezi, Mohammad; Ghaemi, PouyanPhysical Review Research (2021), 3 (2), 023039CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)We propose a mechanism for light-induced unconventional supercond. in a two-valley semiconductor with a massive Dirac-type band structure. The superconducting phase results from the out-of-equil. excitation of carriers in the presence of Coulomb repulsion and is stabilized by coupling the driven semiconductor to a bosonic or fermionic thermal bath. We consider a circularly polarized light pump and show that by controlling the detuning of the pump frequency relative to the band gap, different types of chiral supercond. would be induced. The emergence of novel superconducting states, such as the chiral p-wave pairing, results from the Floquet engineering of the interaction. This is realized by modifying the form of the Coulomb interaction by projecting it into the states that are resonant with the pump frequency. We show that the resulting unconventional pairing in our system can host topol. protected chiral bound states. We discuss a promising exptl. platform to realize our proposal and detect the signatures of the emergent superconducting state.**4**Disa, A. S.; Nova, T. F.; Cavalleri, A. Engineering Crystal Structures with Light.*Nat. Phys.*2021,*17*(10), 1087– 1092, DOI: 10.1038/s41567-021-01366-14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitF2nsLzF&md5=2e012e8596e698decdeb4cd29ed2255bEngineering crystal structures with lightDisa, Ankit S.; Nova, Tobia F.; Cavalleri, AndreaNature Physics (2021), 17 (10), 1087-1092CODEN: NPAHAX; ISSN:1745-2473. (Nature Portfolio)Abstr.: The crystal structure of a solid largely dictates its electronic, optical and mech. properties. Indeed, much of the exploration of quantum materials in recent years including the discovery of new phases and phenomena in correlated, topol. and two-dimensional materials-has been based on the ability to rationally control crystal structures through materials synthesis, strain engineering or heterostructuring of van der Waals bonded materials. These static approaches, while enormously powerful, are limited by thermodn. and elastic constraints. An emerging avenue of study has focused on extending such structural control to the dynamical regime by using resonant laser pulses to drive vibrational modes in a crystal. This paradigm of 'nonlinear phononics' provides a basis for rationally designing the structure and symmetry of crystals with light, allowing for the manipulation of functional properties at high speed and, in many instances, beyond what may be possible in equil. Here we provide an overview of the developments in this field, discussing the theory, applications and future prospects of optical crystal structure engineering.**5**Castro, A.; De Giovannini, U.; Sato, S. A.; Hübener, H.; Rubio, A. Floquet Engineering the Band Structure of Materials with Optimal Control Theory.*Phys. Rev. Res.*2022,*4*(3), 33213, DOI: 10.1103/PhysRevResearch.4.0332135https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38Xis1yls77F&md5=c41cc847f94d308796b5dedad0c5225fFloquet engineering the band structure of materials with optimal control theoryCastro, Alberto; De Giovannini, Umberto; Sato, Shunsuke A.; Hubener, Hannes; Rubio, AngelPhysical Review Research (2022), 4 (3), 033213CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)We demonstrate that the electronic structure of a material can be deformed into Floquet pseudobands with arbitrarily tailored shapes. We achieve this goal with a combination of quantum optimal control theory and Floquet engineering. The power and versatility of this framework is demonstrated here by utilizing the independent-electron tight-binding description of the π electronic system of graphene. We show several prototype examples focusing on the region around the K (Dirac) point of the Brillouin zone: creation of a gap with opposing flat valence and conduction bands, creation of a gap with opposing concave sym. valence and conduction bands (which would correspond to a material with an effective neg. electron-hole mass), and closure of the gap when departing from a modified graphene model with a nonzero field-free gap. We employ time-periodic drives with several frequency components and polarizations, in contrast to the usual monochromatic fields, and use control theory to find the amplitudes of each component that optimize the shape of the bands as desired. In addn., we use quantum control methods to find realistic switch-on pulses that bring the material into the predefined stationary Floquet band structure, i.e., into a state in which the desired Floquet modes of the target bands are fully occupied, so that they should remain stroboscopically stationary, with long lifetimes, when the weak periodic drives are started. Finally, we note that although we have focused on solid state materials, the technique that we propose could be equally used for the Floquet engineering of ultracold atoms in optical lattices and for other nonequil. dynamical and correlated systems.**6**Lu, M.; Reid, G. H.; Fritsch, A. R.; Piñeiro, A. M.; Spielman, I. B. Floquet Engineering Topological Dirac Bands.*Phys. Rev. Lett.*2022,*129*(4), 40402, DOI: 10.1103/PhysRevLett.129.0404026https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitFSgtL%252FO&md5=b7bd00c888495a56e5e47c356e71e23bFloquet Engineering Topological Dirac BandsLu, Mingwu; Reid, G. H.; Fritsch, A. R.; Pineiro, A. M.; Spielman, I. B.Physical Review Letters (2022), 129 (4), 040402CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We exptl. realized a time-periodically modulated 1D lattice for ultracold atoms featuring a pair of linear bands, each with a Floquet winding no. These bands are spin-momentum locked and almost perfectly linear everywhere in the Brillouin zone: a near-ideal realization of the 1D Dirac Hamiltonian. We characterized the Floquet winding no. using a form of quantum state tomog., covering the Brillouin zone and following the micromotion through one Floquet period. Last, we altered the modulation timing to lift the topol. protection, opening a gap at the Dirac point that grew in proportion to the deviation from the topol. configuration.**7**Trevisan, T. V.; Arribi, P. V.; Heinonen, O.; Slager, R.-J.; Orth, P. P. Bicircular Light Floquet Engineering of Magnetic Symmetry and Topology and Its Application to the Dirac Semimetal Cd3As2.*Phys. Rev. Lett.*2022,*128*(6), 66602, DOI: 10.1103/PhysRevLett.128.0666027https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XkvVansro%253D&md5=a75b471ab3f985b9a7b65aba42970014Bicircular Light Floquet Engineering of Magnetic Symmetry and Topology and Its Application to the Dirac Semimetal Cd3As2Trevisan, Thais V.; Arribi, Pablo Villar; Heinonen, Olle; Slager, Robert-Jan; Orth, Peter P.Physical Review Letters (2022), 128 (6), 066602CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We show that bicircular light (BCL) is a versatile way to control magnetic symmetries and topol. in materials. The elec. field of BCL, which is a superposition of two circularly polarized light waves with frequencies that are integer multiples of each other, traces out a rose pattern in the polarization plane that can be chosen to break selective symmetries, including spatial inversion. Using a realistic low-energy model, we theor. demonstrate that the three-dimensional Dirac semimetal Cd3As2 is a promising platform for BCL Floquet engineering. Without strain, BCL irradn. induces a transition to a noncentrosym. magnetic Weyl semimetal phase with tunable energy sepn. between the Weyl nodes. In the presence of strain, we predict the emergence of a magnetic topol. cryst. insulator with exotic unpinned surface Dirac states that are protected by a combination of twofold rotation and time reversal (2') and can be controlled by light.**8**Bhattacharya, U.; Chaudhary, S.; Grass, T.; Johnson, A. S.; Wall, S.; Lewenstein, M. Fermionic Chern Insulator from Twisted Light with Linear Polarization.*Phys. Rev. B*2022,*105*(8), L081406, DOI: 10.1103/PhysRevB.105.L0814068https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XntlCitrk%253D&md5=ed1e99024ca533b4f5e1751334570df8Fermionic Chern insulator from twisted light with linear polarizationBhattacharya, Utso; Chaudhary, Swati; Grass, Tobias; Johnson, Allan S.; Wall, Simon; Lewenstein, MaciejPhysical Review B (2022), 105 (8), L081406CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)The breaking of time-reversal symmetry is a crucial ingredient to topol. bands. It can occur intrinsically in materials with magnetic order, or be induced by external fields, such as magnetic fields in quantum Hall systems or circularly polarized light fields in Floquet Chern insulators. Apart from polarization, photons can carry another degree of freedom, orbital angular momentum, through which time-reversal symmetry can be broken. In this Letter we pose the question of whether this property allows for inducing topol. bands via a linearly polarized but twisted light beam. To this end we study a graphenelike model of electrons on a honeycomb lattice interacting with a twisted light field. To identify the topol. behavior of the electrons, we calc. their local markers of Chern no. and monitor the presence of in-gap edge states. Our results are shown to be fully analogous to the behavior found in paradigmatic models for static and driven Chern insulators, and realizing the state is exptl. straightforward. With this, our work establishes a mechanism for generating fermionic topol. phases of matter that can harness the central phase singularity of an optical vortex beam.**9**Uzan-Narovlansky, A. J.; Jimenez-Galan, A.; Orenstein, G.; Silva, R. E. F.; Arusi-Parpar, T.; Shames, S.; Bruner, B. D.; Yan, B.; Smirnova, O.; Ivanov, M.; Dudovich, N. Observation of Light-Driven Band Structure via Multiband High-Harmonic Spectroscopy.*Nat. Photonics*2022,*16*, 428– 432, DOI: 10.1038/s41566-022-01010-19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsFKgtLzE&md5=38996d61df8f9395e3a638e25842da91Observation of light-driven band structure via multiband high-harmonic spectroscopyUzan-Narovlansky, Ayelet J.; Jimenez-Galan, Alvaro; Orenstein, Gal; Silva, Rui E. F.; Arusi-Parpar, Talya; Shames, Sergei; Bruner, Barry D.; Yan, Binghai; Smirnova, Olga; Ivanov, Misha; Dudovich, NiritNature Photonics (2022), 16 (6), 428-432CODEN: NPAHBY; ISSN:1749-4885. (Nature Portfolio)Intense light-matter interactions have revolutionized our ability to probe and manipulate quantum systems at sub-femtosecond timescales1, opening routes to the all-optical control of electronic currents in solids at petahertz rates2-7. Such control typically requires elec.-field amplitudes in the range of almost volts per angstrom, when the voltage drop across a lattice site becomes comparable to the characteristic bandgap energies. In this regime, intense light-matter interaction induces notable modifications to the electronic and optical properties8-10, dramatically modifying the crystal band structure. Yet, identifying and characterizing such modifications remain an outstanding problem. As the oscillating elec. field changes within the driving field's cycle, does the band structure follow and how can it be defined. Here we address this fundamental question, proposing all-optical spectroscopy to probe the laser-induced closing of the bandgap between adjacent conduction bands. Our work reveals the link between nonlinear light-matter interactions in strongly driven crystals and the sub-cycle modifications in their effective band structure.**10**Bloch, J.; Cavalleri, A.; Galitski, V.; Hafezi, M.; Rubio, A. Strongly Correlated Electron–Photon Systems.*Nature*2022,*606*(7912), 41– 48, DOI: 10.1038/s41586-022-04726-w10https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhtlyjurfO&md5=6d0f03a30e70b06b578199d5bca0eb35Strongly correlated electron-photon systemsBloch, Jacqueline; Cavalleri, Andrea; Galitski, Victor; Hafezi, Mohammad; Rubio, AngelNature (London, United Kingdom) (2022), 606 (7912), 41-48CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Abstr.: An important goal of modern condensed-matter physics involves the search for states of matter with emergent properties and desirable functionalities. Although the tools for material design remain relatively limited, notable advances have been recently achieved by controlling interactions at heterointerfaces, precise alignment of low-dimensional materials and the use of extreme pressures. Here we highlight a paradigm based on controlling light-matter interactions, which provides a way to manipulate and synthesize strongly correlated quantum matter. We consider the case in which both electron-electron and electron-photon interactions are strong and give rise to a variety of phenomena. Photon-mediated supercond., cavity fractional quantum Hall physics and optically driven topol. phenomena in low dimensions are among the frontiers discussed in this Perspective, which highlights a field that we term here 'strongly correlated electron-photon science'.**11**Esin, I.; Rudner, M. S.; Lindner, N. H. Floquet Metal-to-Insulator Phase Transitions in Semiconductor Nanowires.*Sci. Adv.*2020,*6*(35), eaay4922 DOI: 10.1126/sciadv.aay4922There is no corresponding record for this reference.**12**Topp, G. E.; Jotzu, G.; McIver, J. W.; Xian, L.; Rubio, A.; Sentef, M. A. Topological Floquet Engineering of Twisted Bilayer Graphene.*Phys. Rev. Res.*2019,*1*(2), 023031, DOI: 10.1103/PhysRevResearch.1.02303112https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhvVOhtrnL&md5=1e7134e69316bd9efcaf8348bb607130Topological floquet engineering of twisted bilayer grapheneTopp, Gabriel E.; Jotzu, Gregor; McIver, James W.; Xian, Lede; Rubio, Angel; Sentef, Michael A.Physical Review Research (2019), 1 (2), 023031CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)We investigate the topol. properties of Floquet-engineered twisted bilayer graphene above the so-called magic angle driven by circularly polarized laser pulses. Employing a full Moire-unit-cell tight-binding Hamiltonian based on first-principles electronic structure, we show that the band topol. in the bilayer, at twisting angles above 1.05°, essentially corresponds to the one of single-layer graphene. However, the ability to open topol. trivial gaps in this system by a bias voltage between the layers enables the full topol. phase diagram to be explored, which is not possible in single-layer graphene. Circularly polarized light induces a transition to a topol. nontrivial Floquet band structure with the Berry curvature analogus to a Chern insulator. Importantly, the twisting allows for tuning electronic energy scales, which implies that the electronic bandwidth can be tailored to match realistic driving frequencies in the UV or midinfrared photon-energy regimes. This implies that Moire superlattices are an ideal playground for combining twistronics, Floquet engineering, and strongly interacting regimes out of thermal equil.**13**Hübener, H.; Sentef, M. A.; De Giovannini, U.; Kemper, A. F.; Rubio, A. Creating Stable Floquet-Weyl Semimetals by Laser-Driving of 3D Dirac Materials.*Nat. Commun.*2017,*8*, 13940, DOI: 10.1038/ncomms13940There is no corresponding record for this reference.**14**Nag, T.; Slager, R.-J.; Higuchi, T.; Oka, T. Dynamical Synchronization Transition in Interacting Electron Systems.*Phys. Rev. B*2019,*100*(13), 134301, DOI: 10.1103/PhysRevB.100.13430114https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXit1ygt7fL&md5=5a14fcbd33acf3b0dc2c0372198ed387Dynamical synchronization transition in interacting electron systemsNag, Tanay; Slager, Robert-Jan; Higuchi, Takuya; Oka, TakashiPhysical Review B (2019), 100 (13), 134301CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)A review. Synchronization is a ubiquitous phenomenon in nature and we propose its new perspective in ultrafast dynamics in interacting electron systems. In particular, using graphene irradiated by an intense bicircular pulse laser as a prototypical and exptl. viable example, we theor. investigate how to selectively generate a coherent oscillation of electronic order such as charge d. orders (CDOs). The key is to use tailored fields that match the cryst. symmetry broken by the target order. After the pump, a macroscopic no. of electrons start oscillating and coherence is built up through a transition. The resulting physics is detectable as a coherent light emission at the synchronizion frequency and may be used as a purely electronic way of realizing Floquet states respecting exotic space-time cryst. symmetries. In the process, we also explore possible flipping of existing static CDOs and generation of higher harmonics. The general framework for the coherent electronic order is found to be analogous with the celebrated Kuramoto model, describing the classical synchronization of coupled pendulums.**15**Oka, T.; Kitamura, S. Floquet Engineering of Quantum Materials.*Annu. Rev. Condens. Matter Phys.*2019,*10*(1), 387– 408, DOI: 10.1146/annurev-conmatphys-031218-013423There is no corresponding record for this reference.**16**Nathan, F.; Abanin, D.; Berg, E.; Lindner, N. H.; Rudner, M. S. Anomalous Floquet Insulators.*Phys. Rev. B*2019,*99*(19), 195133, DOI: 10.1103/PhysRevB.99.19513316https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhsVOju7rL&md5=af5ea40c5eeed0455783f2f2668ce3e9Anomalous Floquet insulatorsNathan, Frederik; Abanin, Dmitry; Berg, Erez; Lindner, Netanel H.; Rudner, Mark S.Physical Review B (2019), 99 (19), 195133CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)Landau's theory of phase transitions provides a framework for describing phases of matter in thermodn. equil. Recently, an intriguing new class of quantum many-body localized (MBL) systems that do not reach thermodn. equil. was discovered. The possibility of MBL systems to not heat up under periodic driving, which drastically changes the nature of dynamics in the system, opens the door for new, truly nonequil. phases of matter. In this paper we find a two-dimensional nonequil. topol. phase, the anomalous Floquet insulator (AFI), which arises from the combination of periodic driving and MBL. Having no counterpart in equil., the AFI is characterized by an MBL bulk, and topol. protected delocalized (thermalizing) chiral states at its boundaries. After establishing the regime of stability of the AFI phase in a simple yet exptl. realistic model, we investigate the interplay between the thermalizing edge and the localized bulk via numerical simulations of an AFI in a geometry with edges. We find that nonuniform particle d. profiles remain stable in the bulk up to the longest timescales that we can access, while the propagating edge states persist and thermalize. These findings open the possibility of observing quantized edge transport in interacting systems at high temp.**17**Frisk Kockum, A.; Miranowicz, A.; De Liberato, S.; Savasta, S.; Nori, F. Ultrastrong Coupling between Light and Matter.*Nat. Rev. Phys.*2019,*1*(1), 19– 40, DOI: 10.1038/s42254-018-0006-2There is no corresponding record for this reference.**18**Rudner, M. S.; Lindner, N. H. Band Structure Engineering and Non-Equilibrium Dynamics in Floquet Topological Insulators.*Nat. Rev. Phys.*2020,*2*(5), 229– 244, DOI: 10.1038/s42254-020-0170-z18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXosVyrtbo%253D&md5=6ad0b274d105cc77c9f4045bcf822e1cBand structure engineering and non-equilibrium dynamics in Floquet topological insulatorsRudner, Mark S.; Lindner, Netanel H.Nature Reviews Physics (2020), 2 (5), 229-244CODEN: NRPACZ; ISSN:2522-5820. (Nature Research)Abstr.: Non-equil. topol. phenomena can be induced in quantum many-body systems using time-periodic fields (for example, by laser or microwave illumination). This Review begins with the key principles underlying Floquet band engineering, wherein such fields are used to change the topol. properties of a system's single-particle spectrum. In contrast to equil. systems, non-trivial band structure topol. in a driven many-body system does not guarantee that robust topol. behavior will be obsd. In particular, periodically driven many-body systems tend to absorb energy from their driving fields and thereby tend to heat up. We survey various strategies for overcoming this challenge of heating and for obtaining new topol. phenomena in this non-equil. setting. We describe how drive-induced topol. edge states can be probed in the regime of mesoscopic transport, and three routes for observing topol. phenomena beyond the mesoscopic regime: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of the regimes covered, and their exptl. realizations in solid-state, cold at., and photonic systems.**19**Rodriguez-Vega, M.; Vogl, M.; Fiete, G. A. Floquet Engineering of Twisted Double Bilayer Graphene.*Phys. Rev. Res.*2020,*2*(3), 33494, DOI: 10.1103/PhysRevResearch.2.03349419https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitV2gsL7O&md5=f157c4f131a83c97e107e7dce3ac4065Floquet engineering of twisted double bilayer grapheneRodriguez-Vega, Martin; Vogl, Michael; Fiete, Gregory A.Physical Review Research (2020), 2 (3), 033494CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)Motivated by the recent exptl. realization of twisted double bilayer graphene (TDBG) samples, we study, both anal. and numerically, the effects of circularly polarized light propagating in free space and confined in a waveguide on the band structure and topol. properties of these systems. These two complementary Floquet protocols allow us to selectively tune different parameters of the system by varying the intensity and light frequency. For the drive protocol in free space, in the high-frequency regime, we find that in TDBG with AB/BA stacking, we can selectively close the zone-center quasienergy gaps around one valley while increasing the gaps near the opposite valley by tuning the parameters of the drive. In TDBG with AB/AB stacking, a similar effect can be obtained upon the application of a perpendicular static elec. field. Furthermore, we study the topol. properties of the driven system in different settings, provide accurate effective Floquet Hamiltonians, and show that relatively strong drives can generate flat bands. On the other hand, longitudinal light confined in a waveguide couples to the components of the interlayer hopping that are perpendicular to the TDBG sheet, allowing for selective engineering of the bandwidth of Floquet zone-center quasienergy bands without breaking the symmetries of the static system.**20**Jiménez-Galán, Á.; Silva, R. E. F.; Smirnova, O.; Ivanov, M. Lightwave Control of Topological Properties in 2D Materials for Sub-Cycle and Non-Resonant Valley Manipulation.*Nat. Photonics*2020,*14*(12), 728– 732, DOI: 10.1038/s41566-020-00717-320https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitlGrs7rN&md5=3fb5017b99030a16460b371a46acc5c6Lightwave control of topological properties in 2D materials for sub-cycle and non-resonant valley manipulationJimenez-Galan, A.; Silva, R. E. F.; Smirnova, O.; Ivanov, M.Nature Photonics (2020), 14 (12), 728-732CODEN: NPAHBY; ISSN:1749-4885. (Nature Research)Modern light generation technol. offers extraordinary capabilities for sculpting light pulses, with full control over individual elec. field oscillations within each laser cycle1-3. These capabilities are at the core of lightwave electronics-the dream of ultrafast lightwave control over electron dynamics in solids on a sub-cycle timescale, aiming at information processing at petahertz rates4-8. Here, bringing the frequency-domain concept of topol. Floquet systems9,10 to the few-femtosecond time domain, we develop a theor. method that can be implemented with existing technol., to control the topol. properties of two-dimensional materials on few-femtosecond timescales by controlling the sub-cycle structure of non-resonant driving fields. We use this method to propose an all-optical, non-element-specific technique, phys. transparent in real space, to coherently write, manipulate and read selective valley excitation using fields carried in a wide range of frequencies and on timescales that are orders of magnitude shorter than the valley lifetime, crucial for the implementation of valleytronic devices11,12.**21**Shan, J.-Y.; Ye, M.; Chu, H.; Lee, S.; Park, J.-G.; Balents, L.; Hsieh, D. Giant Modulation of Optical Nonlinearity by Floquet Engineering.*Nature*2021,*600*(7888), 235– 239, DOI: 10.1038/s41586-021-04051-821https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXis12qtrnP&md5=3ef6f175f80d7f6bf66176e30418e1ddGiant modulation of optical nonlinearity by Floquet engineeringShan, Jun-Yi; Ye, M.; Chu, H.; Lee, Sungmin; Park, Je-Geun; Balents, L.; Hsieh, D.Nature (London, United Kingdom) (2021), 600 (7888), 235-239CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Strong periodic driving with light offers the potential to coherently manipulate the properties of quantum materials on ultrafast timescales. Recently, strategies have emerged to drastically alter electronic and magnetic properties by optically inducing non-trivial band topologies1-6, emergent spin interactions7-11 and even supercond.12. However, the prospects and methods of coherently engineering optical properties on demand are far less understood13. Here we demonstrate coherent control and giant modulation of optical nonlinearity in a van der Waals layered magnetic insulator, manganese phosphorus trisulfide (MnPS3). By driving far off-resonance from the lowest on-site manganese d-d transition, we observe a coherent on-off switching of its optical second harmonic generation efficiency on the timescale of 100 fs with no measurable dissipation. At driving elec. fields of the order of 109 V per m, the on-off ratio exceeds 10, which is limited only by the sample damage threshold. Floquet theory calcns.14 based on a single-ion model of MnPS3 are able to reproduce the measured driving field amplitude and polarization dependence of the effect. Our approach can be applied to a broad range of insulating materials and could lead to dynamically designed nonlinear optical elements.**22**Lindner, N. H.; Refael, G.; Galitski, V. Floquet Topological Insulator in Semiconductor Quantum Wells.*Nat. Phys.*2011,*7*(6), 490– 495, DOI: 10.1038/nphys192622https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXmvVartro%253D&md5=fe24c43703ca957d00a378f792ee7fb4Floquet topological insulator in semiconductor quantum wellsLindner, Netanel H.; Refael, Gil; Galitski, VictorNature Physics (2011), 7 (6), 490-495CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)Topol. phases of matter have captured our imagination over the past few years, with tantalizing properties such as robust edge modes and exotic non-Abelian excitations, and potential applications ranging from semiconductor spintronics to topol. quantum computation. Despite recent advancements in the field, our ability to control topol. transitions remains limited, and usually requires changing material or structural properties. We show, using Floquet theory, that a topol. state can be induced in a semiconductor quantum well, initially in the trivial phase. This can be achieved by irradn. with microwave frequencies, without changing the well structure, closing the gap and crossing the phase transition. We show that the quasi-energy spectrum exhibits a single pair of helical edge states. We discuss the necessary exptl. parameters for our proposal. This proposal provides an example and a proof of principle of a new non-equil. topol. state, the Floquet topol. insulator, introduced in this paper.**23**Kitagawa, T.; Oka, T.; Brataas, A.; Fu, L.; Demler, E. Transport Properties of Nonequilibrium Systems under the Application of Light: Photoinduced Quantum Hall Insulators without Landau Levels.*Phys. Rev. B*2011,*84*(23), 235108, DOI: 10.1103/PhysRevB.84.23510823https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XisVKjtg%253D%253D&md5=297e145524f14ba9f4511adc2e5944b6Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levelsKitagawa, Takuya; Oka, Takashi; Brataas, Arne; Fu, Liang; Demler, EugenePhysical Review B: Condensed Matter and Materials Physics (2011), 84 (23), 235108/1-235108/13CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)In this paper, we study transport properties of nonequil. systems under the application of light in many-terminal measurements, using the Floquet picture. We propose and demonstrate that the quantum transport properties can be controlled in materials such as graphene and topol. insulators, via the application of light. Remarkably, under the application of off-resonant light, topol. transport properties can be induced; these systems exhibit quantum Hall effects in the absence of a magnetic field with a near quantization of the Hall conductance, realizing so-called quantum Hall systems without Landau levels first proposed by Haldane.**24**Usaj, G.; Perez-Piskunow, P. M.; Foa Torres, L. E. F.; Balseiro, C. A. Irradiated Graphene as a Tunable Floquet Topological Insulator.*Phys. Rev. B*2014,*90*(11), 115423, DOI: 10.1103/PhysRevB.90.11542324https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitFOltrrF&md5=24bc9f58440c9a75fef3a611b67d7681Irradiated graphene as a tunable Floquet topological insulatorUsaj, Gonzalo; Perez-Piskunow, P. M.; Foa Torres, L. E. F.; Balseiro, C. A.Physical Review B: Condensed Matter and Materials Physics (2014), 90 (11), 115423/1-115423/12, 12 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)In the presence of a circularly polarized mid-IR radiation graphene develops dynamical band gaps in its quasienergy band structure and becomes a Floquet insulator. Here, we analyze how topol. protected edge states arise inside these gaps in the presence of an edge. Our results show that the gap appearing at ℏΩ/2, where ℏΩ is the photon energy, is bridged by two chiral edge states whose propagation direction is set by the direction of the polarization of the radiation field. Therefore, both the propagation direction and the energy window where the states appear can be controlled externally. We present both anal. and numerical calcns. that fully characterize these states. This is complemented by simple topol. arguments that account for them and by numerical calcns. for the case of the semi-infinite sample, thereby eliminating finite-size effects.**25**Titum, P.; Lindner, N. H.; Rechtsman, M. C.; Refael, G. Disorder-Induced Floquet Topological Insulators.*Phys. Rev. Lett.*2015,*114*(5), 056801, DOI: 10.1103/PhysRevLett.114.05680125https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXktlaku7g%253D&md5=b1b69aa2d51f6cd5caf59f156d628404Disorder-induced Floquet topological insulatorTitum, Paraj; Lindner, Netanel H.; Rechtsman, Mikael C.; Refael, GilPhysical Review Letters (2015), 114 (5), 056801CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We investigate the possibility of realizing a disorder-induced topol. Floquet spectrum in two-dimensional periodically driven systems. Such a state would be a dynamical realization of the topol. Anderson insulator. We establish that a disorder-induced trivial-to-topol. transition indeed occurs, and characterize it by computing the disorder averaged Bott index, suitably defined for the time-dependent system. The presence of edge states in the topol. state is confirmed by exact numerical time evolution of wave packets on the edge of the system. We consider the optimal driving regime for exptl. observing the Floquet topol. Anderson insulator, and discuss its possible realization in photonic lattices.**26**Mikami, T.; Kitamura, S.; Yasuda, K.; Tsuji, N.; Oka, T.; Aoki, H. Brillouin-Wigner Theory for High-Frequency Expansion in Periodically Driven Systems: Application to Floquet Topological Insulators.*Phys. Rev. B*2016,*93*(14), 144307, DOI: 10.1103/PhysRevB.93.14430726https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsF2ks7fK&md5=7a8329e5dd5971b0d1310662dc040eb6Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: application to Floquet topological insulatorsMikami, Takahiro; Kitamura, Sota; Yasuda, Kenji; Tsuji, Naoto; Oka, Takashi; Aoki, HideoPhysical Review B (2016), 93 (14), 144307/1-144307/25CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)We construct a systematic high-frequency expansion for periodically driven quantum systems based on the Brillouin-Wigner (BW) perturbation theory, which generates an effective Hamiltonian on the projected zero-photon subspace in the Floquet theory, reproducing the quasienergies and eigenstates of the original Floquet Hamiltonian up to desired order in 1/ω, with ω being the frequency of the drive. The advantage of the BW method is that it is not only efficient in deriving higher-order terms, but even enables us to write down the whole infinite series expansion, as compared to the van Vleck degenerate perturbation theory. The expansion is also free from a spurious dependence on the driving phase, which has been an obstacle in the Floquet-Magnus expansion. We apply the BW expansion to various models of noninteracting electrons driven by circularly polarized light. As the amplitude of the light is increased, the system undergoes a series of Floquet topol.-to-topol. phase transitions, whose phase boundary in the high-frequency regime is well explained by the BW expansion. As the frequency is lowered, the high-frequency expansion breaks down at some point due to band touching with nonzero-photon sectors, where we find numerically even more intricate and richer Floquet topol. phases spring out. We have then analyzed, with the Floquet dynamical mean-field theory, the effects of electron-electron interaction and energy dissipation. We have specifically revealed that phase transitions from Floquet-topol. to Mott insulators emerge, where the phase boundaries can again be captured with the high-frequency expansion.**27**Holthaus, M. Floquet Engineering with Quasienergy Bands of Periodically Driven Optical Lattices.*J. Phys. B At. Mol. Opt. Phys.*2016,*49*(1), 13001, DOI: 10.1088/0953-4075/49/1/01300127https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XksVemsb8%253D&md5=2c53a9ad94a7ca3337e1326a303358c4Floquet engineering with quasienergy bands of periodically driven optical latticesHolthaus, MartinJournal of Physics B: Atomic, Molecular and Optical Physics (2016), 49 (1), 013001/1-013001/26CODEN: JPAPEH; ISSN:0953-4075. (IOP Publishing Ltd.)A primer on the Floquet theory of periodically time-dependent quantum systems is provided, and it is shown how to apply this framework for computing the quasienergy band structure governing the dynamics of ultracold atoms in driven optical cosine lattices. Such systems are viewed here as spatially and temporally periodic structures living in an extended Hilbert space, giving rise to spatio-temporal Bloch waves whose dispersion relations can be manipulated at will by exploiting ac-Stark shifts and multiphoton resonances. The elements required for numerical calcns. are introduced in a tutorial manner, and some example calcns. are discussed in detail, thereby illustrating future prospects of Floquet engineering.**28**Sato, S. A.; McIver, J. W.; Nuske, M.; Tang, P.; Jotzu, G.; Schulte, B.; Hübener, H.; De Giovannini, U.; Mathey, L.; Sentef, M. A.; Cavalleri, A.; Rubio, A. Microscopic Theory for the Light-Induced Anomalous Hall Effect in Graphene.*Phys. Rev. B*2019,*99*(21), 214302, DOI: 10.1103/PhysRevB.99.21430228https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhslWltLvJ&md5=c726c54e327336a7c1c5b474f7b5d2d5Microscopic theory for the light-induced anomalous Hall effect in grapheneSato, S. A.; McIver, J. W.; Nuske, M.; Tang, P.; Jotzu, G.; Schulte, B.; Hubener, H.; De Giovannini, U.; Mathey, L.; Sentef, M. A.; Cavalleri, A.; Rubio, A.Physical Review B (2019), 99 (21), 214302CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)We employ a quantum Liouville equation with relaxation to model the recently obsd anomalous Hall effect in graphene irradiated by an ultrafast pulse of circularly polarized light. In the weak-field regime, we demonstrate that the Hall effect originates from an asym population of photocarriers in the Dirac bands. By contrast, in the strong-field regime, the system is driven into a nonequil. steady state that is well described by topol nontrivial Floquet-Bloch bands. Here, the anomalous Hall current originates from the combination of a population imbalance in these dressed bands together with a smaller anomalous velocity contribution arising from their Berry curvature. This robust and general finding enables the simulation of elec transport from light-induced Floquet-Bloch bands in an exptl relevant parameter regime and creates a pathway to designing ultrafast quantum devices with Floquet-engineered transport properties.**29**McIver, J. W.; Schulte, B.; Stein, F.-U.; Matsuyama, T.; Jotzu, G.; Meier, G.; Cavalleri, A. Light-Induced Anomalous Hall Effect in Graphene.*Nat. Phys.*2020,*16*(1), 38– 41, DOI: 10.1038/s41567-019-0698-y29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXitV2msbzL&md5=57bf09d294b4c31eb11c03aa8a18ecd1Light-induced anomalous Hall effect in grapheneMcIver, J. W.; Schulte, B.; Stein, F.-U.; Matsuyama, T.; Jotzu, G.; Meier, G.; Cavalleri, A.Nature Physics (2020), 16 (1), 38-41CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)Many non-equil. phenomena have been discovered or predicted in optically driven quantum solids1. Examples include light-induced supercond.2,3 and Floquet-engineered topol. phases4-8. These are short-lived effects that should lead to measurable changes in elec. transport, which can be characterized using an ultrafast device architecture based on photoconductive switches9. Here, we report the observation of a light-induced anomalous Hall effect in monolayer graphene driven by a femtosecond pulse of circularly polarized light. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect a Floquet-engineered topol. band structure4,5, similar to the band structure originally proposed by Haldane10. This includes an approx. 60 meV wide conductance plateau centered at the Dirac point, where a gap of equal magnitude is predicted to open. We find that when the Fermi level lies within this plateau the estd. anomalous Hall conductance sats. around 1.8 ± 0.4 e2/h.**30**Schüler, M.; De Giovannini, U.; Hübener, H.; Rubio, A.; Sentef, M. A.; Devereaux, T. P.; Werner, P. How Circular Dichroism in Time- and Angle-Resolved Photoemission Can Be Used to Spectroscopically Detect Transient Topological States in Graphene.*Phys. Rev. X*2020,*10*(4), 41013, DOI: 10.1103/PhysRevX.10.041013There is no corresponding record for this reference.**31**Broers, L.; Mathey, L. Observing Light-Induced Floquet Band Gaps in the Longitudinal Conductivity of Graphene.*Commun. Phys.*2021,*4*(1), 248, DOI: 10.1038/s42005-021-00746-631https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXisFyhs77L&md5=099b2e9634b5457be791a6a3007fe800Observing light-induced Floquet band gaps in the longitudinal conductivity of grapheneBroers, Lukas; Mathey, LudwigCommunications Physics (2021), 4 (1), 248CODEN: CPOHDJ; ISSN:2399-3650. (Nature Research)Floquet engineering presents a versatile method of dynamically controlling material properties. The light-induced Floquet-Bloch bands of graphene feature band gaps, which have not yet been obsd. directly. We propose optical longitudinal cond. as a realistic observable to detect light-induced Floquet band gaps in graphene. These gaps manifest as resonant features in the cond., when resolved with respect to the probing frequency and the driving field strength. The electron distribution follows the light-induced Floquet-Bloch bands, resulting in a natural interpretation as occupations of these bands. Furthermore, we show that there are population inversions of the Floquet-Bloch bands at the band gaps for sufficiently strong driving field strengths. This strongly reduces the cond. at the corresponding frequencies. Therefore our proposal puts forth not only an unambiguous demonstration of light-induced Floquet-Bloch bands, which advances the field of Floquet engineering in solids, but also points out the control of transport properties via light, that derives from the electron distribution on these bands.**32**Aeschlimann, S.; Sato, S. A.; Krause, R.; Chávez-Cervantes, M.; De Giovannini, U.; Hübener, H.; Forti, S.; Coletti, C.; Hanff, K.; Rossnagel, K.; Rubio, A.; Gierz, I. Survival of Floquet–Bloch States in the Presence of Scattering.*Nano Lett.*2021,*21*(12), 5028– 5035, DOI: 10.1021/acs.nanolett.1c0080132https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXht1WnsLfI&md5=11719ccf347a3cb579a5d9baee235838Survival of Floquet-Bloch States in the Presence of ScatteringAeschlimann, Sven; Sato, Shunsuke A.; Krause, Razvan; Chavez-Cervantes, Mariana; De Giovannini, Umberto; Huebener, Hannes; Forti, Stiven; Coletti, Camilla; Hanff, Kerstin; Rossnagel, Kai; Rubio, Angel; Gierz, IsabellaNano Letters (2021), 21 (12), 5028-5035CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)Floquet theory has spawned many exciting possibilities for electronic structure control with light, with enormous potential for future applications. The exptl. demonstration in solids, however, remains largely unrealized. In particular, the influence of scattering on the formation of Floquet-Bloch states remains poorly understood. Here, we combine time- and angle-resolved photoemission spectroscopy with time-dependent d. functional theory and a two-level model with relaxation to investigate the survival of Floquet-Bloch states in the presence of scattering. We find that Floquet-Bloch states will be destroyed if scattering - activated by electronic excitations - prevents the Bloch electrons from following the driving field coherently. The two-level model also shows that Floquet-Bloch states reappear at high field intensities where energy exchange with the driving field dominates over energy dissipation to the bath. Our results clearly indicate the importance of long scattering times combined with strong driving fields for the successful realization of various Floquet phenomena.**33**Broers, L.; Mathey, L. Detecting Light-Induced Floquet Band Gaps of Graphene via TrARPES.*Phys. Rev. Res.*2022,*4*(1), 13057, DOI: 10.1103/PhysRevResearch.4.01305733https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XpsFOrtLg%253D&md5=85a8b3d961ac780a3cd7938b38306686Detecting light-induced Floquet band gaps of graphene via trARPESBroers, Lukas; Mathey, LudwigPhysical Review Research (2022), 4 (1), 013057CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)We propose a realistic regime to detect the light-induced topol. band gap in graphene via time-resolved angle-resolved photoelectron spectroscopy (trARPES), which can be achieved with current technol. The direct observation of Floquet-Bloch bands in graphene is limited by low-mobility, Fourier-broadening, laser-assisted photoemission (LAPE), probe-pulse energy-resoln. bounds, space-charge effects, and more. We characterize a regime of low driving frequency and high amplitude of the circularly polarized light that induces an effective band gap at the Dirac point that exceeds the Floquet zone. This circumvents limitations due to energy resolns. and band broadening. The electron distribution across the Floquet replicas in this limit allows for distinguishing LAPE replicas from Floquet replicas. We derive our results from a dissipative master equation approach that gives access to two-point correlation functions and the electron distribution relevant for trARPES measurements.**34**Broers, L.; Mathey, L. Observing Light-Induced Floquet Band Gaps in the Longitudinal Conductivity of Graphene.*Commun. Phys.*2021,*4*(1), 248, DOI: 10.1038/s42005-021-00746-635https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXisFyhs77L&md5=099b2e9634b5457be791a6a3007fe800Observing light-induced Floquet band gaps in the longitudinal conductivity of grapheneBroers, Lukas; Mathey, LudwigCommunications Physics (2021), 4 (1), 248CODEN: CPOHDJ; ISSN:2399-3650. (Nature Research)**35**Zhou, S.; Bao, C.; Fan, B.; Zhou, H.; Gao, Q.; Zhong, H.; Lin, T.; Liu, H.; Yu, P.; Tang, P.; Meng, S.; Duan, W.; Zhou, S. Pseudospin-Selective Floquet Band Engineering in Black Phosphorus.*Nature*2023,*614*(7946), 75– 80, DOI: 10.1038/s41586-022-05610-336https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXis1Siu78%253D&md5=dfeae9aaf904cc04c9f55b3097c5c15ePseudospin-selective Floquet band engineering in black phosphorusZhou, Shaohua; Bao, Changhua; Fan, Benshu; Zhou, Hui; Gao, Qixuan; Zhong, Haoyuan; Lin, Tianyun; Liu, Hang; Yu, Pu; Tang, Peizhe; Meng, Sheng; Duan, Wenhui; Zhou, ShuyunNature (London, United Kingdom) (2023), 614 (7946), 75-80CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Time-periodic light field has emerged as a control knob for manipulating quantum states in solid-state materials1-3, cold atoms4 and photonic systems5 through hybridization with photon-dressed Floquet states6 in the strong-coupling limit, dubbed Floquet engineering. Such interaction leads to tailored properties of quantum materials7-11, for example, modifications of the topol. properties of Dirac materials12,13 and modulation of the optical response14-16. Despite extensive research interests over the past decade3,8,17-20, there is no exptl. evidence of momentum-resolved Floquet band engineering of semiconductors, which is a crucial step to extend Floquet engineering to a wide range of solid-state materials. Here, on the basis of time and angle-resolved photoemission spectroscopy measurements, we report exptl. signatures of Floquet band engineering in a model semiconductor, black phosphorus. On near-resonance pumping at a photon energy of 340-440 meV, a strong band renormalization is obsd. near the band edges. In particular, light-induced dynamical gap opening is resolved at the resonance points, which emerges simultaneously with the Floquet sidebands. Moreover, the band renormalization shows a strong selection rule favoring pump polarization along the armchair direction, suggesting pseudospin selectivity for the Floquetband engineering as enforced by the lattice symmetry. Our work demonstrates pseudospin-selective Floquet band engineering in black phosphorus and provides important guiding principles for Floquet engineering of semiconductors.**36**Rodriguez-Lopez, P.; Betouras, J. J.; Savel’ev, S. E. Dirac Fermion Time-Floquet Crystal: Manipulating Dirac Points.*Phys. Rev. B*2014,*89*(15), 155132, DOI: 10.1103/PhysRevB.89.15513237https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhtVSns7zK&md5=61aedfd34d447346c994a34051424f32Dirac fermion time-Floquet crystal: manipulating Dirac pointsRodriguez-Lopez, Pablo; Betouras, Joseph J.; Savel'ev, Sergey E.Physical Review B: Condensed Matter and Materials Physics (2014), 89 (15), 155132/1-155132/9CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We demonstrate how to control the spectra and current flow of Dirac electrons in both a graphene sheet and a topol. insulator (TI) by applying either two linearly polarized laser fields with frequencies ω and 2ω or a monochromatic (one-frequency) laser field together with a spatially periodic static potential (graphene/TI superlattice). Using the Floquet theory and the resonance approxn., we show that a Dirac point in the electron spectrum can be split into several Dirac points whose relative location in momentum space can be efficiently manipulated by changing the characteristics of the laser fields. In addn., the laser-field-controlled Dirac fermion band structure-a Dirac fermion time-Floquet crystal-allows the manipulation of the electron currents in graphene and topol. insulators. Furthermore, the generation of dc currents of desirable intensity in a chosen direction occurs when the biharmonic laser field is applied, which can provide a straightforward exptl. test of the predicted phenomena.**37**Wang, Y.; Walter, A.-S.; Jotzu, G.; Viebahn, K. Topological Floquet Engineering Using Two Frequencies in Two Dimensions.*Phys. Rev. A*2023,*107*, 043309, DOI: 10.1103/PhysRevA.107.04330934https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXhtVeku7vM&md5=925a18a07f2ef0f3a092b790e71eb4dbTopological Floquet engineering using two frequencies in two dimensionsWang, Yixiao; Walter, Anne-Sophie; Jotzu, Gregor; Viebahn, KonradPhysical Review A (2023), 107 (4), 043309CODEN: PRAHC3; ISSN:2469-9934. (American Physical Society)Using two-frequency driving in two dimensions opens up new possibilities for Floquet engineering, which range from controlling specific symmetries to tuning the properties of resonant gaps. In this work, we study two-band lattice models subject to two-tone Floquet driving and analyze the resulting effective Floquet band structures both numerically and anal. On the one hand, we extend the methodol. of Sandholzer et al. [Phys.Rev.Res.4, 013056 (2022)2643-156410.1103/PhysRevResearch.4.013056] from one to two dimensions and find competing topol. phases in a simple Bravais lattice when the two resonant drives at 1ω and 2ω interfere. On the other hand, we explore driving-induced symmetry breaking in the hexagonal lattice, in which the breaking of either inversion or time-reversal symmetry can be tuned independently via the Floquet modulation. Possible applications of our work include a simpler generation of topol. bands for ultracold atoms and the realization of nonlinear Hall effects as well as Haldane's parity anomaly in inversion-sym. parent lattices.**38**Gui, G.; Li, J.; Zhong, J. Band Structure Engineering of Graphene by Strain: First-Principles Calculations.*Phys. Rev. B*2008,*78*(7), 75435, DOI: 10.1103/PhysRevB.78.07543538https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXhtVKitLzM&md5=eefa8bc2bb38eca389cb08286edb4357Band structure engineering of graphene by strain: First-principles calculationsGui, Gui; Li, Jin; Zhong, JianxinPhysical Review B: Condensed Matter and Materials Physics (2008), 78 (7), 075435/1-075435/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We have investigated the electronic structure of graphene under different planar strain distributions using the first-principles pseudopotential plane-wave method and the tight-binding approach. We found that graphene with a sym. strain distribution is always a zero band-gap semiconductor and its pseudogap decreases linearly with the strain strength in the elastic regime. However, asym. strain distributions in graphene result in opening of band gaps at the Fermi level. For the graphene with a strain distribution parallel to C-C bonds, its band gap continuously increases to its max. width of 0.486 eV as the strain increases up to 12.2%. For the graphene with a strain distribution perpendicular to C-C bonds, its band gap continuously increases only to its max. width of 0.170 eV as the strain increases up to 7.3%. The anisotropic nature of graphene is also reflected by different Poisson ratios under large strains in different directions. We found that the Poisson ratio approaches to a const. of 0.1732 under small strains but decreases differently under large strains along different directions.**39**Cocco, G.; Cadelano, E.; Colombo, L. Gap Opening in Graphene by Shear Strain.*Phys. Rev. B*2010,*81*(24), 241412, DOI: 10.1103/PhysRevB.81.24141239https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXosVyiurY%253D&md5=a18172c411810ff9d65fdeb6e9a233b2Gap opening in graphene by shear strainCocco, Giulio; Cadelano, Emiliano; Colombo, LucianoPhysical Review B: Condensed Matter and Materials Physics (2010), 81 (24), 241412/1-241412/4CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We exploit the concept of strain-induced band-structure engineering in graphene through the calcn. of its electronic properties under uniaxial, shear, and combined uniaxial-shear deformations. We show that by combining shear deformations to uniaxial strains it is possible modulate the graphene energy-gap value from zero up to 0.9 eV. Interestingly enough, the use of a shear component allows for a gap opening at moderate abs. deformation, safely smaller than the graphene failure strain.**40**Koghee, S.; Lim, L.-K.; Goerbig, M. O.; Smith, C. M. Merging and Alignment of Dirac Points in a Shaken Honeycomb Optical Lattice.*Phys. Rev. A*2012,*85*(2), 23637, DOI: 10.1103/PhysRevA.85.02363740https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XjvFyhtLk%253D&md5=3f42312573e66ce0ab3cc09a4c6005e4Merging and alignment of Dirac points in a shaken honeycomb optical latticeKoghee, Selma; Lim, Lih-King; Goerbig, M. O.; Smith, C. MoraisPhysical Review A: Atomic, Molecular, and Optical Physics (2012), 85 (2-B), 023637/1-023637/11CODEN: PLRAAN; ISSN:1050-2947. (American Physical Society)Inspired by the recent creation of a honeycomb optical lattice and the realization of a Mott-insulating state in a square lattice by shaking, we study here the shaken honeycomb optical lattice. For a periodic shaking of the lattice, Floquet theory may be applied to derive a time-independent Hamiltonian. In this effective description, the hopping parameters are renormalized by a Bessel function, which depends on the shaking direction, amplitude, and frequency. Consequently, the hopping parameters can vanish and even change sign, in an anisotropic manner, thus yielding different band structures. Here, we study the merging and the alignment of Dirac points and dimensional crossovers from the two-dimensional system to one-dimensional chains and zero-dimensional dimers. We also consider next-nearest-neighbor hopping, which breaks the particle-hole symmetry and leads to a metallic phase when it becomes dominant over the nearest-neighbor hopping. Furthermore, we include weak repulsive on-site interactions and find the d. profiles for different values of the hopping parameters and interactions, both in a homogeneous system and in the presence of a trapping potential. Our results may be exptl. obsd. by use of momentum-resolved Raman spectroscopy.**41**Jotzu, G.; Messer, M.; Desbuquois, R.; Lebrat, M.; Uehlinger, T.; Greif, D.; Esslinger, T. Experimental Realization of the Topological Haldane Model with Ultracold Fermions.*Nature*2014,*515*(7526), 237– 240, DOI: 10.1038/nature1391541https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXitVyku77E&md5=84fdb73ca8a11182595106e875745031Experimental realization of the topological Haldane model with ultracold fermionsJotzu, Gregor; Messer, Michael; Desbuquois, Remi; Lebrat, Martin; Uehlinger, Thomas; Greif, Daniel; Esslinger, TilmanNature (London, United Kingdom) (2014), 515 (7526), 237-240CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)The Haldane model on a honeycomb lattice is a paradigmatic example of a Hamiltonian featuring topol. distinct phases of matter. It describes a mechanism through which a quantum Hall effect can appear as an intrinsic property of a band structure, rather than being caused by an external magnetic field. Although phys. implementation has been considered unlikely, the Haldane model has provided the conceptual basis for theor. and exptl. research exploring topol. insulators and superconductors. Here we report the exptl. realization of the Haldane model and the characterization of its topol. band structure, using ultracold fermionic atoms in a periodically modulated optical honeycomb lattice. The Haldane model is based on breaking both time-reversal symmetry and inversion symmetry. To break time-reversal symmetry, we introduce complex next-nearest-neighbor tunnelling terms, which we induce through circular modulation of the lattice position. To break inversion symmetry, we create an energy offset between neighboring sites. Breaking either of these symmetries opens a gap in the band structure, which we probe using momentum-resolved interband transitions. We explore the resulting Berry curvatures, which characterize the topol. of the lowest band, by applying a const. force to the atoms and find orthogonal drifts analogous to a Hall current. The competition between the two broken symmetries gives rise to a transition between topol. distinct regimes. By identifying the vanishing gap at a single Dirac point, we map out this transition line exptl. and quant. compare it to calcns. using Floquet theory without free parameters. We verify that our approach, which allows us to tune the topol. properties dynamically, is suitable even for interacting fermionic systems. Furthermore, we propose a direct extension to realize spin-dependent topol. Hamiltonians.**42**Delplace, P.; Gómez-León, Á.; Platero, G. Merging of Dirac Points and Floquet Topological Transitions in Ac-Driven Graphene.*Phys. Rev. B*2013,*88*(24), 245422, DOI: 10.1103/PhysRevB.88.24542242https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXisVGktLs%253D&md5=711547e6a7e7ecd70c8b6c1682d3c541Merging of Dirac points and Floquet topological transitions in ac-driven grapheneDelplace, Pierre; Gomez-Leon, Alvaro; Platero, GloriaPhysical Review B: Condensed Matter and Materials Physics (2013), 88 (24), 245422/1-245422/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)We investigate the effect of an in-plane ac elec. field coupled to electrons in the honeycomb lattice and show that it can be used to manipulate the Dirac points of the electronic structure. We find that the position of the Dirac points can be controlled by the amplitude and the polarization of the field for high-frequency drivings, providing a new platform to achieve their merging, a topol. transition which has not been obsd. yet in electronic systems. Importantly, for lower frequencies we find that the multiphoton absorptions and emissions processes yield the creation of addnl. pairs of Dirac points. This provides an addnl. method to achieve the merging transition by just tuning the frequency of the driving. Our approach, based on Floquet formalism, is neither restricted to specific choice of amplitude or polarization of the field, nor to a low-energy approxn. for the Hamiltonian.**43**Schaibley, J. R.; Yu, H.; Clark, G.; Rivera, P.; Ross, J. S.; Seyler, K. L.; Yao, W.; Xu, X. Valleytronics in 2D Materials.*Nat. Rev. Mater.*2016,*1*(11), 16055, DOI: 10.1038/natrevmats.2016.5543https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhtVertbw%253D&md5=c8ac26ba3b7f390bb15df8bb643c59cdValleytronics in 2D materialsSchaibley, John R.; Yu, Hongyi; Clark, Genevieve; Rivera, Pasqual; Ross, Jason S.; Seyler, Kyle L.; Yao, Wang; Xu, XiaodongNature Reviews Materials (2016), 1 (11), 16055CODEN: NRMADL; ISSN:2058-8437. (Nature Publishing Group)Semiconductor technol. is currently based on the manipulation of electronic charge; however, electrons have addnl. degrees of freedom, such as spin and valley, that can be used to encode and process information. Over the past several decades, there has been significant progress in manipulating electron spin for semiconductor spintronic devices, motivated by potential spin-based information processing and storage applications. However, exptl. progress towards manipulating the valley degree of freedom for potential valleytronic devices has been limited until very recently. We review the latest advances in valleytronics, which have largely been enabled by the isolation of 2D materials (such as graphene and semiconducting transition metal dichalcogenides) that host an easily accessible electronic valley degree of freedom, allowing for dynamic control.**44**Ye, Z.; Sun, D.; Heinz, T. F. Optical Manipulation of Valley Pseudospin.*Nat. Phys.*2017,*13*(1), 26– 29, DOI: 10.1038/nphys389144https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhsV2rtb%252FO&md5=5b91bd253616b1c3264a1da1d6d4d95fOptical manipulation of valley pseudospinYe, Ziliang; Sun, Dezheng; Heinz, Tony F.Nature Physics (2017), 13 (1), 26-29CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)The coherent manipulation of spin and pseudospin underlies existing and emerging quantum technologies, including quantum communication and quantum computation. Valley polarization, assocd. with the occupancy of degenerate, but quantum mech. distinct valleys in momentum space, closely resembles spin polarization and has been proposed as a pseudospin carrier for the future quantum electronics. Valley exciton polarization has been created in the transition metal dichalcogenide monolayers using excitation by circularly polarized light and has been detected both optically and elec. In addn., the existence of coherence in the valley pseudospin has been identified exptl. The manipulation of such valley coherence has, however, remained out of reach. Here we demonstrate all-optical control of the valley coherence by means of the pseudomagnetic field assocd. with the optical Stark effect. Using below-bandgap circularly polarized light, we rotate the valley exciton pseudospin in monolayer WSe2 on the femtosecond timescale. Both the direction and speed of the rotation can be manipulated optically by tuning the dynamic phase of excitons in opposite valleys.**45**Geondzhian, A.; Rubio, A.; Altarelli, M. Valley Selectivity of Soft X-Ray Excitations of Core Electrons in Two-Dimensional Transition Metal Dichalcogenides.*Phys. Rev. B*2022,*106*(11), 115433, DOI: 10.1103/PhysRevB.106.11543345https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XislaqtL7O&md5=0638eb1eeebb895b6b1c7c47c2ae3242Valley selectivity of soft x-ray excitations of core electrons in two-dimensional transition metal dichalcogenidesGeondzhian, Andrey; Rubio, Angel; Altarelli, MassimoPhysical Review B (2022), 106 (11), 115433CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)Optical properties of semiconducting monolayer transition metal dichalcogenides have received a lot of attention in recent years, following the discovery of the valley selective optical population of either K+ or K- valleys at the direct band gap, depending on the polarization of the incoming light. We use group theor. selection rules, as well as ab initio DFT calcns., to investigate whether this valley selectivity effect is also present in x-ray optical transitions from the flat core level of the transition metal atom to the valence and conduction band K valleys. Valley selectivity is predicted for s, p1/2, and p3/2 edges in transitions to and from the valence band edges with circularly polarized radiation. Possible novel applications to the diagnostics of valleytronic properties and intervalley dynamics are investigated and the feasibility of ultrafast pump-probe and Kerr rotations expts. with suitable soft-x-ray free-electron laser sources is discussed.**46**Cheng, J.; Huang, D.; Jiang, T.; Shan, Y.; Li, Y.; Wu, S.; Liu, W.-T. Chiral Selection Rules for Multi-Photon Processes in Two-Dimensional Honeycomb Materials.*Opt. Lett.*2019,*44*(9), 2141– 2144, DOI: 10.1364/OL.44.00214146https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhvFWnt7nO&md5=e11fa1e9e763f6e298de5514933adceaChiral selection rules for multi-photon processes in two-dimensional honeycomb materialsCheng, Jingxin; Huang, Di; Jiang, Tao; Shan, Yuwei; Li, Yingguo; Wu, Shiwei; Liu, Wei-TaoOptics Letters (2019), 44 (9), 2141-2144CODEN: OPLEDP; ISSN:1539-4794. (Optical Society of America)We examine the chirality-dependent optical selection rules in two-dimensional monolayer materials with honeycomb lattices, and, based on symmetry argument, we generalize these rules to multi-photon transitions of arbitrary orders. We also present the phase relations between incident and outgoing photons in such processes. The results agree nicely with our exptl. observations of second- and third-harmonic generation. In particular, we demonstrate that the phase relation of chiral second-harmonic generation can serve as a handy tool for imaging domains and domain boundaries of these monolayers. Our results can benefit future studies on chirality-related optical phenomena and opto-electronic applications of such materials.**47**Huang, S.-M.; Xu, S.-Y.; Belopolski, I.; Lee, C.-C.; Chang, G.; Chang, T.-R.; Wang, B.; Alidoust, N.; Bian, G.; Neupane, M.; Sanchez, D.; Zheng, H.; Jeng, H.-T.; Bansil, A.; Neupert, T.; Lin, H.; Hasan, M. Z. New Type of Weyl Semimetal with Quadratic Double Weyl Fermions.*Proc. Natl. Acad. Sci. U. S. A.*2016,*113*(5), 1180– 1185, DOI: 10.1073/pnas.151458111347https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhtFSht7o%253D&md5=c381afb9ba354df495011c64e4c679a5New type of Weyl semimetal with quadratic double Weyl fermionsHuang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. ZahidProceedings of the National Academy of Sciences of the United States of America (2016), 113 (5), 1180-1185CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The exptl. realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theor. interest to the realm of exptl. studies and device applications, it is of crucial importance to identify other robust candidates that are exptl. feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compd. strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topol. Weyl physics that is not possible in TaAs.**48**Wang, Z.; Sun, Y.; Chen, X.-Q.; Franchini, C.; Xu, G.; Weng, H.; Dai, X.; Fang, Z. Dirac Semimetal and Topological Phase Transitions in A3 Bi (A = Na,K,Rb).*Phys. Rev. B*2012,*85*(19), 195320, DOI: 10.1103/PhysRevB.85.19532048https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhtVWjur3N&md5=fed822f06a1335d52abcf311ea6ec195Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb)Wang, Zhijun; Sun, Yan; Chen, Xing-Qiu; Franchini, Cesare; Xu, Gang; Weng, Hongming; Dai, Xi; Fang, ZhongPhysical Review B: Condensed Matter and Materials Physics (2012), 85 (19), 195320/1-195320/5CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Three-dimensional (3D) Dirac point, where two Weyl points overlap in momentum space, is usually unstable and hard to realize. Here we show, based on the first-principles calcns. and effective model anal., that cryst. A3Bi (A = Na, K, Rb) are Dirac semimetals with bulk 3D Dirac points protected by crystal symmetry. They possess nontrivial Fermi arcs on the surfaces and can be driven into various topol. distinct phases by explicit breaking of symmetries. Giant diamagnetism, linear quantum magnetoresistance, and quantum spin Hall effect will be expected for such compds.**49**Liu, Z. K.; Zhou, B.; Zhang, Y.; Wang, Z. J.; Weng, H. M.; Prabhakaran, D.; Mo, S.-K.; Shen, Z. X.; Fang, Z.; Dai, X.; Hussain, Z.; Chen, Y. L. Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi.*Science*2014,*343*(6173), 864– 867, DOI: 10.1126/science.124508549https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXis1Cgsr8%253D&md5=047f0a9c3918d63013604938e88af330Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3BiLiu, Z. K.; Zhou, B.; Zhang, Y.; Wang, Z. J.; Weng, H. M.; Prabhakaran, D.; Mo, S.-K.; Shen, Z. X.; Fang, Z.; Dai, X.; Hussain, Z.; Chen, Y. L.Science (Washington, DC, United States) (2014), 343 (6173), 864-867CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)Three-dimensional (3D) topol. Dirac semimetals (TDSs) represent an unusual state of quantum matter that can be viewed as "3D graphene. "In contrast to 2D Dirac fermions in graphene or on the surface of 3D topol. insulators, TDSs possess 3D Dirac fermions in the bulk. By investigating the electronic structure of Na3Bi with angle-resolved photoemission spectroscopy, we detected 3D Dirac fermions with linear dispersions along all momentum directions. Furthermore, we demonstrated the robustness of 3D Dirac fermions in Na3Bi against in situ surface doping. Our results establish Na3Bi as a model system for 3D TDSs, which can serve as an ideal platform for the systematic study of quantum phase transitions between rich topol. quantum states.**50**Wang, Y.; Huang, C.; Li, D.; Li, P.; Yu, J.; Zhang, Y.; Xu, J. Tight-Binding Model for Electronic Structure of Hexagonal Boron Phosphide Monolayer and Bilayer.*J. Phys.: Condens. Matter*2019,*31*(28), 285501, DOI: 10.1088/1361-648X/ab152850https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXht12gtrrN&md5=a03350384f2e90a8d22089d9253f845eTight-binding model for electronic structure of hexagonal boron phosphide monolayer and bilayerWang, Ying; Huang, Changbao; Li, Dong; Li, Ping; Yu, Jiangying; Zhang, Yuzhong; Xu, JinrongJournal of Physics: Condensed Matter (2019), 31 (28), 285501CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)Graphene-like hexagonal boron phosphide BP with its moderate band gap and high carrier mobility is considered to be a high potential material for electronics and optoelectronics. In this work, the tight-binding Hamiltonian of hexagonal boron phosphide monolayer and bilayer with two stacking orders are derived in detail. Including up to fifth-nearest-neighbor in plane and next-nearest-neighbor interlayer hoppings, the tight-binding approximated band structure can well reproduce the first-principle calcns. based on the screened Heyd-Scuseria-Ernzerhof hybrid functional level over the entire Brillouin zone. The band gap deviations for monolayer and bilayer between our tight-binding and first-principle results are only 2 meV. The low-energy effective Hamiltonian matrix and band structure are obtained by expanding the full band structure close to the K point. The results show that the isoenergetic lines of max. valence band in the vicinity of K point undergo a pseudo-Lifshitz transition from h-BP monolayer to AB_B-P or AB_B-B bilayer. The mechanism of pseudo-Lifshitz transition can be attributed to two interlayer hoppings rather than one.**51**Castro, A.; Appel, H.; Oliveira, M.; Rozzi, C. A.; Andrade, X.; Lorenzen, F.; Marques, M. A. L.; Gross, E. K. U.; Rubio, A. Octopus: A Tool for the Application of Time-Dependent Density Functional Theory.*Phys. status solidi*2006,*243*(11), 2465– 2488, DOI: 10.1002/pssb.20064206751https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xpsl2msLY%253D&md5=a2fdd76ba81266f00fab34c1ae4e3f53Octopus: a tool for the application of time-dependent density functional theoryCastro, Alberto; Appel, Heiko; Oliveira, Micael; Rozzi, Carlo A.; Andrade, Xavier; Lorenzen, Florian; Marques, M. A. L.; Gross, E. K. U.; Rubio, AngelPhysica Status Solidi B: Basic Solid State Physics (2006), 243 (11), 2465-2488CODEN: PSSBBD; ISSN:0370-1972. (Wiley-VCH Verlag GmbH)A review. We report on the background, current status, and current lines of development of the octopus project. This program materializes the main equations of d.-functional theory in the ground state, and of time-dependent d.-functional theory for dynamical effects. The focus is nowadays placed on the optical (i.e. electronic) linear response properties of nanostructures and biomols., and on the non-linear response to high-intensity fields of finite systems, with particular attention to the coupled ionic-electronic motion (i.e. photo-chem. processes). In addn., we are currently extending the code to the treatment of periodic systems (both to one-dimensional chains, two-dimensional slabs, or fully periodic solids), magnetic properties (ground state properties and excitations), and to the field of quantum-mech. transport or "mol. electronics.". In this communication, we conc. on the development of the methodol.: we review the essential numerical schemes used in the code, and report on the most recent implementations, with special attention to the introduction of adaptive coordinates, to the extension of our real-space technique to tackle periodic systems, and on large-scale parallelization.**52**Andrade, X.; Strubbe, D.; De Giovannini, U.; Larsen, A. H.; Oliveira, M. J. T.; Alberdi-Rodriguez, J.; Varas, A.; Theophilou, I.; Helbig, N.; Verstraete, M. J.; Stella, L.; Nogueira, F.; Aspuru-Guzik, A.; Castro, A.; Marques, M. A. L.; Rubio, A. Real-Space Grids and the Octopus Code as Tools for the Development of New Simulation Approaches for Electronic Systems.*Phys. Chem. Chem. Phys.*2015,*17*(47), 31371– 31396, DOI: 10.1039/C5CP00351B52https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXjtVyktLw%253D&md5=2457aa1e92d75da4f45ac2d66297c5caReal-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systemsAndrade, Xavier; Strubbe, David; De Giovannini, Umberto; Larsen, Ask Hjorth; Oliveira, Micael J. T.; Alberdi-Rodriguez, Joseba; Varas, Alejandro; Theophilou, Iris; Helbig, Nicole; Verstraete, Matthieu J.; Stella, Lorenzo; Nogueira, Fernando; Aspuru-Guzik, Alan; Castro, Alberto; Marques, Miguel A. L.; Rubio, AngelPhysical Chemistry Chemical Physics (2015), 17 (47), 31371-31396CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new phys. models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calc. response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact soln. of the Schr.ovrddot.odinger equation for low-dimensionality systems.**53**Tancogne-Dejean, N.; Oliveira, M. J. T.; Andrade, X.; Appel, H.; Borca, C. H.; Le Breton, G.; Buchholz, F.; Castro, A.; Corni, S.; Correa, A. A.; De Giovannini, U.; Delgado, A.; Eich, F. G.; Flick, J.; Gil, G.; Gomez, A.; Helbig, N.; Hübener, H.; Jestädt, R.; Jornet-Somoza, J.; Larsen, A. H.; Lebedeva, I. V.; Lüders, M.; Marques, M. A. L.; Ohlmann, S. T.; Pipolo, S.; Rampp, M.; Rozzi, C. A.; Strubbe, D. A.; Sato, S. A.; Schäfer, C.; Theophilou, I.; Welden, A.; Rubio, A. Octopus, a Computational Framework for Exploring Light-Driven Phenomena and Quantum Dynamics in Extended and Finite Systems.*J. Chem. Phys.*2020,*152*(12), 124119, DOI: 10.1063/1.514250253https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXmtl2ktbs%253D&md5=2f758c867e416d566cc26a1268ecac68Octopus, a computational framework for exploring light-driven phenomena and quantum dynamics in extended and finite systemsTancogne-Dejean, Nicolas; Oliveira, Micael J. T.; Andrade, Xavier; Appel, Heiko; Borca, Carlos H.; Le Breton, Guillaume; Buchholz, Florian; Castro, Alberto; Corni, Stefano; Correa, Alfredo A.; De Giovannini, Umberto; Delgado, Alain; Eich, Florian G.; Flick, Johannes; Gil, Gabriel; Gomez, Adrian; Helbig, Nicole; Huebener, Hannes; Jestaedt, Rene; Jornet-Somoza, Joaquim; Larsen, Ask H.; Lebedeva, Irina V.; Lueders, Martin; Marques, Miguel A. L.; Ohlmann, Sebastian T.; Pipolo, Silvio; Rampp, Markus; Rozzi, Carlo A.; Strubbe, David A.; Sato, Shunsuke A.; Schaefer, Christian; Theophilou, Iris; Welden, Alicia; Rubio, AngelJournal of Chemical Physics (2020), 152 (12), 124119CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)A review. Over the last few years, extraordinary advances in exptl. and theor. tools have allowed one to monitor and control matter at short time and at. scales with a high degree of precision. An appealing and challenging route toward engineering materials with tailored properties is to find ways to design or selectively manipulate materials, esp. at the quantum level. To this end, having a state-of-the-art ab initio computer simulation tool that enables a reliable and accurate simulation of light-induced changes in the phys. and chem. properties of complex systems is of utmost importance. The 1st principles real-space-based Octopus project was born with that idea in mind, i.e., to provide a unique framework that allows one to describe nonequil. phenomena in mol. complexes, low dimensional materials, and extended systems by accounting for electronic, ionic, and photon quantum mech. effects within a generalized time-dependent d. functional theory. This article aims to present the new features that were implemented over the last few years, including tech. developments related to performance and massive parallelism. The authors also describe the major theor. developments to address ultrafast light-driven processes, such as the new theor. framework of quantum electrodynamics d.-functional formalism for the description of novel light-matter hybrid states. Those advances, and others being released soon as part of the Octopus package, will allow the scientific community to simulate and characterize spatial and time-resolved spectroscopies, ultrafast phenomena in mols. and materials, and new emergent states of matter (quantum electrodynamical-materials). (c) 2020 American Institute of Physics.**54**Zhang, Y.; Tan, Y.-W.; Stormer, H. L.; Kim, P. Experimental Observation of the Quantum Hall Effect and Berry’s Phase in Graphene.*Nature*2005,*438*(7065), 201– 204, DOI: 10.1038/nature0423554https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtF2nsrnJ&md5=9e5c67d812c899a4f0ab95df50cd25b7Experimental observation of the quantum Hall effect and Berry's phase in grapheneZhang, Yuanbo; Tan, Yan-Wen; Stormer, Horst L.; Kim, PhilipNature (London, United Kingdom) (2005), 438 (7065), 201-204CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)When electrons are confined in two-dimensional materials, quantum-mech. enhanced transport phenomena such as the quantum Hall effect can be obsd. Graphene, consisting of an isolated single at. layer of graphite, is an ideal realization of such a two-dimensional system. However, its behavior is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron-hole degeneracy and vanishing carrier mass near the point of charge neutrality. Indeed, a distinctive half-integer quantum Hall effect was predicted theor., as has the existence of a nonzero Berry's phase (a geometric quantum phase) of the electron wavefunction-a consequence of the exceptional topol. of the graphene band structure. Recent advances in micromech. extn. and fabrication techniques for graphite structures now permit such exotic two-dimensional electron systems to be probed exptl. Here the authors report an exptl. study of magneto-transport in a high-mobility single layer of graphene. Adjusting the chem. potential using the elec. field effect, the authors observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these expts. is confirmed by magneto-oscillations. In addn. to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.**55**Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Two-Dimensional Gas of Massless Dirac Fermions in Graphene.*Nature*2005,*438*(7065), 197– 200, DOI: 10.1038/nature0423355https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXhtF2nsrnI&md5=56138229370ff26ece1857a049f00f53Two-dimensional gas of massless Dirac fermions in grapheneNovoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A.Nature (London, United Kingdom) (2005), 438 (7065), 197-200CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmol. and from astrophysics to quantum chem. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known exptl. systems that can be described accurately by the non-relativistic Schroedinger equation. Here we report an exptl. study of a condensed-matter system (graphene, a single at. layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* ≈ 106 m s-1. Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have obsd. the following: first, graphene's cond. never falls below a min. value corresponding to the quantum unit of conductance, even when concns. of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass mc of massless carriers in graphene is described by E = mcc*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top expt.**56**Dutreix, C.; González-Herrero, H.; Brihuega, I.; Katsnelson, M. I.; Chapelier, C.; Renard, V. T. Measuring the Berry Phase of Graphene from Wavefront Dislocations in Friedel Oscillations.*Nature*2019,*574*(7777), 219– 222, DOI: 10.1038/s41586-019-1613-556https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhvVOqurbK&md5=d8871e70558c9ccb6b0357bb6d2ef8c6Measuring the Berry phase of graphene from wavefront dislocations in Friedel oscillationsDutreix, C.; Gonzalez-Herrero, H.; Brihuega, I.; Katsnelson, M. I.; Chapelier, C.; Renard, V. T.Nature (London, United Kingdom) (2019), 574 (7777), 219-222CODEN: NATUAS; ISSN:0028-0836. (Nature Research)Electronic band structures dictate the mech., optical and elec. properties of cryst. solids. Their exptl. detn. is therefore crucial for technol. applications. Although the spectral distribution in energy bands is routinely measured by various techniques1, it is more difficult to access the topol. properties of band structures such as the quantized Berry phase, γ, which is a gauge-invariant geometrical phase accumulated by the wavefunction along an adiabatic cycle2. In graphene, the quantized Berry phase γ = π accumulated by massless relativistic electrons along cyclotron orbits is evidenced by the anomalous quantum Hall effect4,5. It is usually thought that measuring the Berry phase requires the application of external electromagnetic fields to force the charged particles along closed trajectories3. Contradicting this belief, here we demonstrate that the Berry phase of graphene can be measured in the absence of any external magnetic field. We observe edge dislocations in oscillations of the charge d. ρ (Friedel oscillations) that are formed at hydrogen atoms chemisorbed on graphene. Following Nye and Berry6 in describing these topol. defects as phase singularities of complex fields, we show that the no. of addnl. wavefronts in the dislocation is a real-space measure of the Berry phase of graphene. Because the electronic dispersion relation can also be detd. from Friedel oscillations7, our study establishes the charge d. as a powerful observable with which to det. both the dispersion relation and topol. properties of wavefunctions. This could have profound consequences for the study of the band-structure topol. of relativistic and gapped phases in solids.**57**Neufeld, O.; Podolsky, D.; Cohen, O. Floquet Group Theory and Its Application to Selection Rules in Harmonic Generation.*Nat. Commun.*2019,*10*(1), 405, DOI: 10.1038/s41467-018-07935-y57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB3cjltVeisw%253D%253D&md5=ebd7778c81f2f0e754968bb0e4181958Floquet group theory and its application to selection rules in harmonic generationNeufeld Ofer; Cohen Oren; Neufeld Ofer; Podolsky Daniel; Cohen OrenNature communications (2019), 10 (1), 405 ISSN:.Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. Here we formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems, and derive their correspondence to observable selection rules. We apply the theory to harmonic generation, deriving closed-form tables linking DSs of the driving laser and medium (gas, liquid, or solid) in (2+1)D and (3+1)D geometries to the allowed and forbidden harmonic orders and their polarizations. We identify symmetries, including time-reversal-based, reflection-based, and elliptical-based DSs, which lead to selection rules that are not explained by currently known conservation laws. We expect the theory to be useful for ultrafast high harmonic symmetry-breaking spectroscopy, as well as in various other systems such as Floquet topological insulators.**58**Tarruell, L.; Greif, D.; Uehlinger, T.; Jotzu, G.; Esslinger, T. Creating, Moving and Merging Dirac Points with a Fermi Gas in a Tunable Honeycomb Lattice.*Nature*2012,*483*(7389), 302– 305, DOI: 10.1038/nature1087158https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XktVaku7k%253D&md5=aadfa8754e07cc2b1b97d1a3a2ccdef7Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb latticeTarruell, Leticia; Greif, Daniel; Uehlinger, Thomas; Jotzu, Gregor; Esslinger, TilmanNature (London, United Kingdom) (2012), 483 (7389), 302-305CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Dirac points are central to many phenomena in condensed-matter physics, from massless electrons in graphene to the emergence of conducting edge states in topol. insulators. At a Dirac point, two energy bands intersect linearly and the electrons behave as relativistic Dirac fermions. In solids, the rigid structure of the material dets. the mass and velocity of the electrons, as well as their interactions. A different, highly flexible means of studying condensed-matter phenomena is to create model systems using ultracold atoms trapped in the periodic potential of interfering laser beams. Here we report the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a min. bandgap inside the Brillouin zone at the positions of the two Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to change the positions of the Dirac points inside the Brillouin zone. When the anisotropy exceeds a crit. limit, the two Dirac points merge and annihilate each other - a situation that has recently attracted considerable theor. interest but that is extremely challenging to observe in solids. We map out this topol. transition in lattice parameter space and find excellent agreement with ab initio calcns. Our results not only pave the way to model materials in which the topol. of the band structure is crucial, but also provide an avenue to exploring many-body phases resulting from the interplay of complex lattice geometries with interactions.**59**Brinkmann, A. Introduction to Average Hamiltonian Theory. I. Basics.*Concepts Magn. Reson. Part A*2016,*45A*(6), e21414 DOI: 10.1002/cmr.a.21414There is no corresponding record for this reference.**60**Bukov, M.; D’Alessio, L.; Polkovnikov, A. Universal High-Frequency Behavior of Periodically Driven Systems: From Dynamical Stabilization to Floquet Engineering.*Adv. Phys.*2015,*64*(2), 139– 226, DOI: 10.1080/00018732.2015.1055918There is no corresponding record for this reference.**61**Eckardt, A.; Anisimovas, E. High-Frequency Approximation for Periodically Driven Quantum Systems from a Floquet-Space Perspective.*New J. Phys.*2015,*17*(9), 93039, DOI: 10.1088/1367-2630/17/9/09303961https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XmtlGksLk%253D&md5=9770891cc2ea820d238c904c02b59152High-frequency approximation for periodically driven quantum systems from a Floquet-space perspectiveEckardt, Andre; Anisimovas, EgidijusNew Journal of Physics (2015), 17 (Sept.), 093039/1-093039/35CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)Wederive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the extended Floquet Hilbert space by means of degenerate perturbation theory. The final results are equiv. to those obtained within a different approach and can also be related to the Floquet-Magnus expansion.We discuss that the dependence on the driving phase, which plagues the latter, can lead to artifactual symmetry breaking. The high-frequency approach is illustrated using the example of a periodically driven Hubbard model. Moreover, we discuss the nature of the approxn. and its limitations for systems of many interacting particles.**62**Galler, A.; Rubio, A.; Neufeld, O. Mapping Light-Dressed Floquet Bands by Highly Nonlinear Optical Excitations and Valley Polarization.*arXiv (Optics)*, March 27, 2023, arxiv:2303.15055. DOI: 10.48550/arXiv.2303.15055 . (Accessed 07–28–2023).There is no corresponding record for this reference.**63**Neufeld, O.; Mao, W.; Hübener, H.; Tancogne-Dejean, N.; Sato, S. A.; De Giovannini, U.; Rubio, A. Time- and Angle-Resolved Photoelectron Spectroscopy of Strong-Field Light-Dressed Solids: Prevalence of the Adiabatic Band Picture.*Phys. Rev. Res.*2022,*4*(3), 033101, DOI: 10.1103/PhysRevResearch.4.03310163https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38Xis1OnsrzK&md5=6cfc4ba43adf3f3d3e7043ae24a392c7Time- and angle-resolved photoelectron spectroscopy of strong-field light-dressed solids: Prevalence of the adiabatic band pictureNeufeld, Ofer; Mao, Wenwen; Huebener, Hannes; Tancogne-Dejean, Nicolas; Sato, Shunsuke A.; De Giovannini, Umberto; Rubio, AngelPhysical Review Research (2022), 4 (3), 033101CODEN: PRRHAI; ISSN:2643-1564. (American Physical Society)In recent years, strong-field physics in condensed matter was pioneered as a potential approach for controlling material properties through laser dressing, as well as for ultrafast spectroscopy via nonlinear light-matter interactions (e.g., harmonic generation). A potential controversy arising from these advancements is that it is sometimes vague which band picture should be used to interpret strong-field expts.: The field-free bands, the adiabatic (instantaneous) field-dressed bands, Floquet bands, or some other intermediate picture. Here, we try to resolve this issue by performing theor. expts. of time- and angle-resolved photoelectron spectroscopy (Tr-ARPES) for a strong-field laser-pumped solid, which should give access to the actual observable bands of the irradiated material. To our surprise, we find that the adiabatic band picture survives quite well up to high field intensities (∼1012W/cm2) and in a wide frequency range (driving wavelengths of 4000 to 800 nm, with Keldysh parameters ranging up to ∼7). We conclude that, to first order, the adiabatic instantaneous bands should be the std. blueprint for interpreting ultrafast electron dynamics in solids when the field is highly off resonant with characteristic energy scales of the material. We then discuss weaker effects of modifications of the bands beyond this picture that are nonadiabatic, showing that by using bichromatic fields the deviations from the std. picture can be probed with enhanced sensitivity. In this paper, we outline a clear band picture for the physics of strong-field interactions in solids, which should be useful for designing and analyzing strong-field exptl. observables and to formulate simpler semi-empirical models.**64**Hartwigsen, C.; Goedecker, S.; Hutter, J. Relativistic Separable Dual-Space Gaussian Pseudopotentials from H to Rn.*Phys. Rev. B*1998,*58*(7), 3641– 3662, DOI: 10.1103/PhysRevB.58.364164https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1cXltVSktbc%253D&md5=b4cb04039858295984bc02009985d739Relativistic separable dual-space Gaussian pseudopotentials from H to RnHartwigsen, C.; Goedecker, S.; Hutter, J.Physical Review B: Condensed Matter and Materials Physics (1998), 58 (7), 3641-3662CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)We generalize the concept of separable dual-space Gaussian pseudopotentials to the relativistic case. This allows us to construct this type of pseudopotential for the whole Periodic Table, and we present a complete table of pseudopotential parameters for all the elements from H to Rn. The relativistic version of this pseudopotential retains all the advantages of its nonrelativistic version. It is separable by construction, it is optimal for integration on a real-space grid, it is highly accurate, and, due to its analytic form, it can be specified by a very small no. of parameters. The accuracy of the pseudopotential is illustrated by an extensive series of mol. calcns.**65**Scrinzi, A. Fully Differential Two-Electron Photo-Emission Spectra.*New J. Phys.*2012,*14*(8), 085008, DOI: 10.1088/1367-2630/14/8/08500865https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhsF2iu7zP&md5=e85d1dc0947abfcc3a2bd9158a3cfb3ct-SURFF: fully differential two-electron photo-emission spectraScrinzi, ArminNew Journal of Physics (2012), 14 (Aug.), 085008/1-085008/17CODEN: NJOPFM; ISSN:1367-2630. (Institute of Physics Publishing)The time-dependent surface flux (t-SURFF) method is extended to single and double ionization of two-electron systems. Fully differential double emission spectra by strong pulses at extreme UV and IR wavelengths are calcd. using simulation vols. that only accommodate the effective range of the at. binding potential and the quiver radius of free electrons in the external field. For a model system, we found a pronounced dependence of shake-up and non-sequential double ionization on the phase and duration of the laser pulse. The extension to fully three-dimensional calcns. is discussed.**66**De Giovannini, U.; Hübener, H.; Rubio, A. A First-Principles Time-Dependent Density Functional Theory Framework for Spin and Time-Resolved Angular-Resolved Photoelectron Spectroscopy in Periodic Systems.*J. Chem. Theory Comput.*2017,*13*(1), 265– 273, DOI: 10.1021/acs.jctc.6b0089766https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhvFKns77P&md5=d1b1532a9697a3b98356e04595f0f65bA First-Principles Time-Dependent Density Functional Theory Framework for Spin and Time-Resolved Angular-Resolved Photoelectron Spectroscopy in Periodic SystemsDe Giovannini, Umberto; Hubener, Hannes; Rubio, AngelJournal of Chemical Theory and Computation (2017), 13 (1), 265-273CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)The authors present a novel theor. approach to simulate spin-, time-, and angle-resolved photoelectron spectroscopy (ARPES) from 1st principles that is applicable to surfaces, thin films, few layer systems, and low-dimensional nanostructures. The method is based on a general formulation in the framework of time-dependent d. functional theory (TDDFT) to describe the real time-evolution of electrons escaping from a surface under the effect of any external (arbitrary) laser field. By extending the so called t-SURFF method to periodic systems 1 can calc. the final photoelectron spectrum by collecting the flux of the ionization current through an analyzing surface. The resulting approach, named t-SURFFP, allows describing a wide range of irradn. conditions without any assumption on the dynamics of the ionization process allowing for pump-probe simulations on an equal footing. To illustrate the wide scope of applicability of the method, applications to graphene, mono and bilayer WSe2, and hexagonal BN (hBN) under different laser configurations are presented.**67**Neufeld, O.; Cohen, O. Background-Free Measurement of Ring Currents by Symmetry-Breaking High-Harmonic Spectroscopy.*Phys. Rev. Lett.*2019,*123*(10), 103202, DOI: 10.1103/PhysRevLett.123.10320267https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXit1SjtbvL&md5=fa8873e37505b38c76331e9ef993beb6Background-Free Measurement of Ring Currents by Symmetry-Breaking High-Harmonic SpectroscopyNeufeld, Ofer; Cohen, OrenPhysical Review Letters (2019), 123 (10), 103202CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We propose and explore an all-optical technique for ultrafast characterization of electronic ring currents in atoms and mols., based on high-harmonic generation (HHG). In our approach, a medium is irradiated by an intense reflection-sym. laser pulse that leads to HHG, where the polarization of the emitted harmonics is strictly linear if the medium is reflection invariant (e.g., randomly oriented at. or mol. media). The presence of a ring current in the medium breaks this symmetry, causing the emission of elliptically polarized harmonics, where the harmonics' polarization directly maps the ring current, and the signal is background-free. Scanning the delay between the current excitation and the HHG driving pulse provides an attosecond time-resolved signal for the multielectron dynamics in the excited current (including electron-electron interactions). We analyze the responsible phys. mechanism and derive the analytic dependence of the HHG emission on the ring current. The method is numerically demonstrated using quantum models for neon and benzene, as well as through ab initio calcns.**68**Dong, S.; Beaulieu, S.; Selig, M.; Rosenzweig, P.; Christiansen, D.; Pincelli, T.; Dendzik, M.; Ziegler, J. D.; Maklar, J.; Xian, R. P.; Neef, A.; Mohammed, A.; Schulz, A.; Stadler, M.; Jetter, M.; Michler, P.; Taniguchi, T.; Watanabe, K.; Takagi, H.; Starke, U.; Chernikov, A.; Wolf, M.; Nakamura, H.; Knorr, A.; Rettig, L.; Ernstorfer, R. Observation of Ultrafast Interfacial Meitner-Auger Energy Transfer in a van Der Waals Heterostructure.*arXiv (Materials Science)*, August 15, 2021, arxiv:2108.06803, ver. 2. DOI: 10.48550/arXiv.2108.06803 . (Accessed 07–28–2023).There is no corresponding record for this reference.**69**Schönhense, G.; Kutnyakhov, D.; Pressacco, F.; Heber, M.; Wind, N.; Agustsson, S. Y.; Babenkov, S.; Vasilyev, D.; Fedchenko, O.; Chernov, S.; Rettig, L.; Schönhense, B.; Wenthaus, L.; Brenner, G.; Dziarzhytski, S.; Palutke, S.; Mahatha, S. K.; Schirmel, N.; Redlin, H.; Manschwetus, B.; Hartl, I.; Matveyev, Y.; Gloskovskii, A.; Schlueter, C.; Shokeen, V.; Duerr, H.; Allison, T. K.; Beye, M.; Rossnagel, K.; Elmers, H. J.; Medjanik, K. Suppression of the Vacuum Space-Charge Effect in Fs-Photoemission by a Retarding Electrostatic Front Lens.*Rev. Sci. Instrum.*2021,*92*(5), 53703, DOI: 10.1063/5.004656769https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB2c3pslCqtw%253D%253D&md5=798974eb1617c1e4ab4fdfa1a0ade61eSuppression of the vacuum space-charge effect in fs-photoemission by a retarding electrostatic front lensSchonhense G; Agustsson S Y; Babenkov S; Vasilyev D; Fedchenko O; Elmers H J; Medjanik K; Kutnyakhov D; Pressacco F; Heber M; Wenthaus L; Brenner G; Dziarzhytski S; Palutke S; Schirmel N; Redlin H; Manschwetus B; Hartl I; Matveyev Yu; Gloskovskii A; Schlueter C; Beye M; Wind N; Chernov S; Allison T K; Rettig L; Schonhense B; Mahatha S K; Rossnagel K; Shokeen V; Duerr HThe Review of scientific instruments (2021), 92 (5), 053703 ISSN:.The performance of time-resolved photoemission experiments at fs-pulsed photon sources is ultimately limited by the e-e Coulomb interaction, downgrading energy and momentum resolution. Here, we present an approach to effectively suppress space-charge artifacts in momentum microscopes and photoemission microscopes. A retarding electrostatic field generated by a special objective lens repels slow electrons, retaining the k-image of the fast photoelectrons. The suppression of space-charge effects scales with the ratio of the photoelectron velocities of fast and slow electrons. Fields in the range from -20 to -1100 V/mm for Ekin = 100 eV to 4 keV direct secondaries and pump-induced slow electrons back to the sample surface. Ray tracing simulations reveal that this happens within the first 40 to 3 μm above the sample surface for Ekin = 100 eV to 4 keV. An optimized front-lens design allows switching between the conventional accelerating and the new retarding mode. Time-resolved experiments at Ekin = 107 eV using fs extreme ultraviolet probe pulses from the free-electron laser FLASH reveal that the width of the Fermi edge increases by just 30 meV at an incident pump fluence of 22 mJ/cm(2) (retarding field -21 V/mm). For an accelerating field of +2 kV/mm and a pump fluence of only 5 mJ/cm(2), it increases by 0.5 eV (pump wavelength 1030 nm). At the given conditions, the suppression mode permits increasing the slow-electron yield by three to four orders of magnitude. The feasibility of the method at high energies is demonstrated without a pump beam at Ekin = 3830 eV using hard x rays from the storage ring PETRA III. The approach opens up a previously inaccessible regime of pump fluences for photoemission experiments.**70**Schmid, C. P.; Weigl, L.; Grössing, P.; Junk, V.; Gorini, C.; Schlauderer, S.; Ito, S.; Meierhofer, M.; Hofmann, N.; Afanasiev, D.; Crewse, J.; Kokh, K. A.; Tereshchenko, O. E.; Güdde, J.; Evers, F.; Wilhelm, J.; Richter, K.; Höfer, U.; Huber, R. Tunable Non-Integer High-Harmonic Generation in a Topological Insulator.*Nature*2021,*593*(7859), 385– 390, DOI: 10.1038/s41586-021-03466-770https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhtFanurzO&md5=5712be253d0ee22de2d5cf6ed6d85c08Tunable non-integer high-harmonic generation in a topological insulatorSchmid, C. P.; Weigl, L.; Groessing, P.; Junk, V.; Gorini, C.; Schlauderer, S.; Ito, S.; Meierhofer, M.; Hofmann, N.; Afanasiev, D.; Crewse, J.; Kokh, K. A.; Tereshchenko, O. E.; Guedde, J.; Evers, F.; Wilhelm, J.; Richter, K.; Hoefer, U.; Huber, R.Nature (London, United Kingdom) (2021), 593 (7859), 385-390CODEN: NATUAS; ISSN:0028-0836. (Nature Portfolio)Abstr.: When intense lightwaves accelerate electrons through a solid, the emerging high-order harmonic (HH) radiation offers key insights into the material1-11. Sub-optical-cycle dynamics-such as dynamical Bloch oscillations2-5, quasiparticle collisions6,12, valley pseudospin switching13 and heating of Dirac gases10-leave fingerprints in the HH spectra of conventional solids. Topol. non-trivial matter14,15 with invariants that are robust against imperfections has been predicted to support unconventional HH generation16-20. Here we exptl. demonstrate HH generation in a three-dimensional topol. insulator-bismuth telluride. The frequency of the terahertz driving field sharply discriminates between HH generation from the bulk and from the topol. surface, where the unique combination of long scattering times owing to spin-momentum locking17 and the quasi-relativistic dispersion enables unusually efficient HH generation. Intriguingly, all obsd. orders can be continuously shifted to arbitrary non-integer multiples of the driving frequency by varying the carrier-envelope phase of the driving field-in line with quantum theory. The anomalous Berry curvature warranted by the non-trivial topol. enforces meandering ballistic trajectories of the Dirac fermions, causing a hallmark polarization pattern of the HH emission. Our study provides a platform to explore topol. and relativistic quantum physics in strong-field control, and could lead to non-dissipative topol. electronics at IR frequencies.**71**Ghimire, S.; Reis, D. A. High-Harmonic Generation from Solids.*Nat. Phys.*2019,*15*(1), 10– 16, DOI: 10.1038/s41567-018-0315-571https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXit1Crsb%252FF&md5=f303d68070480de031be39c88dd19d5aHigh-harmonic generation from solidsGhimire, Shambhu; Reis, David A.Nature Physics (2019), 15 (1), 10-16CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)A review. High-harStanford PULSE Institutemonic generation in at. gases has been studied for decades, and has formed the basis of attosecond science. Observation of high-order harmonics from bulk crystals was, however, reported much more recently, in 2010. This Review surveys the subsequent efforts aimed at understanding the microscopic mechanism of solid-state harmonics in terms of what it can tell us about the electronic structure of the source materials, how it can be used to probe driven ultrafast dynamics and its prospects for novel, compact short-wavelength light sources. Although most of this work has focused on bulk materials as the source, recent expts. have investigated high-harmonic generation from engineered structures, which could form flexible platforms for attosecond photonics.**72**Yue, L.; Gaarde, M. B. Introduction to Theory of High-Harmonic Generation in Solids: Tutorial.*J. Opt. Soc. Am. B*2022,*39*(2), 535– 555, DOI: 10.1364/JOSAB.44860272https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XmsFKns7c%253D&md5=051a2f3e5697dfddd9d673ef536f59e4Introduction to theory of high-harmonic generation in solids: tutorialYue, Lun; Gaarde, Mette B.Journal of the Optical Society of America B: Optical Physics (2022), 39 (2), 535-555CODEN: JOBPDE; ISSN:1520-8540. (Optica Publishing Group)A review. High-harmonic generation (HHG) in solids has emerged in recent years as a rapidly expanding and interdisciplinary field, attracting attention from both the condensed-matter and the at., mol., and optics communities. It has exciting prospects for the engineering of new light sources and the probing of ultrafast carrier dynamics in solids, and the theor. understanding of this process is of fundamental importance. This tutorial provides a hands-on introduction to the theor. description of the strong-field laser-matter interactions in a condensed-phase system that give rise to HHG. We provide an overview ranging from a detailed description of different approaches to calcg. the microscopic dynamics and how these are intricately connected to the description of the crystal structure, through the conceptual understanding of HHG in solids as supported by the semiclassical recollision model. Finally, we offer a brief description of how to calc. the macroscopic response. We also give a general introduction to the Berry phase, and we discuss important subtleties in the modeling of HHG, such as the choice of structure and laser gauges, and the construction of a smooth and periodic structure gauge for both nondegenerate and degenerate bands. The advantages and drawbacks of different structure and laser-gauge choices are discussed, both in terms of their ability to address specific questions and in terms of their numerical feasibility.**73**Lakhotia, H.; Kim, H. Y.; Zhan, M.; Hu, S.; Meng, S.; Goulielmakis, E. Laser Picoscopy of Valence Electrons in Solids.*Nature*2020,*583*(7814), 55– 59, DOI: 10.1038/s41586-020-2429-z73https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtlShtbvO&md5=ce057e01e0529cbd4eb00703739c5ec6Laser picoscopy of valence electrons in solidsLakhotia, H.; Kim, H. Y.; Zhan, M.; Hu, S.; Meng, S.; Goulielmakis, E.Nature (London, United Kingdom) (2020), 583 (7814), 55-59CODEN: NATUAS; ISSN:0028-0836. (Nature Research)High harmonics were used to reconstruct images of the valence potential and electron d. in cryst. MgF2 and CaF2 with a spatial resoln. of ∼26 pm. The pm-scale imaging of valence electrons could enable direct probing of the chem., electronic, optical and topol. properties of materials.**74**Schiffrin, A.; Paasch-Colberg, T.; Karpowicz, N.; Apalkov, V.; Gerster, D.; Mühlbrandt, S.; Korbman, M.; Reichert, J.; Schultze, M.; Holzner, S.; Barth, J. V.; Kienberger, R.; Ernstorfer, R.; Yakovlev, V. S.; Stockman, M. I.; Krausz, F. Optical-Field-Induced Current in Dielectrics.*Nature*2013,*493*(7430), 70– 74, DOI: 10.1038/nature1156774https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC3s7pvVGhsw%253D%253D&md5=8b0d62e9a60740ae0a3cccc60af75519Optical-field-induced current in dielectricsSchiffrin Agustin; Paasch-Colberg Tim; Karpowicz Nicholas; Apalkov Vadym; Gerster Daniel; Muhlbrandt Sascha; Korbman Michael; Reichert Joachim; Schultze Martin; Holzner Simon; Barth Johannes V; Kienberger Reinhard; Ernstorfer Ralph; Yakovlev Vladislav S; Stockman Mark I; Krausz FerencNature (2013), 493 (7430), 70-4 ISSN:.The time it takes to switch on and off electric current determines the rate at which signals can be processed and sampled in modern information technology. Field-effect transistors are able to control currents at frequencies of the order of or higher than 100 gigahertz, but electric interconnects may hamper progress towards reaching the terahertz (10(12) hertz) range. All-optical injection of currents through interfering photoexcitation pathways or photoconductive switching of terahertz transients has made it possible to control electric current on a subpicosecond timescale in semiconductors. Insulators have been deemed unsuitable for both methods, because of the need for either ultraviolet light or strong fields, which induce slow damage or ultrafast breakdown, respectively. Here we report the feasibility of electric signal manipulation in a dielectric. A few-cycle optical waveform reversibly increases--free from breakdown--the a.c. conductivity of amorphous silicon dioxide (fused silica) by more than 18 orders of magnitude within 1 femtosecond, allowing electric currents to be driven, directed and switched by the instantaneous light field. Our work opens the way to extending electronic signal processing and high-speed metrology into the petahertz (10(15) hertz) domain.**75**Higuchi, T.; Heide, C.; Ullmann, K.; Weber, H. B.; Hommelhoff, P. Light-Field-Driven Currents in Graphene.*Nature*2017,*550*(7675), 224– 228, DOI: 10.1038/nature2390075https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1M%252FivV2ltw%253D%253D&md5=1d61c91141d83548e9b9c571d1673365Light-field-driven currents in grapheneHiguchi Takuya; Heide Christian; Hommelhoff Peter; Ullmann Konrad; Weber Heiko BNature (2017), 550 (7675), 224-228 ISSN:.The ability to steer electrons using the strong electromagnetic field of light has opened up the possibility of controlling electron dynamics on the sub-femtosecond (less than 10(-15) seconds) timescale. In dielectrics and semiconductors, various light-field-driven effects have been explored, including high-harmonic generation, sub-optical-cycle interband population transfer and the non-perturbative change of the transient polarizability. In contrast, much less is known about light-field-driven electron dynamics in narrow-bandgap systems or in conductors, in which screening due to free carriers or light absorption hinders the application of strong optical fields. Graphene is a promising platform with which to achieve light-field-driven control of electrons in a conducting material, because of its broadband and ultrafast optical response, weak screening and high damage threshold. Here we show that a current induced in monolayer graphene by two-cycle laser pulses is sensitive to the electric-field waveform, that is, to the exact shape of the optical carrier field of the pulse, which is controlled by the carrier-envelope phase, with a precision on the attosecond (10(-18) seconds) timescale. Such a current, dependent on the carrier-envelope phase, shows a striking reversal of the direction of the current as a function of the driving field amplitude at about two volts per nanometre. This reversal indicates a transition of light-matter interaction from the weak-field (photon-driven) regime to the strong-field (light-field-driven) regime, where the intraband dynamics influence interband transitions. We show that in this strong-field regime the electron dynamics are governed by sub-optical-cycle Landau-Zener-Stuckelberg interference, composed of coherent repeated Landau-Zener transitions on the femtosecond timescale. Furthermore, the influence of this sub-optical-cycle interference can be controlled with the laser polarization state. These coherent electron dynamics in graphene take place on a hitherto unexplored timescale, faster than electron-electron scattering (tens of femtoseconds) and electron-phonon scattering (hundreds of femtoseconds). We expect these results to have direct ramifications for band-structure tomography and light-field-driven petahertz electronics.**76**Neufeld, O.; Tancogne-Dejean, N.; De Giovannini, U.; Hübener, H.; Rubio, A. Light-Driven Extremely Nonlinear Bulk Photogalvanic Currents.*Phys. Rev. Lett.*2021,*127*(12), 126601, DOI: 10.1103/PhysRevLett.127.12660176https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXitFGnur7J&md5=e03baa734d3a5945c4bf9b32bba82ceaLight-Driven Extremely Nonlinear Bulk Photogalvanic CurrentsNeufeld, Ofer; Tancogne-Dejean, Nicolas; De Giovannini, Umberto; Huebener, Hannes; Rubio, AngelPhysical Review Letters (2021), 127 (12), 126601CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We predict the generation of bulk photocurrents in materials driven by bichromatic fields that are circularly polarized and corotating. The nonlinear photocurrents have a fully controllable directionality and amplitude without requiring carrier-envelope-phase stabilization or few-cycle pulses, and can be generated with photon energies much smaller than the band gap (reducing heating in the photoconversion process). We demonstrate with ab initio calcns. that the photocurrent generation mechanism is universal and arises in gaped materials (Si, diamond, MgO, hBN), in semimetals (graphene), and in two- and three-dimensional systems. Photocurrents are shown to rely on sub-laser-cycle asymmetries in the nonlinear response that build-up coherently from cycle to cycle as the conduction band is populated. Importantly, the photocurrents are always transverse to the major axis of the co-circular lasers regardless of the material's structure and orientation (analogously to a Hall current), which we find originates from a generalized time-reversal symmetry in the driven system. At high laser powers (~ 1013 W/cm2) this symmetry can be spontaneously broken by vast electronic excitations, which is accompanied by an onset of carrier-envelope-phase sensitivity and ultrafast many-body effects. Our results are directly applicable for efficient light-driven control of electronics, and for enhancing sub-band-gap bulk photogalvanic effects.**77**Okyay, M. S.; Kulahlioglu, A. H.; Kochan, D.; Park, N. Resonant Amplification of the Inverse Faraday Effect Magnetization Dynamics of Time Reversal Symmetric Insulators.*Phys. Rev. B*2020,*102*(10), 104304, DOI: 10.1103/PhysRevB.102.10430477https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXitVOitLfI&md5=5c85b158cdfd9cace2442974e4f830d5Resonant amplification of the inverse Faraday effect magnetization dynamics of time reversal symmetric insulatorsOkyay, Mahmut Sait; Kulahlioglu, Adem Halil; Kochan, Denis; Park, NoejungPhysical Review B (2020), 102 (10), 104304CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)All-optical helicity-dependent manipulations of magnetism have attracted broad attention in the context of ultrafast control of magnetic units. Here, we investigate the spin dynamics in time reversal sym. insulators induced by strong circularly polarized light. We perform real-time time-dependent d. functional theory calcns. together with model Hamiltonian analyses for MoS2 and WS2 monolayers, which are exemplary spin-orbit-coupled time reversal sym. insulators. We trace the evolution of dynamical spin states, starting from the Kramers-paired electronic ground state, and find that the induced magnetization exhibits a sharp resonance peak when the applied light frequency is close to half the spin-flipping energy gap. The resonance condition is secondarily affected by the field strength and the pulse width. We suggest that low-energy time reversal broken excitations of insulators can be pursued with a sharp frequency selection as another class of ultrafast phenomena.**78**Neufeld, O.; Tancogne-Dejean, N.; De Giovannini, U.; Hübener, H.; Rubio, A. Attosecond Magnetization Dynamics in Non-Magnetic Materials Driven by Intense Femtosecond Lasers.*npj Comput. Mater.*2023,*9*(1), 39, DOI: 10.1038/s41524-023-00997-778https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXmtVansrc%253D&md5=b55b4ebb58251a654bdb3470c61cd1fcAttosecond magnetization dynamics in non-magnetic materials driven by intense femtosecond lasersNeufeld, Ofer; Tancogne-Dejean, Nicolas; De Giovannini, Umberto; Huebener, Hannes; Rubio, Angelnpj Computational Materials (2023), 9 (1), 39CODEN: NCMPCS; ISSN:2057-3960. (Nature Portfolio)Irradiating solids with ultrashort laser pulses is known to initiate femtosecond timescale magnetization dynamics. However, sub-femtosecond spin dynamics have not yet been obsd. or predicted. Here, we explore ultrafast light-driven spin dynamics in a highly nonresonant strong-field regime. Through state-of-the-art ab initio calcns., we predict that a nonmagnetic material can transiently transform into a magnetic one via dynamical extremely nonlinear spin-flipping processes, which occur on attosecond timescales and are mediated by cascaded multi-photon and spin-orbit interactions. These are nonperturbative nonresonant analogs to the inverse Faraday effect, allowing the magnetization to evolve in very high harmonics of the laser frequency (e.g. here up to the 42nd, oscillating at ∼100 as), and providing control over the speed of magnetization by tuning the laser power and wavelength. Remarkably, we show that even for linearly polarized driving, where one does not intuitively expect the onset of an induced magnetization, the magnetization transiently oscillates as the system interacts with light. This response is enabled by transverse light-driven currents in the solid, and typically occurs on timescales of ∼500 as (with the slower femtosecond response suppressed). An exptl. setup capable of measuring these dynamics through pump-probe transient absorption spectroscopy is simulated. Our results pave the way for attosecond regimes of manipulation of magnetism.**79**Bai, Y.; Fei, F.; Wang, S.; Li, N.; Li, X.; Song, F.; Li, R.; Xu, Z.; Liu, P. High-Harmonic Generation from Topological Surface States.*Nat. Phys.*2021,*17*(3), 311– 315, DOI: 10.1038/s41567-020-01052-879https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXisVWjur7L&md5=0a3f1498ebcaf6a31aa294a76fd0bf42High-harmonic generation from topological surface statesBai, Ya; Fei, Fucong; Wang, Shuo; Li, Na; Li, Xiaolu; Song, Fengqi; Li, Ruxin; Xu, Zhizhan; Liu, PengNature Physics (2021), 17 (3), 311-315CODEN: NPAHAX; ISSN:1745-2473. (Nature Research)Abstr.: Three-dimensional topol. insulators are a phase of matter that hosts unique spin-polarized gapless surface states that are protected by time-reversal symmetry. They exhibit unconventional charge and spin transport properties1,2. Intense laser fields can drive ballistic charge dynamics in Dirac bands3,4 or they can coherently steer spin5 and valley pseudospin6. Similarly, high-harmonic generation (HHG) in solids provides insights into the dynamics of the electrons in topol. insulators7-13. Despite several theor. attempts to identify a topol. signature in the high-harmonic spectrum14-16, a unique fingerprint has yet to be found exptl. Here, we observe HHG that arises from topol. surface states in the intrinsic topol. insulator BiSbTeSe2. The components of the even-order harmonics that are polarized along the pump polarization stem from the spin current in helical surface states, whereas the perpendicular components originate from the out-of-plane spin polarization related to the hexagonal wrapping effect17. The dependence of HHG on surface doping in ambient air also suggests the presence of a Rashba-split two-dimensional electron gas, whose strength can be enhanced by an increase in the intensity of the mid-IR pump.**80**Baykusheva, D.; Chacón, A.; Lu, J.; Bailey, T. P.; Sobota, J. A.; Soifer, H.; Kirchmann, P. S.; Rotundu, C.; Uher, C.; Heinz, T. F.; Reis, D. A.; Ghimire, S. All-Optical Probe of Three-Dimensional Topological Insulators Based on High-Harmonic Generation by Circularly Polarized Laser Fields.*Nano Lett.*2021,*21*(21), 8970– 8978, DOI: 10.1021/acs.nanolett.1c0214580https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXit1yhur3N&md5=95f27545bf48679f75cc1469dd901925All-Optical Probe of Three-Dimensional Topological Insulators Based on High-Harmonic Generation by Circularly Polarized Laser FieldsBaykusheva, Denitsa; Chacon, Alexis; Lu, Jian; Bailey, Trevor P.; Sobota, Jonathan A.; Soifer, Hadas; Kirchmann, Patrick S.; Rotundu, Costel; Uher, Ctirad; Heinz, Tony F.; Reis, David A.; Ghimire, ShambhuNano Letters (2021), 21 (21), 8970-8978CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)We report the observation of an anomalous nonlinear optical response of the prototypical three-dimensional topol. insulator bismuth selenide through the process of high-order harmonic generation. We find that the generation efficiency increases as the laser polarization is changed from linear to elliptical, and it becomes max. for circular polarization. With the aid of a microscopic theory and a detailed anal. of the measured spectra, we reveal that such anomalous enhancement encodes the characteristic topol. of the band structure that originates from the interplay of strong spin-orbit coupling and time-reversal symmetry protection. The implications are in ultrafast probing of topol. phase transitions, light-field driven dissipationless electronics, and quantum computation.**81**Lv, Y.-Y.; Xu, J.; Han, S.; Zhang, C.; Han, Y.; Zhou, J.; Yao, S.-H.; Liu, X.-P.; Lu, M.-H.; Weng, H.; Xie, Z.; Chen, Y. B.; Hu, J.; Chen, Y.-F.; Zhu, S. High-Harmonic Generation in Weyl Semimetal β-WP2 Crystals.*Nat. Commun.*2021,*12*(1), 6437, DOI: 10.1038/s41467-021-26766-y81https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXisVegtrvO&md5=7433a01378085a7b7b1b7ead8da79e2dHigh-harmonic generation in Weyl semimetal β-WP2 crystalsLv, Yang-Yang; Xu, Jinlong; Han, Shuang; Zhang, Chi; Han, Yadong; Zhou, Jian; Yao, Shu-Hua; Liu, Xiao-Ping; Lu, Ming-Hui; Weng, Hongming; Xie, Zhenda; Chen, Y. B.; Hu, Jianbo; Chen, Yan-Feng; Zhu, ShiningNature Communications (2021), 12 (1), 6437CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)As a quantum material, Weyl semimetal has a series of electronic-band-structure features, including Weyl points with left and right chirality and corresponding Berry curvature, which have been obsd. in expts. These band-structure features also lead to some unique nonlinear properties, esp. high-order harmonic generation (HHG) due to the dynamic process of electrons under strong laser excitation, which has remained unexplored previously. Herein, we obtain effective HHG in type-II Weyl semimetal β-WP2 crystals, where both odd and even orders are obsd., with spectra extending into the vacuum UV region (190 nm, 10th order), even under fairly low femtosecond laser intensity. In-depth studies have interpreted that odd-order harmonics come from the Bloch electron oscillation, while even orders are attributed to Bloch oscillations under the "spike-like" Berry curvature at Weyl points. With crystallog. orientation-dependent HHG spectra, we further quant. retrieved the electronic band structure and Berry curvature of β-WP2. These findings may open the door for exploiting metallic/semimetallic states as solid platforms for deep UV radiation and offer an all-optical and pragmatic soln. to characterize the complicated multiband electronic structure and Berry curvature of quantum topol. materials.**82**Heide, C.; Kobayashi, Y.; Baykusheva, D. R.; Jain, D.; Sobota, J. A.; Hashimoto, M.; Kirchmann, P. S.; Oh, S.; Heinz, T. F.; Reis, D. A.; Ghimire, S. Probing Topological Phase Transitions Using High-Harmonic Generation.*Nat. Photonics*2022,*16*(9), 620– 624, DOI: 10.1038/s41566-022-01050-782https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitFKgtLjI&md5=370314fe9ff6e6da30c5f99c9a5847b0Probing topological phase transitions using high-harmonic generationHeide, Christian; Kobayashi, Yuki; Baykusheva, Denitsa R.; Jain, Deepti; Sobota, Jonathan A.; Hashimoto, Makoto; Kirchmann, Patrick S.; Oh, Seongshik; Heinz, Tony F.; Reis, David A.; Ghimire, ShambhuNature Photonics (2022), 16 (9), 620-624CODEN: NPAHBY; ISSN:1749-4885. (Nature Portfolio)Abstr.: The prediction and realization of topol. insulators have sparked great interest in exptl. approaches to the classification of materials1-3. The phase transition between non-trivial and trivial topol. states is important, not only for basic materials science but also for next-generation technol., such as dissipation-free electronics4. It is therefore crucial to develop advanced probes that are suitable for a wide range of samples and environments. Here we demonstrate that circularly polarized laser-field-driven high-harmonic generation is distinctly sensitive to the non-trivial and trivial topol. phases in the prototypical three-dimensional topol. insulator bismuth selenide5. The phase transition is chem. initiated by reducing the spin-orbit interaction strength through the substitution of bismuth with indium atoms6,7. We find strikingly different high-harmonic responses of trivial and non-trivial topol. surface states that manifest themselves as a conversion efficiency and elliptical dichroism that depend both on the driving laser ellipticity and the crystal orientation. The origins of the anomalous high-harmonic response are corroborated by calcns. using the semiconductor optical Bloch equations with pairs of surface and bulk bands. As a purely optical approach, this method offers sensitivity to the electronic structure of the material, including its nonlinear response, and is compatible with a wide range of samples and sample environments.**83**Neufeld, O.; Tancogne-Dejean, N.; Hubener, H.; De Giovannini, U.; Rubio, A. Are There Universal Signatures of Topological Phases in High Harmonic Generation? Probably Not.*Phys. Rev. X*2023,*13*(3), 031011, DOI: 10.1103/PhysRevX.13.031011There is no corresponding record for this reference.

## Supporting Information

## Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.3c02139.

Technical details of the tight-binding model. Technical details about the DFT calculations and fitting procedures of the tight binding hopping amplitudes. Technical details of the TDDFT calculations and ARPES calculations. Technical details of the Floquet calculations in material systems other than graphene. Extended proof that all higher-order even Magnus expansion terms vanish in the Dirac Hamiltonian driven by time-reversal symmetric light. Extended numerical investigation of the pseudogap opening in graphene and its scaling with laser parameters and tight-binding parameters. Additional results of tr-ARPES in graphene for other laser parameters. (PDF)

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