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Physical Insights into Materials and Molecular Properties

Light-Induced Nonthermal Phase Transition to the Topological Crystalline Insulator State in SnSe
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The Journal of Physical Chemistry Letters

Cite this: J. Phys. Chem. Lett. 2023, 14, 41, 9329–9334
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https://doi.org/10.1021/acs.jpclett.3c02450
Published October 11, 2023

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Abstract

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Femtosecond pulses have been used to reveal hidden broken symmetry states and induce transitions to metastable states. However, these states are mostly transient and disappear after laser removal. Photoinduced phase transitions toward crystalline metastable states with a change of topological order are rare and difficult to predict and realize experimentally. Here, by using constrained density functional perturbation theory and accounting for light-induced quantum anharmonicity, we show that ultrafast lasers can permanently transform the topologically trivial orthorhombic structure of SnSe into the topological crystalline insulating rocksalt phase via a first-order nonthermal phase transition. We describe the reaction path and evaluate the critical fluence and possible decay channels after photoexcitation. Our simulations of the photoexcited structural and vibrational properties are in excellent agreement with recent pump–probe data in the intermediate fluence regime below the transition with an error on the curvature of the quantum free energy of the photoexcited state that is smaller than 2%.

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The development of ultrafast laser light with femtosecond (fs) pulses has led to the possibility of inducing a substantial electron–hole population unbalance in semiconductors. (1) After some tens of femtoseconds, this electron–hole plasma is well described by a two-chemical potential model, where both electrons and holes are characterized by a thermal distribution. Thus, the ions feel an out-of-equilibrium electronic population with a substantial occupation of conduction or antibonding states that can lead to structural phase transitions before electron–hole recombination takes place. In this scenario, ultrafast pulses can be used to overcome free-energy barriers and synthesize crystal structures that cannot be reached by conventional thermodynamical paths. This kind of structural transformation is labeled nonthermal, to distinguish it from the much slower ones involved in conventional (thermal) material synthesis. Experimental demonstrations of nonthermal phenomena induced by fs pulses are order–disorder phase transitions, (2) charge density waves, (3) nonthermal melting of solids, (4) transient topological phase transitions (5) and light-induced suppression of incipient ferroelectricity. (6) In all of these cases, ultrafast light induces short-lived transient states. Much less common are light-induced nonthermal permanent structural modifications. In this work, we show that nonthermal processes can be used to permanently stabilize topological crystalline insulating (TCI) phases. (7−11) In this work, we will focus our attention on tin selenide (SnSe), a IV–VI p-type narrow gap semiconductor that has become popular due to its attractive thermoelectric properties (12−15) (zT = 2.6 at T = 923 K). At ambient conditions, tin selenide crystallizes in the orthorhombic Pnma structure, as sketched in Figure 1. At T ≈ 813 K (16) or finite pressure, (17) it undergoes a second-order phase transition to an orthorhombic Cmcm structure. (17−20) In SnSe the topological nontrivial state occurs neither in the Pnma phase, nor in the Cmcm phase, but in a metastable rocksalt structure, which cannot be reached via a thermal transition, but it can only be synthesized in thin films via epitaxial growth techniques on a cubic substrate. (21)

Figure 1

Figure 1. Pictorial representation of the nonthermal pathway connecting the topologically trivial Pnma structure with the TCI Fm3̅m structure. For each phase, sketched crystal structures and band structures are represented. Fs pulses induce a first-order transformation toward a transient phase with Immm symmetry. This phase spontaneously decays into the Fm3̅m structure after electron–hole recombination.

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Here we design a different approach to obtain the topological crystalline phase of SnSe (see Figure 1), namely we consider the effect of ultrafast pulses on the topologically trivial Pnma phase, which is close to a band inversion. (22) By laser pumping with a near-infrared pulse (1.55 eV) and monitoring the time evolution with time-resolved Raman and X-ray diffraction, it was recently shown that structural modifications occur in SnSe, signaled by Ag modes softening and fluence-dependent atomic displacements, (23) interpreted as the precursor of a symmetrization toward a different orthorhombic structure with Immm symmetry. However, no transition to this new crystal phase was detected, and first-principles simulations were unable to reproduce the observed structural distortion.

In this Letter, we investigate the nonthermal structural transformations of the Pnma structure after irradiation with fs pulses by combining constrained density functional perturbation theory (c-DFPT) (24) and stochastic self-consistent harmonic approximation (SSCHA), (25) accounting for quantum anharmonicity in the presence of an electron–hole plasma for the first time. Further technical details are provided in the Supporting Information, which includes refs (26−43). We identify the nonthermal pathway (see Figure 1) and the critical fluence for the structural transition from the ground-state Pnma to the transient Immm phase. Our calculated structural distortions and softenings of the Ag modes along the reaction path are in excellent agreement with experimental data. (23) Most importantly, we show that the transient Immm phase spontaneously decays into the TCI rocksalt Fm3̅m SnSe structure after electron–hole recombination and that the structural transformation is permanent by virtue of the free-energy barrier between the rocksalt and the Pnma phase.

In Figure 2a,b we display the optimized tin Wyckoff x and z coordinates as functions of the photocarrier concentration (PC), ne, expressed as the number of photoexcited electrons per unit cell (u.c.). Our results are compared with time-resolved diffraction data from ref (23) (see also Supporting Information, Section S3) measured in the first 5 ps after illumination. After photoexcitation, both the internal equilibrium positions and lattice parameters can change. However, the time scale for the two phenomena is generally different. (44) To unambiguously disentangle cell deformation and internal displacements at a fixed cell, we perform structural optimization at a fixed cell, Figure 2a, and at a variable cell, Figure 2b, in the presence of an electron–hole plasma (the procedure regarding fluence/PC mapping is reported in the Supporting Information).

Figure 2

Figure 2. Tin Wyckoff positions x and z as functions of the photocarrier concentration for fixed (a) and variable (b) volume crystal structure optimization. The red and blue dots are labeled with the z and x coordinates of tin, respectively. (c) Normalized phonon frequencies at Γ for the three relevant Ag modes versus PC. The red, blue, and orange dots stand for the Ag,1, Ag,2, and Ag,4 modes, respectively. The theoretical harmonic, anharmonic, and experimental values of ω0 are reported in the Supporting Information. The experimental data are from ref (23).

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Our calculation at a fixed cell is in excellent agreement with time-resolved X-ray diffraction data in the first 5 ps, while that at a variable cell substantially deviates. This confirms that in the first picoseconds after irradiation the atoms are displaced at a fixed cell. Previous calculations from ref (23) (see Figure S5) obtained Sn displacements 1 order of magnitude larger than the experimental ones. Conversely, we report an excellent agreement between our c-DFT calculations and experimental data within our framework. (24) The stark disagreement among the calculation of ref (23) and experiments arises because in ref (23) the electron and hole occupations are not self-consistently relaxed. This procedure does not lead to a correctly thermalized quasi-equilibrium Fermi–Dirac distribution. An explanation of the main differences between the approach of ref (23) and the c-DFT approach of refs (45and24) used in this work is reported in Section S3.1 in the Supporting Information.

The discontinuity in the zSn and xSn in Figure 2a,b at nec ≈ 0.6e–/ u.c. signals the occurrence of a first-order phase transition. The phase transition can be easily identified by noting that for ne ≥ 0.6 e–/u.c. the Wyckoff positions of tin correspond to that of the Immm structure, where they are fixed by symmetry. Thus, we predict the phase transition from Pnma to Immm to occur at a value of ne that is approximately a factor of 2 larger than the highest photocarrier concentration measured in ref (23).

Additional validation of our findings arises from the Ag harmonic and anharmonic phonon frequency calculation at a fixed cell. The results are shown in Figure 2c where they are compared with the measured frequencies of oscillation of the Bragg peaks in the first ps after pumping as a function of ne. (23) We plot the value of the harmonic Ag phonon frequencies (full circles) at a given photocarrier concentration (i.e., ω(ne)) divided by the harmonic phonon frequency in the ground state (i.e., ω0 = ω(ne = 0)). The softening of harmonic modes Ag,1 and Ag,4 induced by the photoexcitation is in excellent agreement with the experimental data. Concerning the Ag,2 mode, c-DFPT overestimates the softening induced by the electron–hole plasma within the harmonic approximation. A possible reason for this discrepancy is the presence of strong anharmonic renormalization for the Ag,2 mode. Thus, we calculated the anharmonic phonon frequencies in the absence of photocarriers and for ne = 0.2 e–/u.c. at T = 0 K. Our results are depicted in Figure 2c, where the values of the normalized anharmonic phonon frequencies (ω(ne)/ω0) are represented as filled squares. The anharmonic corrections to the phonon frequencies of the Ag,1 and Ag,4 modes are mild and do not change the overall trend obtained at the harmonic level. On the contrary, the Ag,2 mode is substantially affected by anharmonicity, resulting in an improved agreement with the experimental data. The maximum relative error in the predicted quantum phonon frequency softening is roughly 2%.

The Ag,2 mode plays a crucial role in the Pnma → Immm phase transition. The observed strong anharmonic renormalization of the Ag,2 mode indicates that the Born–Oppenheimer free-energy surface surrounding the minimum energy state corresponding to the Pnma phase becomes progressively more anharmonic along the path of the transition.

The crucial role of quantum anharmonicity becomes even more evident if the electronic structures together with the harmonic and quantum anharmonic dispersions of the Pnma and Immm phase are considered (in Figure 3). The insulating ground state (Figure 3a) displays a finite electronic gap (∼0.52 eV) and dynamically stable harmonic phonons (Figure 3c). The quantum anharmonic corrections on the phonon spectrum are essentially negligible. On the contrary, the light-induced Immm phase in the presence of an electron–hole plasma at ne = 0.6 e–/u.c. has a metallic electronic structure with electron and hole Fermi surfaces located close to the high-symmetry Y and Z points (Figure 3b). These Fermi surfaces are nested (see the Supporting Information, Section S3) and trigger the emergence of a Peierls instability at the harmonic level signaled by imaginary phonons along the Γ–X direction at a wave-vector compatible with the nesting condition (Figure 3d). Structural minimization shows the emergence of a 2 × 1 × 1 one-dimensional chain-like charge density wave with an energy gain of ∼1.5 meV/atom with respect to the undistorted structure (see the Supporting Information). When quantum-anharmonic corrections are included within the SSCHA at ne = 0.6 e–/u.c., we find that the instability is removed and a sharp one-dimensional Kohn-anomaly appears (Figure 3d). Thus, light-induced quantum anharmonicity stabilizes the Immm phase in the transient state at ne = 0.6 e–/u.c.

Figure 3

Figure 3. Ground-state electronic structure of the Pnma phase (a) and of the Immm transient phase at ne = 0.6 e–/u.c. (b). The Fermi level in panel a and the holes and electron Fermi levels in panel b are depicted as dashed lines. Harmonic and anharmonic phonon spectra for the Pnma phase at ne = 0.0 e–/u.c. (c) and for the transient Immm phase at ne = 0.6 e–/u.c. (d). Both plots are at T = 0 K. The inset shows the removal of the dynamic instability by quantum anharmonic effects.

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The critical PC of ne = 0.6 e–/u.c., corresponding to ∼4.8 mJ/cm2, is achievable in ultrafast experiments; similar or larger values have already been achieved in narrow gap semiconductors without inducing significant damage to the sample. (46−48)

Having demonstrated the accuracy of our approach to describe the structural evolution after photoexcitation, we now try to understand more in detail the reaction path and the nature of this transition. In Figure 4, we display the energy along the paths relative to the (a) Pnma → Immm and (b) Pnma → Cmcm transitions, for a few values of ne. The path is parametrized by the reaction coordinate η, where η = 0 stands for the Pnma structure while η = 1 represents either the Immm or Cmcm structure.

Figure 4

Figure 4. Total energy curves along the Pnma → Immm (a) and Pnma → Cmcm (b) reaction paths: η = 0 corresponds to the Pnma phase while η = 1 to the Immm (a) or Cmcm (b) phase. (c) Possible decay channels for the Immm phase: Immm → Pnma, Immm → Cmcm, and Immm → Fm3̅m. We recall that 1 mRy/u.c. corresponds to 40 K while 1 meV/u.c. corresponds to 3 K.

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Considering the ne = 0.0 e–/u.c. case, both the reactions toward Immm and Cmcm present a large kinetic barrier. As the PC is increased, the Pnma → Immm barrier is gradually suppressed and becomes zero for ne ≃ nec. Since the lowest-energy configuration corresponds to the Immm phase for ne > nec, the Pnma → Immm reaction becomes spontaneous. Conversely, the Pnma → Cmcm barrier remains finite for every value of PC.

The question arises if the structural transformation toward the Immm is permanent, i.e. if the Immm phase remains stable at longer times after carrier recombination has taken place. To correctly describe the slow structural dynamics, one must also include volume relaxation effects.

To this aim, we consider variable-volume reaction paths in the absence of photoexcitation starting from the Immm structure, namely, Immm → Pnma, Immm → Cmcm, and Immm → Fm3̅m. The initial Immm structure corresponds to the photoinduced transient phase, while the final structures are obtained through variable volume optimization with zero PC. Along the reactions, both the internal coordinates and the structural parameters vary. The results of our calculations are listed in Figure 4c. Both the transformations Immm → Pnma and Immm → Cmcm present large energy barriers and thus are not spontaneous. Conversely, the Immm → Fm3̅m reaction does not have a barrier and can occur spontaneously. Hence, once the transient Immm phase has been stabilized, electron–hole recombination takes place, and the system decays into the TCI Fm3̅m phase.

In addition, we stress that a large free-energy barrier, amounting to 15 mRy/u.c., exists between the Fm3̅m and the Pnma (see Figure S6). Hence, the topological rocksalt phase can survive thermal fluctuations corresponding to ∼600 K before decaying into the Pnma phase. This finding demonstrates the occurrence of a nonthermal path stabilizing the SnSe rocksalt structure and provides a nonthermal synthesis mechanism for the rocksalt TCI phase.

We stress the fundamental role played by light-induced symmetrization. The TCI phase of rocksalt-SnSe is protected by a combination of time-reversal and C4 symmetry, the latter being absent in both the Pnma and Immm phases. Crucially, we showed that laser irradiation favors the Pnma → Immm symmetrization, allowing the crystal to access a metastable region of the phase diagram, in close proximity to the Fm3̅m structure, which is successively stabilized after the laser removal, finally restoring the cubic C4 symmetry necessary to protect the topological crystalline order. (7)

In conclusion, we have shown that ultrafast pulses can permanently transform the topologically trivial Pnma phase of SnSe into the TCI rocksalt phase. The mechanism is nonthermal and does not require epitaxial growth on particular substrates. This is one of the rare cases when ultrafast pulses change the topological properties of the material. We identified the transition path and evaluated its critical fluence. A strong validation for the accuracy and predictivity of our theoretical framework is the excellent agreement of our quantum anharmonic calculations in the photoexcited regime with recent pump–probe X-ray free electron-laser measurements in the low fluence regime below the transition.

Finally, we point out that our findings demonstrate that light can be used to reshape the free-energy landscape, allowing access to otherwise unreachable regions of the phase diagram. This general result is relevant for the exploration of new phases in a broad class of materials, including monochalcogenides, (49) which are highly relevant for energy applications, insulating/semiconducting 2D materials with strong spin–orbit coupling, and, in general, all semiconducting materials in the proximity of structural instability.

Data Availability

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The data underlying this study are openly available in Zenodo at https://doi.org/10.5281/zenodo.8413390.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.3c02450.

  • Description of the computational methods, crystal structures, and comparison of the two different cDFT approaches (PDF)

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Author Information

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Acknowledgments

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Funded by the European Union (ERC, DELIGHT, 101052708). Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them. We acknowledge the CINECA award under the ISCRA initiative for the availability of high-performance computing resources and support. We acknowledge PRACE for awarding us access to Joliot-Curie at GENCI@CEA, France (project file number 2021240020).

References

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    Topological crystalline insulators are new states of matter in which the topological nature of electronic structures arises from crystal symmetries. Here we predict the first material realization of topological crystalline insulator in the semiconductor SnTe by identifying its non-zero topological index. We predict that as a manifestation of this non-trivial topology, SnTe has metallic surface states with an even number of Dirac cones on high-symmetry crystal surfaces such as {001}, {110} and {111}. These surface states form a new type of high-mobility chiral electron gas, which is robust against disorder and topologically protected by reflection symmetry of the crystal with respect to {110} mirror plane. Breaking this mirror symmetry via elastic strain engineering or applying an in-plane magnetic field can open up a continuously tunable band gap on the surface, which may lead to wide-ranging applications in thermoelectrics, infra-red detection and tunable electronics. Closely related semiconductors PbTe and PbSe also become topological crystalline insulators after band inversion by pressure, strain and alloying.
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    Sun, Y.; Zhong, Z.; Shirakawa, T.; Franchini, C.; Li, D.; Li, Y.; Yunoki, S.; Chen, X.-Q. Rocksalt SnS and SnSe: Native topological crystalline insulators. Phys. Rev. B 2013, 88, 235122,  DOI: 10.1103/PhysRevB.88.235122
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    Rocksalt SnS and SnSe: native topological crystalline insulators
    Sun, Yan; Zhong, Zhicheng; Shirakawa, Tomonori; Franchini, Cesare; Li, Dianzhong; Li, Yiyi; Yunoki, Seiji; Chen, Xing-Qiu
    Physical Review B: Condensed Matter and Materials Physics (2013), 88 (23), 235122/1-235122/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    Unlike time-reversal topol. insulators, surface metallic states with Dirac cone dispersion in the recently discovered topol. cryst. insulators (TCIs) are protected by crystal symmetry. To date, TCI behaviors have been obsd. in SnTe and the related alloys Pb1-xSnxSe/Te, which incorporate heavy elements with large spin-orbit coupling (SOC). Here, by combining first-principles and ab initio tight-binding calcns., we report the formation of a TCI in relatively lighter rocksalt SnS and SnSe. This TCI is characterized by an even no. of Dirac cones at the high-symmetry (001), (110), and (111) surfaces, which are protected by the reflection symmetry with respect to the (‾110) mirror plane. We find that both SnS and SnSe have an intrinsically inverted band structure even without the SOC and the SOC is necessary only to open the bulk band gap. The bulk band gap evolution upon vol. expansion reveals a topol. transition from an ambient pressure TCI to a topol. trivial insulator. Our results indicate that the SOC alone is not sufficient to drive the topol. transition.
  10. 10
    Dziawa, P.; Kowalski, B. J.; Dybko, K.; Buczko, R.; Szczerbakow, A.; Szot, M.; Łusakowska, E.; Balasubramanian, T.; Wojek, B. M.; Berntsen, M. H. Topological crystalline insulator states in Pb1-xSnxSe. Nat. Mater. 2012, 11, 1023– 1027,  DOI: 10.1038/nmat3449
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    10
    Topological crystalline insulator states in Pb1-xSnxSe
    Dziawa, P.; Kowalski, B. J.; Dybko, K.; Buczko, R.; Szczerbakow, A.; Szot, M.; Lusakowska, E.; Balasubramanian, T.; Wojek, B. M.; Berntsen, M. H.; Tjernberg, O.; Story, T.
    Nature Materials (2012), 11 (12), 1023-1027CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
    Topol. insulators are a class of quantum materials in which time-reversal symmetry, relativistic effects, and an inverted band structure result in the occurrence of electronic metallic states on the surfaces of insulating bulk crystals. These helical states exhibit a Dirac-like energy dispersion across the bulk bandgap, and they are topol. protected. Recent theor. results have suggested the existence of topol. cryst. insulators (TCIs), a class of topol. insulators in which cryst. symmetry replaces the role of time-reversal symmetry in ensuring topol. protection. We show that the narrow-gap semiconductor Pb1-xSnxSe is a TCI for x = 0.23. Temp.-dependent angle-resolved photoelectron spectroscopy demonstrates that the material undergoes a temp.-driven topol. phase transition from a trivial insulator to a TCI. These exptl. findings add a new class to the family of topol. insulators, and we anticipate that they will lead to a considerable body of further research as well as detailed studies of topol. phase transitions.
  11. 11
    Ma, J.; Yi, C.; Lv, B.; Wang, Z.; Nie, S.; Wang, L.; Kong, L.; Huang, Y.; Richard, P.; Zhang, P. Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb. Science Advances 2017, 3, e1602415  DOI: 10.1126/sciadv.1602415
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    Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb
    Ma, Junzhang; Yi, Changjiang; Lv, Baiqing; Wang, Zhi Jun; Nie, Simin; Wang, Le; Kong, Lingyuan; Huang, Yaobo; Richard, Pierre; Zhang, Peng; Yaji, Koichiro; Kuroda, Kenta; Shin, Shik; Weng, Hongming; Bernevig, Bogdan Andrei; Shi, Youguo; Qian, Tian; Ding, Hong
    Science Advances (2017), 3 (5), e1602415/1-e1602415/6CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
    Topol. insulators (TIs) host novel states of quantum matter characterized by nontrivial conducting boundary states connecting valence and conduction bulk bands. All TIs discovered exptl. so far rely on either time-reversal or mirror crystal symmorphic symmetry to protect massless Dirac-like boundary states. Several materials were recently proposed to be TIs with nonsymmorphic symmetry, where a glide mirror protects exotic surface fermions with hourglass-shaped dispersion. However, an exptl. confirmation of this new fermion is missing. Using angle-resolved photoemission spectroscopy, we provide exptl. evidence of hourglass fermions on the (010) surface of cryst. KHgSb, whereas the (001) surface has no boundary state, in agreement with first-principles calcns. Our study will stimulate further research activities of topol. properties of nonsymmorphic materials.
  12. 12
    Guo, R.; Wang, X.; Kuang, Y.; Huang, B. First-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnS. Phys. Rev. B 2015, 92, 115202,  DOI: 10.1103/PhysRevB.92.115202
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    12
    First-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnS
    Guo, Ruiqiang; Wang, Xinjiang; Kuang, Youdi; Huang, Baoling
    Physical Review B: Condensed Matter and Materials Physics (2015), 92 (11), 115202/1-115202/13CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
    Tin selenide (SnSe) and tin sulfide (SnS) have recently attracted particular interest due to their great potential for large-scale thermoelec. applications. A complete prediction of the thermoelec. performance and the understanding of underlying heat and charge transport details are the key to further improvement of their thermoelec. efficiency. We conduct comprehensive investigations of both thermal and elec. transport properties of SnSe and SnS using first-principles calcns. combined with the Boltzmann transport theory. Due to the distinct layered lattice structure, SnSe and SnS exhibit similarly anisotropic thermal and elec. behaviors. The cross-plane lattice thermal cond. κL is 40-60% lower than the in-plane values. Extremely low κL is found for both materials because of high anharmonicity, while the av. κL of SnS is ∼8% higher than that of SnSe from 300 to 750 K. It is suggested that nanostructuring would be difficult to further decrease κL because of the short mean free paths of dominant phonon modes (1-30 nm at 300 K), while alloying would be efficient in reducing κL considering that the relative κL contribution (∼65%) of optical phonons is remarkably large. On the elec. side, the anisotropic elec. conductivities are mainly due to the different effective masses of holes and electrons along the a, b, and c axes. This leads to the highest optimal ZT values along the b axis and lowest ones along the a axis in both p-type materials. However, the n-type ones exhibit the highest ZTs along the a axis due to the enhancement of power factor when the chem. potential gradually approaches the secondary conduction band valley that causes significant increase in electron mobility and d. of states. Owing to the larger mobility and smaller κL along the given direction, SnSe exhibits larger optimal ZTs compared with SnS in both p- and n-type materials. For both materials, the peak ZTs of n-type materials are much higher than those of p-type ones along the same direction. The predicted highest ZT values at 750 K are 1.0 in SnSe and 0.6 in SnS along the b axis for the p-type doping, while those for the n-type doping reach 2.7 in SnSe and 1.5 in SnS along the a axis, rendering them among the best bulk thermoelec. materials for large-scale applications. Our calcns. show reasonable agreements with the exptl. results and quant. predict the great potential in further enhancing the thermoelec. performance of SnSe and SnS, esp. for the n-type materials.
  13. 13
    Xie, L.; He, D.; He, J. SnSe, the rising star thermoelectric material: A new paradigm in atomic blocks, building intriguing physical properties. Materials Horizons 2021, 8, 1847– 1865,  DOI: 10.1039/D1MH00091H
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    SnSe, the rising star thermoelectric material: a new paradigm in atomic blocks, building intriguing physical properties
    Xie, Lin; He, Dongsheng; He, Jiaqing
    Materials Horizons (2021), 8 (7), 1847-1865CODEN: MHAOBM; ISSN:2051-6355. (Royal Society of Chemistry)
    A review. Thermoelec. (TE) materials, which enable direct energy conversion between waste heat and electricity, have witnessed enormous and exciting developments over last several decades due to innovative breakthroughs both in materials and the synergistic optimization of structures and properties. Among the promising state-of-the-art materials for next-generation thermoelecs., tin selenide (SnSe) has attracted rapidly growing research interest for its high TE performance and the intrinsic layered structure that leads to strong anisotropy. Moreover, complex interactions between lattice, charge, and orbital degrees of freedom in SnSe make up a large phase space for the optimization of its TE properties via the simultaneous tuning of structural and chem. features. Various techniques, esp. advanced electron microscopy (AEM), have been devoted to exploring these crit. multidiscipline correlations between TE properties and microstructures. In this review, we first focus on the intrinsic layered structure as well as the extrinsic structural "imperfectness" of various dimensions in SnSe as studied by AEM. Based on these characterization results, we give a comprehensive discussion on the current understanding of the structure-property relationship. We then point out the challenges and opportunities as provided by modern AEM techniques toward a deeper knowledge of SnSe based on electronic structures and lattice dynamics at the nanometer or even at. scale, for example, the measurements of local charge and elec. field distribution, phonon vibrations, bandgap, valence state, temp., and resultant TE effects.
  14. 14
    Chandra, S.; Dutta, P.; Biswas, K. High-Performance Thermoelectrics Based on Solution-Grown SnSe Nanostructures. ACS Nano 2022, 16, 7– 14,  DOI: 10.1021/acsnano.1c10584
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    14
    High-Performance Thermoelectrics Based on Solution-Grown SnSe Nanostructures
    Chandra, Sushmita; Dutta, Prabir; Biswas, Kanishka
    ACS Nano (2022), 16 (1), 7-14CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
    A review. Two-dimensional layered tin selenide (SnSe) has attracted immense interest in thermoelecs. due to its ultralow lattice thermal cond. and high thermoelec. performance. To date, the majority of thermoelec. studies of SnSe have been based on single crystals. However, because synthesizing SnSe single crystals is an expensive, time-consuming process that requires high temps. and because SnSe single crystals have relatively weaker mech. stability, they are not favorable for scaling up synthesis, commercialization, or practical applications. As a result, research on nanocryst. SnSe that can be produced in large quantities by simple and low-temp. soln.-phase synthesis is needed. In this Perspective, we discuss the progress in thermoelec. properties of SnSe with a particular emphasis on nanocryst. SnSe, which is grown in soln. We first describe the state-of-the-art high-performance single crystal and polycrystals of SnSe and their importance and drawbacks and discuss how nanocryst. SnSe can solve some of these challenges. We illustrate different soln.-phase synthesis procedures to produce various SnSe nanostructures and discuss their thermoelec. properties. We also highlight a unique soln.-phase synthesis technique to prep. CdSe-coated SnSe nanocomposites and its unprecedented thermoelec. figure of merit (ZT) of 2.2 at 786 K, as reported in this issue of ACS Nano. In general, soln. synthesis showed excellent control over nanoscale grain growth, and nanocryst. SnSe shows ultralow thermal cond. due to strong phonon scattering by the nanoscale grain boundaries. Finally, we offer insight into the opportunities and challenges assocd. with nanocryst. SnSe synthesized by the soln. route and its future in thermoelec. energy conversion.
  15. 15
    Zhao, L.-D.; Lo, S.-H.; Zhang, Y.; Sun, H.; Tan, G.; Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G. Ultralow thermal conductivity and high thermoelectric figure of merit in snse crystals. Nature 2014, 508, 373– 377,  DOI: 10.1038/nature13184
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    15
    Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals
    Zhao, Li-Dong; Lo, Shih-Han; Zhang, Yongsheng; Sun, Hui; Tan, Gangjian; Uher, Ctirad; Wolverton, C.; Dravid, Vinayak P.; Kanatzidis, Mercouri G.
    Nature (London, United Kingdom) (2014), 508 (7496), 373-377CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
    The thermoelec. effect enables direct and reversible conversion between thermal and elec. energy, and provides a viable route for power generation from waste heat. The efficiency of thermoelec. materials is dictated by the dimensionless figure of merit, ZT (where Z is the figure of merit and T is abs. temp.), which governs the Carnot efficiency for heat conversion. Enhancements above the generally high threshold value of 2.5 have important implications for com. deployment, esp. for compds. free of Pb and Te. Here we report an unprecedented ZT of 2.6 ± 0.3 at 923 K, realized in SnSe single crystals measured along the b axis of the room-temp. orthorhombic unit cell. This material also shows a high ZT of 2.3 ± 0.3 along the c axis but a significantly reduced ZT of 0.8 ± 0.2 along the a axis. We attribute the remarkably high ZT along the b axis to the intrinsically ultralow lattice thermal cond. in SnSe. The layered structure of SnSe derives from a distorted rock-salt structure, and features anomalously high Grueneisen parameters, which reflect the anharmonic and anisotropic bonding. We attribute the exceptionally low lattice thermal cond. (0.23 ± 0.03 W m-1 K-1 at 973 K) in SnSe to the anharmonicity. These findings highlight alternative strategies to nanostructuring for achieving high thermoelec. performance.
  16. 16
    Chattopadhyay, T.; Pannetier, J.; Von Schnering, H. Neutron diffraction study of the structural phase transition in SnS and SnSe. J. Phys. Chem. Solids 1986, 47, 879– 885,  DOI: 10.1016/0022-3697(86)90059-4
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    16
    Neutron diffraction study on the structural phase transition in tin sulfide (SnS) and tin selenide (SnSe)
    Chattopadhyay, T.; Pannetier, J.; Von Schnering, H. G.
    Journal of Physics and Chemistry of Solids (1986), 47 (9), 879-85CODEN: JPCSAW; ISSN:0022-3697.
    The structural phase transitions in SnS and SnSe were investigated by neutron diffraction at 295-1000 K using a high temp. furnace. Accurate positional and thermal parameters were obtained as a function of temp. both in the α- (GeS-type, B16) and β-phase (TII-type, B33). These investigations indicate that the α →β phase transitions in SnS and SnSe are of 2nd-order displacive type, and consist mainly of the continuous movement of Sn and S/Se atoms almost entirely along the [100] direction, and suggest the soft-mode behavior of a zone-boundary phonon of the β-phase.
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    Loa, I.; Husband, R. J.; Downie, R. A.; Popuri, S. R.; Bos, J.-W. G. Structural changes in thermoelectric SnSe at high pressures. J. Phys.: Condens. Matter 2015, 27, 072202,  DOI: 10.1088/0953-8984/27/7/072202
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    17
    Structural changes in thermoelectric SnSe at high pressures
    Loa, I.; Husband, R. J.; Downie, R. A.; Popuri, S. R.; Bos, J-W. G.
    Journal of Physics: Condensed Matter (2015), 27 (7), 072202CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
    The crystal structure of the thermoelec. material tin selenide was investigated with angle-dispersive synchrotron x-ray powder diffraction under hydrostatic pressure up to 27 GPa. With increasing pressure, a continuous evolution of the crystal structure from the GeS type to the higher-symmetry TlI type was obsd., with a crit. pressure of 10.5(3) GPa. The orthorhombic high-pressure modification, β'-SnSe, is closely related to the pseudo-tetragonal high-temp. modification at ambient pressure. The similarity between the changes of the crystal structure at elevated temps. and at high pressures suggests the possibility that strained thin films of SnSe may provide a route to overcoming the problem of the limited thermal stability of β-SnSe at high temps.
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    Ghosh, A.; Gusmão, M.; Chaudhuri, P.; Michielon de Souza, S.; Mota, C.; Trichês, D.; Frota, H. Electrical properties of SnSe under high-pressure. Computational Condensed Matter 2016, 9, 77– 81,  DOI: 10.1016/j.cocom.2016.11.001
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    Adouby, K.; Perez-Vicente, C.; Jumas, J. C. Structure and temperature transformation of SnSe. Stabilization of a new cubic phase Sn4Bi2Se7. Zeitschrift für Kristallographie - Crystalline Materials 1998, 213, 343– 349,  DOI: 10.1524/zkri.1998.213.6.343
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    Aseginolaza, U.; Bianco, R.; Monacelli, L.; Paulatto, L.; Calandra, M.; Mauri, F.; Bergara, A.; Errea, I. Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe. Phys. Rev. Lett. 2019, 122, 075901,  DOI: 10.1103/PhysRevLett.122.075901
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    20
    Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe
    Aseginolaza, Unai; Bianco, Raffaello; Monacelli, Lorenzo; Paulatto, Lorenzo; Calandra, Matteo; Mauri, Francesco; Bergara, Aitor; Errea, Ion
    Physical Review Letters (2019), 122 (7), 075901CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
    Since 2014 the layered semiconductor SnSe in the high-temp. Cmcm phase is known to be the most efficient intrinsic thermoelec. material. Making use of first-principles calcns. we show that its vibrational and thermal transport properties are detd. by huge nonperturbative anharmonic effects. We show that the transition from the Cmcm phase to the low-symmetry Pnma is a second-order phase transition driven by the collapse of a zone border phonon, whose frequency vanishes at the transition temp. Our calcns. show that the spectral function of the in-plane vibrational modes are strongly anomalous with shoulders and double-peak structures. We calc. the lattice thermal cond. obtaining good agreement with expts. only when nonperturbative anharmonic scattering is included. Our results suggest that the good thermoelec. efficiency of SnSe is strongly affected by the nonperturbative anharmonicity.
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    Mariano, A. N.; Chopra, K. L. Polymorphism in Some IV-VI Compounds Induced by High Pressure and Thin-Film Epitaxial Growth. Appl. Phys. Lett. 1967, 10, 282– 284,  DOI: 10.1063/1.1754812
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    Polymorphism in some IV-VI compounds induced by high pressure and thin-Polymorphism in some IV-VI compounds induced by high pressure and thin-film epitaxial growth
    Mariano, Anthony N.; Chopra, Kasturi L.
    Applied Physics Letters (1967), 10 (10), 282-4CODEN: APPLAB; ISSN:0003-6951.
    X-ray studies have shown that materials such as PbS, PbSe, PbTe, and SnTe, with NaCl (Fm3m) structure at atm. pressure (Type I), transform to an orthorhombic structure (Pnma) similar to that of SnS, SnSe, PbSnS2 (Type II) under pressures varying from 25 to 42 kilobars. On the other hand, films of Type II materials vacuum deposited on freshly cleaved rock salt substrates maintained at elevated temp. exhibit the NaCl structure. This suggests that if a material has polymorphs it may be possible to grow them epitaxially in thin film forms by depositing them under suitable conditions.
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    Hong, J.; Delaire, O. Phase transition and anharmonicity in SnSe. Materials Today Physics 2019, 10, 100093,  DOI: 10.1016/j.mtphys.2019.100093
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    Huang, Y.; Yang, S.; Teitelbaum, S.; De la Peña, G.; Sato, T.; Chollet, M.; Zhu, D.; Niedziela, J. L.; Bansal, D.; May, A. F. Observation of a Novel Lattice Instability in Ultrafast Photoexcited SnSe. Phys. Rev. X 2022, 12, 011029,  DOI: 10.1103/PhysRevX.12.011029
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    23
    Observation of a Novel Lattice Instability in Ultrafast Photoexcited SnSe
    Huang, Yijing; Yang, Shan; Teitelbaum, Samuel; De la Pena, Gilberto; Sato, Takahiro; Chollet, Matthieu; Zhu, Diling; Niedziela, Jennifer L.; Bansal, Dipanshu; May, Andrew F.; Lindenberg, Aaron M.; Delaire, Olivier; Reis, David A.; Trigo, Mariano
    Physical Review X (2022), 12 (1), 011029CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
    There is growing interest in using ultrafast light pulses to drive functional materials into nonequil. states with novel properties. The conventional wisdom is that above-gap photoexcitation behaves similarly to raising the electronic temp. and lacks the desired selectivity in the final state. Here, we report a novel nonthermal lattice instability induced by ultrafast above-gap excitation in SnSe, a representative of the IV-VI class of semiconductors that provides a rich platform for tuning material functionality with ultrafast pulses due to their multiple lattice instabilities. The new lattice instability is accompanied by a drastic softening of the lowest-frequency Ag phonon. This mode has previously been identified as the soft mode in the thermally driven phase transition to a Cmcm structure. However, by a quant. reconstruction of the at. displacements from time-resolved x-ray diffraction for multiple Bragg peaks and excitation densities, we show that ultrafast photoexcitation with near-IR (1.55 eV) light induces a distortion toward a different structure with Immm symmetry. The Immm structure of SnSe is an orthorhombic distortion of the rocksalt structure and does not occur in equil. D. functional theory calcns. reveal that the photoinduced Immm lattice instability arises from electron excitation from the Se 4p- and Sn 5s-derived bands deep below the Fermi level that cannot be excited thermally. The results have implications for optical control of the thermoelec., ferroelec., and topol. properties of the monochalcogenides and related materials. More generally, the results emphasize the need for ultrafast structural probes to reveal distinct at.-scale dynamics that are otherwise too subtle or invisible in conventional spectroscopies.
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    Marini, G.; Calandra, M. Lattice dynamics of photoexcited insulators from constrained density-functional perturbation theory. Phys. Rev. B 2021, 104, 144103,  DOI: 10.1103/PhysRevB.104.144103
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    Lattice dynamics of photoexcited insulators from constrained density-functional perturbation theory
    Marini, Giovanni; Calandra, Matteo
    Physical Review B (2021), 104 (14), 144103CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
    We present a constrained d.-functional perturbation theory scheme for the calcn. of structural and harmonic vibrational properties of insulators in the presence of an excited and thermalized electron-hole plasma. The method is ideal to tame ultrafast light-induced structural transitions in the regime where the photocarriers thermalize faster than the lattice, the electron-hole recombination time is longer than the phonon period, and the photocarrier concn. is large enough to be approximated by an electron-hole plasma. The complete derivation presented here includes total energy, forces and stress tensor, variable cell structural optimization, harmonic vibrational properties, and the electron-phonon interaction. We discuss in detail the case of zone-center optical phonons not conserving the no. of electrons and inducing a Fermi shift in the photoelectron and hole distributions. We validate our implementation by comparing with finite differences in Te and VSe2. By calcg. the evolution of the phonon spectrum of Te, Si, and GaAs as a function of the fluence of the incoming laser light, we demonstrate that even at low fluences, corresponding to approx. 0.05 photocarriers per atom, the phonon spectrum is substantially modified with respect to the ground-state one with new Kohn anomalies appearing and a substantial softening of zone-center optical phonons. Our implementation can be efficiently used to detect reversible transient phases and irreversible structural transitions induced by ultrafast light absorption.
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    Monacelli, L.; Bianco, R.; Cherubini, M.; Calandra, M.; Errea, I.; Mauri, F. The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects. J. Phys.: Condens. Matter 2021, 33, 363001,  DOI: 10.1088/1361-648X/ac066b
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    The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects
    Monacelli, Lorenzo; Bianco, Raffaello; Cherubini, Marco; Calandra, Matteo; Errea, Ion; Mauri, Francesco
    Journal of Physics: Condensed Matter (2021), 33 (36), 363001CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
    The efficient and accurate calcn. of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its at. structure, and phonon spectrum is one of the main challenges of solid state physics, esp. when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approxn. (SSCHA) method. This technique rigorously describes the full thermodn. of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivs. with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles d.-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to det. the phase diagram of any crystal at finite temp. It enables the calcn. of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon spectral functions. We review the theor. framework of the SSCHA and its dynamical extension, making particular emphasis on the phys. inter pretation of the variables present in the theory that can enlighten the comparison with any other anharmonic theory. A modular and flexible Python environment is used for the implementation, which allows for a clean interaction with other packages. We briefly present a toy-model calcn. to illustrate the potential of the code. Several applications of the method in superconducting hydrides, charge-d.-wave materials, and thermoelec. compds. are also reviewed.
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    Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502,  DOI: 10.1088/0953-8984/21/39/395502
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    QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
    Giannozzi Paolo; Baroni Stefano; Bonini Nicola; Calandra Matteo; Car Roberto; Cavazzoni Carlo; Ceresoli Davide; Chiarotti Guido L; Cococcioni Matteo; Dabo Ismaila; Dal Corso Andrea; de Gironcoli Stefano; Fabris Stefano; Fratesi Guido; Gebauer Ralph; Gerstmann Uwe; Gougoussis Christos; Kokalj Anton; Lazzeri Michele; Martin-Samos Layla; Marzari Nicola; Mauri Francesco; Mazzarello Riccardo; Paolini Stefano; Pasquarello Alfredo; Paulatto Lorenzo; Sbraccia Carlo; Scandolo Sandro; Sclauzero Gabriele; Seitsonen Ari P; Smogunov Alexander; Umari Paolo; Wentzcovitch Renata M
    Journal of physics. Condensed matter : an Institute of Physics journal (2009), 21 (39), 395502 ISSN:.
    QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
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    Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Nardelli, M. B.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys.: Condens. Matter 2017, 29, 465901,  DOI: 10.1088/1361-648X/aa8f79
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    Advanced capabilities for materials modelling with QUANTUM ESPRESSO
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Published October 11, 2023

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  • Abstract

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    Figure 1

    Figure 1. Pictorial representation of the nonthermal pathway connecting the topologically trivial Pnma structure with the TCI Fm3̅m structure. For each phase, sketched crystal structures and band structures are represented. Fs pulses induce a first-order transformation toward a transient phase with Immm symmetry. This phase spontaneously decays into the Fm3̅m structure after electron–hole recombination.

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    Figure 2

    Figure 2. Tin Wyckoff positions x and z as functions of the photocarrier concentration for fixed (a) and variable (b) volume crystal structure optimization. The red and blue dots are labeled with the z and x coordinates of tin, respectively. (c) Normalized phonon frequencies at Γ for the three relevant Ag modes versus PC. The red, blue, and orange dots stand for the Ag,1, Ag,2, and Ag,4 modes, respectively. The theoretical harmonic, anharmonic, and experimental values of ω0 are reported in the Supporting Information. The experimental data are from ref (23).

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    Figure 3

    Figure 3. Ground-state electronic structure of the Pnma phase (a) and of the Immm transient phase at ne = 0.6 e–/u.c. (b). The Fermi level in panel a and the holes and electron Fermi levels in panel b are depicted as dashed lines. Harmonic and anharmonic phonon spectra for the Pnma phase at ne = 0.0 e–/u.c. (c) and for the transient Immm phase at ne = 0.6 e–/u.c. (d). Both plots are at T = 0 K. The inset shows the removal of the dynamic instability by quantum anharmonic effects.

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    Figure 4

    Figure 4. Total energy curves along the Pnma → Immm (a) and Pnma → Cmcm (b) reaction paths: η = 0 corresponds to the Pnma phase while η = 1 to the Immm (a) or Cmcm (b) phase. (c) Possible decay channels for the Immm phase: Immm → Pnma, Immm → Cmcm, and Immm → Fm3̅m. We recall that 1 mRy/u.c. corresponds to 40 K while 1 meV/u.c. corresponds to 3 K.

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  • References

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      Physical Review B: Condensed Matter (1995), 51 (20), 14186-98CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
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      Sie, E. J.; Nyby, C. M.; Pemmaraju, C. D.; Park, S. J.; Shen, X.; Yang, J.; Hoffmann, M. C.; Ofori-Okai, B. K.; Li, R.; Reid, A. H. An ultrafast symmetry switch in a Weyl semimetal. Nature 2019, 565, 61– 66,  DOI: 10.1038/s41586-018-0809-4
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      An ultrafast symmetry switch in a Weyl semimetal
      Sie, Edbert J.; Nyby, Clara M.; Pemmaraju, C. D.; Park, Su Ji; Shen, Xiaozhe; Yang, Jie; Hoffmann, Matthias C.; Ofori-Okai, B. K.; Li, Renkai; Reid, Alexander H.; Weathersby, Stephen; Mannebach, Ehren; Finney, Nathan; Rhodes, Daniel; Chenet, Daniel; Antony, Abhinandan; Balicas, Luis; Hone, James; Devereaux, Thomas P.; Heinz, Tony F.; Wang, Xijie; Lindenberg, Aaron M.
      Nature (London, United Kingdom) (2019), 565 (7737), 61-66CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
      Topol. quantum materials exhibit fascinating properties, with important applications for dissipationless electronics and fault-tolerant quantum computers. Manipulating the topol. invariants in these materials would allow the development of topol. switching applications analogous to switching of transistors6. Lattice strain provides the most natural means of tuning these topol. invariants because it directly modifies the electron-ion interactions and potentially alters the underlying cryst. symmetry on which the topol. properties depend. However, conventional means of applying strain through heteroepitaxial lattice mismatch10 and dislocations11 are not extendable to controllable time-varying protocols, which are required in transistors. Integration into a functional device requires the ability to go beyond the robust, topol. protected properties of materials and to manipulate the topol. at high speeds. Here we use crystallog. measurements by relativistic electron diffraction to demonstrate that terahertz light pulses can be used to induce terahertz-frequency interlayer shear strain with large strain amplitude in the Weyl semimetal WTe2, leading to a topol. distinct metastable phase. Sep. nonlinear optical measurements indicate that this transition is assocd. with a symmetry change to a centrosym., topol. trivial phase. We further show that such shear strain provides an ultrafast, energy-efficient way of inducing robust, well sepd. Weyl points or of annihilating all Weyl points of opposite chirality. This work demonstrates possibilities for ultrafast manipulation of the topol. properties of solids and for the development of a topol. switch operating at terahertz frequencies.
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      Jiang, M. P.; Trigo, M.; Savić, I.; Fahy, S.; Murray, E. D.; Bray, C.; Clark, J.; Henighan, T.; Kozina, M.; Chollet, M. The origin of incipient ferroelectricity in lead Telluride. Nat. Commun. 2016, 7, 12291,  DOI: 10.1038/ncomms12291
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      Jiang, M. P.; Trigo, M.; Savic, I.; Fahy, S.; Murray, E. D.; Bray, C.; Clark, J.; Henighan, T.; Kozina, M.; Chollet, M.; Glownia, J. M.; Hoffmann, M. C.; Zhu, D.; Delaire, O.; May, A. F.; Sales, B. C.; Lindenberg, A. M.; Zalden, P.; Sato, T.; Merlin, R.; Reis, D. A.
      Nature Communications (2016), 7 (), 12291CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
      The interactions between electrons and lattice vibrations are fundamental to materials behavior. In the case of group IV-VI, V and related materials, these interactions are strong, and the materials exist near electronic and structural phase transitions. The prototypical example is PbTe whose incipient ferroelec. behavior has been recently assocd. with large phonon anharmonicity and thermoelectricity. Here we show that it is primarily electron-phonon coupling involving electron states near the band edges that leads to the ferroelec. instability in PbTe. Using a combination of nonequil. lattice dynamics measurements and first principles calcns., we find that photoexcitation reduces the Peierls-like electronic instability and reinforces the paraelec. state. This weakens the long-range forces along the cubic direction tied to resonant bonding and low lattice thermal cond. Our results demonstrate how free-electron-laser-based ultrafast X-ray scattering can be utilized to shed light on the microscopic mechanisms that det. materials properties.
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      Fu, L. Topological Crystalline Insulators. Phys. Rev. Lett. 2011, 106, 106802,  DOI: 10.1103/PhysRevLett.106.106802
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      Topological crystalline insulators
      Fu, Liang
      Physical Review Letters (2011), 106 (10), 106802/1-106802/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      The recent discovery of topol. insulators has revived interest in the band topol. of insulators. In this Letter, the authors extend the topol. classification of band structures to include certain crystal point group symmetry. A class of three-dimensional topol. cryst. insulators which have metallic surface states with quadratic band degeneracy on high symmetry crystal surfaces were found. These topol. cryst. insulators are the counterpart of topol. insulators in materials without spin-orbit coupling. Their band structures were characterized by new topol. invariants. The authors hope this work will enlarge the family of topol. phases in band insulators and stimulate the search for them in real materials.
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      Hsieh, T. H.; Lin, H.; Liu, J.; Duan, W.; Bansil, A.; Fu, L. Topological crystalline insulators in the snte material class. Nat. Commun. 2012, 3, 982,  DOI: 10.1038/ncomms1969
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      Topological crystalline insulators in the SnTe material class
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      Nature communications (2012), 3 (), 982 ISSN:.
      Topological crystalline insulators are new states of matter in which the topological nature of electronic structures arises from crystal symmetries. Here we predict the first material realization of topological crystalline insulator in the semiconductor SnTe by identifying its non-zero topological index. We predict that as a manifestation of this non-trivial topology, SnTe has metallic surface states with an even number of Dirac cones on high-symmetry crystal surfaces such as {001}, {110} and {111}. These surface states form a new type of high-mobility chiral electron gas, which is robust against disorder and topologically protected by reflection symmetry of the crystal with respect to {110} mirror plane. Breaking this mirror symmetry via elastic strain engineering or applying an in-plane magnetic field can open up a continuously tunable band gap on the surface, which may lead to wide-ranging applications in thermoelectrics, infra-red detection and tunable electronics. Closely related semiconductors PbTe and PbSe also become topological crystalline insulators after band inversion by pressure, strain and alloying.
    9. 9
      Sun, Y.; Zhong, Z.; Shirakawa, T.; Franchini, C.; Li, D.; Li, Y.; Yunoki, S.; Chen, X.-Q. Rocksalt SnS and SnSe: Native topological crystalline insulators. Phys. Rev. B 2013, 88, 235122,  DOI: 10.1103/PhysRevB.88.235122
      9
      Rocksalt SnS and SnSe: native topological crystalline insulators
      Sun, Yan; Zhong, Zhicheng; Shirakawa, Tomonori; Franchini, Cesare; Li, Dianzhong; Li, Yiyi; Yunoki, Seiji; Chen, Xing-Qiu
      Physical Review B: Condensed Matter and Materials Physics (2013), 88 (23), 235122/1-235122/6CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Unlike time-reversal topol. insulators, surface metallic states with Dirac cone dispersion in the recently discovered topol. cryst. insulators (TCIs) are protected by crystal symmetry. To date, TCI behaviors have been obsd. in SnTe and the related alloys Pb1-xSnxSe/Te, which incorporate heavy elements with large spin-orbit coupling (SOC). Here, by combining first-principles and ab initio tight-binding calcns., we report the formation of a TCI in relatively lighter rocksalt SnS and SnSe. This TCI is characterized by an even no. of Dirac cones at the high-symmetry (001), (110), and (111) surfaces, which are protected by the reflection symmetry with respect to the (‾110) mirror plane. We find that both SnS and SnSe have an intrinsically inverted band structure even without the SOC and the SOC is necessary only to open the bulk band gap. The bulk band gap evolution upon vol. expansion reveals a topol. transition from an ambient pressure TCI to a topol. trivial insulator. Our results indicate that the SOC alone is not sufficient to drive the topol. transition.
    10. 10
      Dziawa, P.; Kowalski, B. J.; Dybko, K.; Buczko, R.; Szczerbakow, A.; Szot, M.; Łusakowska, E.; Balasubramanian, T.; Wojek, B. M.; Berntsen, M. H. Topological crystalline insulator states in Pb1-xSnxSe. Nat. Mater. 2012, 11, 1023– 1027,  DOI: 10.1038/nmat3449
      10
      Topological crystalline insulator states in Pb1-xSnxSe
      Dziawa, P.; Kowalski, B. J.; Dybko, K.; Buczko, R.; Szczerbakow, A.; Szot, M.; Lusakowska, E.; Balasubramanian, T.; Wojek, B. M.; Berntsen, M. H.; Tjernberg, O.; Story, T.
      Nature Materials (2012), 11 (12), 1023-1027CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      Topol. insulators are a class of quantum materials in which time-reversal symmetry, relativistic effects, and an inverted band structure result in the occurrence of electronic metallic states on the surfaces of insulating bulk crystals. These helical states exhibit a Dirac-like energy dispersion across the bulk bandgap, and they are topol. protected. Recent theor. results have suggested the existence of topol. cryst. insulators (TCIs), a class of topol. insulators in which cryst. symmetry replaces the role of time-reversal symmetry in ensuring topol. protection. We show that the narrow-gap semiconductor Pb1-xSnxSe is a TCI for x = 0.23. Temp.-dependent angle-resolved photoelectron spectroscopy demonstrates that the material undergoes a temp.-driven topol. phase transition from a trivial insulator to a TCI. These exptl. findings add a new class to the family of topol. insulators, and we anticipate that they will lead to a considerable body of further research as well as detailed studies of topol. phase transitions.
    11. 11
      Ma, J.; Yi, C.; Lv, B.; Wang, Z.; Nie, S.; Wang, L.; Kong, L.; Huang, Y.; Richard, P.; Zhang, P. Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb. Science Advances 2017, 3, e1602415  DOI: 10.1126/sciadv.1602415
      11
      Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb
      Ma, Junzhang; Yi, Changjiang; Lv, Baiqing; Wang, Zhi Jun; Nie, Simin; Wang, Le; Kong, Lingyuan; Huang, Yaobo; Richard, Pierre; Zhang, Peng; Yaji, Koichiro; Kuroda, Kenta; Shin, Shik; Weng, Hongming; Bernevig, Bogdan Andrei; Shi, Youguo; Qian, Tian; Ding, Hong
      Science Advances (2017), 3 (5), e1602415/1-e1602415/6CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
      Topol. insulators (TIs) host novel states of quantum matter characterized by nontrivial conducting boundary states connecting valence and conduction bulk bands. All TIs discovered exptl. so far rely on either time-reversal or mirror crystal symmorphic symmetry to protect massless Dirac-like boundary states. Several materials were recently proposed to be TIs with nonsymmorphic symmetry, where a glide mirror protects exotic surface fermions with hourglass-shaped dispersion. However, an exptl. confirmation of this new fermion is missing. Using angle-resolved photoemission spectroscopy, we provide exptl. evidence of hourglass fermions on the (010) surface of cryst. KHgSb, whereas the (001) surface has no boundary state, in agreement with first-principles calcns. Our study will stimulate further research activities of topol. properties of nonsymmorphic materials.
    12. 12
      Guo, R.; Wang, X.; Kuang, Y.; Huang, B. First-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnS. Phys. Rev. B 2015, 92, 115202,  DOI: 10.1103/PhysRevB.92.115202
      12
      First-principles study of anisotropic thermoelectric transport properties of IV-VI semiconductor compounds SnSe and SnS
      Guo, Ruiqiang; Wang, Xinjiang; Kuang, Youdi; Huang, Baoling
      Physical Review B: Condensed Matter and Materials Physics (2015), 92 (11), 115202/1-115202/13CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Tin selenide (SnSe) and tin sulfide (SnS) have recently attracted particular interest due to their great potential for large-scale thermoelec. applications. A complete prediction of the thermoelec. performance and the understanding of underlying heat and charge transport details are the key to further improvement of their thermoelec. efficiency. We conduct comprehensive investigations of both thermal and elec. transport properties of SnSe and SnS using first-principles calcns. combined with the Boltzmann transport theory. Due to the distinct layered lattice structure, SnSe and SnS exhibit similarly anisotropic thermal and elec. behaviors. The cross-plane lattice thermal cond. κL is 40-60% lower than the in-plane values. Extremely low κL is found for both materials because of high anharmonicity, while the av. κL of SnS is ∼8% higher than that of SnSe from 300 to 750 K. It is suggested that nanostructuring would be difficult to further decrease κL because of the short mean free paths of dominant phonon modes (1-30 nm at 300 K), while alloying would be efficient in reducing κL considering that the relative κL contribution (∼65%) of optical phonons is remarkably large. On the elec. side, the anisotropic elec. conductivities are mainly due to the different effective masses of holes and electrons along the a, b, and c axes. This leads to the highest optimal ZT values along the b axis and lowest ones along the a axis in both p-type materials. However, the n-type ones exhibit the highest ZTs along the a axis due to the enhancement of power factor when the chem. potential gradually approaches the secondary conduction band valley that causes significant increase in electron mobility and d. of states. Owing to the larger mobility and smaller κL along the given direction, SnSe exhibits larger optimal ZTs compared with SnS in both p- and n-type materials. For both materials, the peak ZTs of n-type materials are much higher than those of p-type ones along the same direction. The predicted highest ZT values at 750 K are 1.0 in SnSe and 0.6 in SnS along the b axis for the p-type doping, while those for the n-type doping reach 2.7 in SnSe and 1.5 in SnS along the a axis, rendering them among the best bulk thermoelec. materials for large-scale applications. Our calcns. show reasonable agreements with the exptl. results and quant. predict the great potential in further enhancing the thermoelec. performance of SnSe and SnS, esp. for the n-type materials.
    13. 13
      Xie, L.; He, D.; He, J. SnSe, the rising star thermoelectric material: A new paradigm in atomic blocks, building intriguing physical properties. Materials Horizons 2021, 8, 1847– 1865,  DOI: 10.1039/D1MH00091H
      13
      SnSe, the rising star thermoelectric material: a new paradigm in atomic blocks, building intriguing physical properties
      Xie, Lin; He, Dongsheng; He, Jiaqing
      Materials Horizons (2021), 8 (7), 1847-1865CODEN: MHAOBM; ISSN:2051-6355. (Royal Society of Chemistry)
      A review. Thermoelec. (TE) materials, which enable direct energy conversion between waste heat and electricity, have witnessed enormous and exciting developments over last several decades due to innovative breakthroughs both in materials and the synergistic optimization of structures and properties. Among the promising state-of-the-art materials for next-generation thermoelecs., tin selenide (SnSe) has attracted rapidly growing research interest for its high TE performance and the intrinsic layered structure that leads to strong anisotropy. Moreover, complex interactions between lattice, charge, and orbital degrees of freedom in SnSe make up a large phase space for the optimization of its TE properties via the simultaneous tuning of structural and chem. features. Various techniques, esp. advanced electron microscopy (AEM), have been devoted to exploring these crit. multidiscipline correlations between TE properties and microstructures. In this review, we first focus on the intrinsic layered structure as well as the extrinsic structural "imperfectness" of various dimensions in SnSe as studied by AEM. Based on these characterization results, we give a comprehensive discussion on the current understanding of the structure-property relationship. We then point out the challenges and opportunities as provided by modern AEM techniques toward a deeper knowledge of SnSe based on electronic structures and lattice dynamics at the nanometer or even at. scale, for example, the measurements of local charge and elec. field distribution, phonon vibrations, bandgap, valence state, temp., and resultant TE effects.
    14. 14
      Chandra, S.; Dutta, P.; Biswas, K. High-Performance Thermoelectrics Based on Solution-Grown SnSe Nanostructures. ACS Nano 2022, 16, 7– 14,  DOI: 10.1021/acsnano.1c10584
      14
      High-Performance Thermoelectrics Based on Solution-Grown SnSe Nanostructures
      Chandra, Sushmita; Dutta, Prabir; Biswas, Kanishka
      ACS Nano (2022), 16 (1), 7-14CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      A review. Two-dimensional layered tin selenide (SnSe) has attracted immense interest in thermoelecs. due to its ultralow lattice thermal cond. and high thermoelec. performance. To date, the majority of thermoelec. studies of SnSe have been based on single crystals. However, because synthesizing SnSe single crystals is an expensive, time-consuming process that requires high temps. and because SnSe single crystals have relatively weaker mech. stability, they are not favorable for scaling up synthesis, commercialization, or practical applications. As a result, research on nanocryst. SnSe that can be produced in large quantities by simple and low-temp. soln.-phase synthesis is needed. In this Perspective, we discuss the progress in thermoelec. properties of SnSe with a particular emphasis on nanocryst. SnSe, which is grown in soln. We first describe the state-of-the-art high-performance single crystal and polycrystals of SnSe and their importance and drawbacks and discuss how nanocryst. SnSe can solve some of these challenges. We illustrate different soln.-phase synthesis procedures to produce various SnSe nanostructures and discuss their thermoelec. properties. We also highlight a unique soln.-phase synthesis technique to prep. CdSe-coated SnSe nanocomposites and its unprecedented thermoelec. figure of merit (ZT) of 2.2 at 786 K, as reported in this issue of ACS Nano. In general, soln. synthesis showed excellent control over nanoscale grain growth, and nanocryst. SnSe shows ultralow thermal cond. due to strong phonon scattering by the nanoscale grain boundaries. Finally, we offer insight into the opportunities and challenges assocd. with nanocryst. SnSe synthesized by the soln. route and its future in thermoelec. energy conversion.
    15. 15
      Zhao, L.-D.; Lo, S.-H.; Zhang, Y.; Sun, H.; Tan, G.; Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G. Ultralow thermal conductivity and high thermoelectric figure of merit in snse crystals. Nature 2014, 508, 373– 377,  DOI: 10.1038/nature13184
      15
      Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals
      Zhao, Li-Dong; Lo, Shih-Han; Zhang, Yongsheng; Sun, Hui; Tan, Gangjian; Uher, Ctirad; Wolverton, C.; Dravid, Vinayak P.; Kanatzidis, Mercouri G.
      Nature (London, United Kingdom) (2014), 508 (7496), 373-377CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
      The thermoelec. effect enables direct and reversible conversion between thermal and elec. energy, and provides a viable route for power generation from waste heat. The efficiency of thermoelec. materials is dictated by the dimensionless figure of merit, ZT (where Z is the figure of merit and T is abs. temp.), which governs the Carnot efficiency for heat conversion. Enhancements above the generally high threshold value of 2.5 have important implications for com. deployment, esp. for compds. free of Pb and Te. Here we report an unprecedented ZT of 2.6 ± 0.3 at 923 K, realized in SnSe single crystals measured along the b axis of the room-temp. orthorhombic unit cell. This material also shows a high ZT of 2.3 ± 0.3 along the c axis but a significantly reduced ZT of 0.8 ± 0.2 along the a axis. We attribute the remarkably high ZT along the b axis to the intrinsically ultralow lattice thermal cond. in SnSe. The layered structure of SnSe derives from a distorted rock-salt structure, and features anomalously high Grueneisen parameters, which reflect the anharmonic and anisotropic bonding. We attribute the exceptionally low lattice thermal cond. (0.23 ± 0.03 W m-1 K-1 at 973 K) in SnSe to the anharmonicity. These findings highlight alternative strategies to nanostructuring for achieving high thermoelec. performance.
    16. 16
      Chattopadhyay, T.; Pannetier, J.; Von Schnering, H. Neutron diffraction study of the structural phase transition in SnS and SnSe. J. Phys. Chem. Solids 1986, 47, 879– 885,  DOI: 10.1016/0022-3697(86)90059-4
      16
      Neutron diffraction study on the structural phase transition in tin sulfide (SnS) and tin selenide (SnSe)
      Chattopadhyay, T.; Pannetier, J.; Von Schnering, H. G.
      Journal of Physics and Chemistry of Solids (1986), 47 (9), 879-85CODEN: JPCSAW; ISSN:0022-3697.
      The structural phase transitions in SnS and SnSe were investigated by neutron diffraction at 295-1000 K using a high temp. furnace. Accurate positional and thermal parameters were obtained as a function of temp. both in the α- (GeS-type, B16) and β-phase (TII-type, B33). These investigations indicate that the α →β phase transitions in SnS and SnSe are of 2nd-order displacive type, and consist mainly of the continuous movement of Sn and S/Se atoms almost entirely along the [100] direction, and suggest the soft-mode behavior of a zone-boundary phonon of the β-phase.
    17. 17
      Loa, I.; Husband, R. J.; Downie, R. A.; Popuri, S. R.; Bos, J.-W. G. Structural changes in thermoelectric SnSe at high pressures. J. Phys.: Condens. Matter 2015, 27, 072202,  DOI: 10.1088/0953-8984/27/7/072202
      17
      Structural changes in thermoelectric SnSe at high pressures
      Loa, I.; Husband, R. J.; Downie, R. A.; Popuri, S. R.; Bos, J-W. G.
      Journal of Physics: Condensed Matter (2015), 27 (7), 072202CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
      The crystal structure of the thermoelec. material tin selenide was investigated with angle-dispersive synchrotron x-ray powder diffraction under hydrostatic pressure up to 27 GPa. With increasing pressure, a continuous evolution of the crystal structure from the GeS type to the higher-symmetry TlI type was obsd., with a crit. pressure of 10.5(3) GPa. The orthorhombic high-pressure modification, β'-SnSe, is closely related to the pseudo-tetragonal high-temp. modification at ambient pressure. The similarity between the changes of the crystal structure at elevated temps. and at high pressures suggests the possibility that strained thin films of SnSe may provide a route to overcoming the problem of the limited thermal stability of β-SnSe at high temps.
    18. 18
      Ghosh, A.; Gusmão, M.; Chaudhuri, P.; Michielon de Souza, S.; Mota, C.; Trichês, D.; Frota, H. Electrical properties of SnSe under high-pressure. Computational Condensed Matter 2016, 9, 77– 81,  DOI: 10.1016/j.cocom.2016.11.001
      There is no corresponding record for this reference.
    19. 19
      Adouby, K.; Perez-Vicente, C.; Jumas, J. C. Structure and temperature transformation of SnSe. Stabilization of a new cubic phase Sn4Bi2Se7. Zeitschrift für Kristallographie - Crystalline Materials 1998, 213, 343– 349,  DOI: 10.1524/zkri.1998.213.6.343
      There is no corresponding record for this reference.
    20. 20
      Aseginolaza, U.; Bianco, R.; Monacelli, L.; Paulatto, L.; Calandra, M.; Mauri, F.; Bergara, A.; Errea, I. Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe. Phys. Rev. Lett. 2019, 122, 075901,  DOI: 10.1103/PhysRevLett.122.075901
      20
      Phonon Collapse and Second-Order Phase Transition in Thermoelectric SnSe
      Aseginolaza, Unai; Bianco, Raffaello; Monacelli, Lorenzo; Paulatto, Lorenzo; Calandra, Matteo; Mauri, Francesco; Bergara, Aitor; Errea, Ion
      Physical Review Letters (2019), 122 (7), 075901CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
      Since 2014 the layered semiconductor SnSe in the high-temp. Cmcm phase is known to be the most efficient intrinsic thermoelec. material. Making use of first-principles calcns. we show that its vibrational and thermal transport properties are detd. by huge nonperturbative anharmonic effects. We show that the transition from the Cmcm phase to the low-symmetry Pnma is a second-order phase transition driven by the collapse of a zone border phonon, whose frequency vanishes at the transition temp. Our calcns. show that the spectral function of the in-plane vibrational modes are strongly anomalous with shoulders and double-peak structures. We calc. the lattice thermal cond. obtaining good agreement with expts. only when nonperturbative anharmonic scattering is included. Our results suggest that the good thermoelec. efficiency of SnSe is strongly affected by the nonperturbative anharmonicity.
    21. 21
      Mariano, A. N.; Chopra, K. L. Polymorphism in Some IV-VI Compounds Induced by High Pressure and Thin-Film Epitaxial Growth. Appl. Phys. Lett. 1967, 10, 282– 284,  DOI: 10.1063/1.1754812
      21
      Polymorphism in some IV-VI compounds induced by high pressure and thin-Polymorphism in some IV-VI compounds induced by high pressure and thin-film epitaxial growth
      Mariano, Anthony N.; Chopra, Kasturi L.
      Applied Physics Letters (1967), 10 (10), 282-4CODEN: APPLAB; ISSN:0003-6951.
      X-ray studies have shown that materials such as PbS, PbSe, PbTe, and SnTe, with NaCl (Fm3m) structure at atm. pressure (Type I), transform to an orthorhombic structure (Pnma) similar to that of SnS, SnSe, PbSnS2 (Type II) under pressures varying from 25 to 42 kilobars. On the other hand, films of Type II materials vacuum deposited on freshly cleaved rock salt substrates maintained at elevated temp. exhibit the NaCl structure. This suggests that if a material has polymorphs it may be possible to grow them epitaxially in thin film forms by depositing them under suitable conditions.
    22. 22
      Hong, J.; Delaire, O. Phase transition and anharmonicity in SnSe. Materials Today Physics 2019, 10, 100093,  DOI: 10.1016/j.mtphys.2019.100093
      There is no corresponding record for this reference.
    23. 23
      Huang, Y.; Yang, S.; Teitelbaum, S.; De la Peña, G.; Sato, T.; Chollet, M.; Zhu, D.; Niedziela, J. L.; Bansal, D.; May, A. F. Observation of a Novel Lattice Instability in Ultrafast Photoexcited SnSe. Phys. Rev. X 2022, 12, 011029,  DOI: 10.1103/PhysRevX.12.011029
      23
      Observation of a Novel Lattice Instability in Ultrafast Photoexcited SnSe
      Huang, Yijing; Yang, Shan; Teitelbaum, Samuel; De la Pena, Gilberto; Sato, Takahiro; Chollet, Matthieu; Zhu, Diling; Niedziela, Jennifer L.; Bansal, Dipanshu; May, Andrew F.; Lindenberg, Aaron M.; Delaire, Olivier; Reis, David A.; Trigo, Mariano
      Physical Review X (2022), 12 (1), 011029CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
      There is growing interest in using ultrafast light pulses to drive functional materials into nonequil. states with novel properties. The conventional wisdom is that above-gap photoexcitation behaves similarly to raising the electronic temp. and lacks the desired selectivity in the final state. Here, we report a novel nonthermal lattice instability induced by ultrafast above-gap excitation in SnSe, a representative of the IV-VI class of semiconductors that provides a rich platform for tuning material functionality with ultrafast pulses due to their multiple lattice instabilities. The new lattice instability is accompanied by a drastic softening of the lowest-frequency Ag phonon. This mode has previously been identified as the soft mode in the thermally driven phase transition to a Cmcm structure. However, by a quant. reconstruction of the at. displacements from time-resolved x-ray diffraction for multiple Bragg peaks and excitation densities, we show that ultrafast photoexcitation with near-IR (1.55 eV) light induces a distortion toward a different structure with Immm symmetry. The Immm structure of SnSe is an orthorhombic distortion of the rocksalt structure and does not occur in equil. D. functional theory calcns. reveal that the photoinduced Immm lattice instability arises from electron excitation from the Se 4p- and Sn 5s-derived bands deep below the Fermi level that cannot be excited thermally. The results have implications for optical control of the thermoelec., ferroelec., and topol. properties of the monochalcogenides and related materials. More generally, the results emphasize the need for ultrafast structural probes to reveal distinct at.-scale dynamics that are otherwise too subtle or invisible in conventional spectroscopies.
    24. 24
      Marini, G.; Calandra, M. Lattice dynamics of photoexcited insulators from constrained density-functional perturbation theory. Phys. Rev. B 2021, 104, 144103,  DOI: 10.1103/PhysRevB.104.144103
      24
      Lattice dynamics of photoexcited insulators from constrained density-functional perturbation theory
      Marini, Giovanni; Calandra, Matteo
      Physical Review B (2021), 104 (14), 144103CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)
      We present a constrained d.-functional perturbation theory scheme for the calcn. of structural and harmonic vibrational properties of insulators in the presence of an excited and thermalized electron-hole plasma. The method is ideal to tame ultrafast light-induced structural transitions in the regime where the photocarriers thermalize faster than the lattice, the electron-hole recombination time is longer than the phonon period, and the photocarrier concn. is large enough to be approximated by an electron-hole plasma. The complete derivation presented here includes total energy, forces and stress tensor, variable cell structural optimization, harmonic vibrational properties, and the electron-phonon interaction. We discuss in detail the case of zone-center optical phonons not conserving the no. of electrons and inducing a Fermi shift in the photoelectron and hole distributions. We validate our implementation by comparing with finite differences in Te and VSe2. By calcg. the evolution of the phonon spectrum of Te, Si, and GaAs as a function of the fluence of the incoming laser light, we demonstrate that even at low fluences, corresponding to approx. 0.05 photocarriers per atom, the phonon spectrum is substantially modified with respect to the ground-state one with new Kohn anomalies appearing and a substantial softening of zone-center optical phonons. Our implementation can be efficiently used to detect reversible transient phases and irreversible structural transitions induced by ultrafast light absorption.
    25. 25
      Monacelli, L.; Bianco, R.; Cherubini, M.; Calandra, M.; Errea, I.; Mauri, F. The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects. J. Phys.: Condens. Matter 2021, 33, 363001,  DOI: 10.1088/1361-648X/ac066b
      25
      The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects
      Monacelli, Lorenzo; Bianco, Raffaello; Cherubini, Marco; Calandra, Matteo; Errea, Ion; Mauri, Francesco
      Journal of Physics: Condensed Matter (2021), 33 (36), 363001CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
      The efficient and accurate calcn. of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its at. structure, and phonon spectrum is one of the main challenges of solid state physics, esp. when strong anharmonicy invalidates any perturbative approach. To tackle this problem, we present the implementation on a modular Python code of the stochastic self-consistent harmonic approxn. (SSCHA) method. This technique rigorously describes the full thermodn. of crystals accounting for nuclear quantum and thermal anharmonic fluctuations. The approach requires the evaluation of the Born-Oppenheimer energy, as well as its derivs. with respect to ionic positions (forces) and cell parameters (stress tensor) in supercells, which can be provided, for instance, by first principles d.-functional-theory codes. The method performs crystal geometry relaxation on the quantum free energy landscape, optimizing the free energy with respect to all degrees of freedom of the crystal structure. It can be used to det. the phase diagram of any crystal at finite temp. It enables the calcn. of phase boundaries for both first-order and second-order phase transitions from the Hessian of the free energy. Finally, the code can also compute the anharmonic phonon spectra, including the phonon linewidths, as well as phonon spectral functions. We review the theor. framework of the SSCHA and its dynamical extension, making particular emphasis on the phys. inter pretation of the variables present in the theory that can enlighten the comparison with any other anharmonic theory. A modular and flexible Python environment is used for the implementation, which allows for a clean interaction with other packages. We briefly present a toy-model calcn. to illustrate the potential of the code. Several applications of the method in superconducting hydrides, charge-d.-wave materials, and thermoelec. compds. are also reviewed.
    26. 26
      Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502,  DOI: 10.1088/0953-8984/21/39/395502
      26
      QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
      Giannozzi Paolo; Baroni Stefano; Bonini Nicola; Calandra Matteo; Car Roberto; Cavazzoni Carlo; Ceresoli Davide; Chiarotti Guido L; Cococcioni Matteo; Dabo Ismaila; Dal Corso Andrea; de Gironcoli Stefano; Fabris Stefano; Fratesi Guido; Gebauer Ralph; Gerstmann Uwe; Gougoussis Christos; Kokalj Anton; Lazzeri Michele; Martin-Samos Layla; Marzari Nicola; Mauri Francesco; Mazzarello Riccardo; Paolini Stefano; Pasquarello Alfredo; Paulatto Lorenzo; Sbraccia Carlo; Scandolo Sandro; Sclauzero Gabriele; Seitsonen Ari P; Smogunov Alexander; Umari Paolo; Wentzcovitch Renata M
      Journal of physics. Condensed matter : an Institute of Physics journal (2009), 21 (39), 395502 ISSN:.
      QUANTUM ESPRESSO is an integrated suite of computer codes for electronic-structure calculations and materials modeling, based on density-functional theory, plane waves, and pseudopotentials (norm-conserving, ultrasoft, and projector-augmented wave). The acronym ESPRESSO stands for opEn Source Package for Research in Electronic Structure, Simulation, and Optimization. It is freely available to researchers around the world under the terms of the GNU General Public License. QUANTUM ESPRESSO builds upon newly-restructured electronic-structure codes that have been developed and tested by some of the original authors of novel electronic-structure algorithms and applied in the last twenty years by some of the leading materials modeling groups worldwide. Innovation and efficiency are still its main focus, with special attention paid to massively parallel architectures, and a great effort being devoted to user friendliness. QUANTUM ESPRESSO is evolving towards a distribution of independent and interoperable codes in the spirit of an open-source project, where researchers active in the field of electronic-structure calculations are encouraged to participate in the project by contributing their own codes or by implementing their own ideas into existing codes.
    27. 27
      Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Nardelli, M. B.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys.: Condens. Matter 2017, 29, 465901,  DOI: 10.1088/1361-648X/aa8f79
      27
      Advanced capabilities for materials modelling with QUANTUM ESPRESSO
      Giannozzi, P.; Andreussi, O.; Brumme, T.; Bunau, O.; Buongiorno Nardelli, M.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Cococcioni, M.; Colonna, N.; Carnimeo, I.; Dal Corso, A.; de Gironcoli, S.; Delugas, P.; Di Stasio, R. A., Jr.; Ferretti, A.; Floris, A.; Fratesi, G.; Fugallo, G.; Gebauer, R.; Gerstmann, U.; Giustino, F.; Gorni, T.; Jia, J.; Kawamura, M.; Ko, H.-Y.; Kokalj, A.; Kucukbenli, E.; Lazzeri, M.; Marsili, M.; Marzari, N.; Mauri, F.; Nguyen, N. L.; Nguyen, H.-V.; Otero-de-la-Roza, A.; Paulatto, L.; Ponce, S.; Rocca, D.; Sabatini, R.; Santra, B.; Schlipf, M.; Seitsonen, A. P.; Smogunov, A.; Timrov, I.; Thonhauser, T.; Umari, P.; Vast, N.; Wu, X.; Baroni, S.
      Journal of Physics: Condensed Matter (2017), 29 (46), 465901/1-465901/30CODEN: JCOMEL; ISSN:0953-8984. (IOP Publishing Ltd.)
      QUANTUM ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on d.-functional theory, d.-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches. QUANTUM ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas. In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software.
    28. 28
      Hamann, D. R. Optimized norm-conserving Vanderbilt pseudopotentials. Phys. Rev. B 2013, 88, 085117,  DOI: 10.1103/PhysRevB.88.085117
      28
      Optimized norm-conserving Vanderbilt pseudopotentials
      Hamann, D. R.
      Physical Review B: Condensed Matter and Materials Physics (2013), 88 (8), 085117/1-085117/10CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
      Fully nonlocal two-projector norm-conserving pseudopotentials are shown to be compatible with a systematic approach to the optimization of convergence with the size of the plane-wave basis. A reformulation of the optimization is developed, including the ability to apply it to pos.-energy at. scattering states and to enforce greater continuity in the pseudopotential. The generalization of norm conservation to multiple projectors is reviewed and recast for the present purposes. Comparisons among the results of all-electron and one- and two-projector norm-conserving pseudopotential calcns. of lattice consts. and bulk moduli are made for a group of solids chosen to represent a variety of types of bonding and a sampling of the periodic table.
    29. 29
      Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865– 3868,  DOI: 10.1103/PhysRevLett.77.3865
      29
      Generalized gradient approximation made simple
      Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
      Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
    30. 30
      Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 2010, 132, 154104,  DOI: 10.1063/1.3382344
      30
      A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
      Grimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, Helge
      Journal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
      The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.
    31. 31
      Monkhorst, H. J.; Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 1976, 13, 5188– 5192,  DOI: 10.1103/PhysRevB.13.5188
      There is no corresponding record for this reference.
    32. 32
      Sundaram, S. K.; Mazur, E. Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses. Nat. Mater. 2002, 1, 217– 224,  DOI: 10.1038/nmat767
      32
      Inducing and probing nonthermal transitions in semiconductors using femtosecond laser pulses
      Sundaram, S. K.; Mazur, E.
      Nature Materials (2002), 1 (4), 217-224CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
      A review on the nature of the nonthermal transitions in laser annealing of semiconductors under femtosecond laser excitation.
    33. 33
      Marzari, N.; Vanderbilt, D.; De Vita, A.; Payne, M. C. Thermal Contraction and Disordering of the Al(110) Surface. Phys. Rev. Lett. 1999, 82, 3296– 3299,  DOI: 10.1103/PhysRevLett.82.3296
      33
      Thermal Contraction and Disordering of the Al(110) Surface
      Marzari, Nicola; Vanderbilt, David; De Vita, Alessandro; Payne, M. C.
      Physical Review Letters (1999), 82 (16), 3296-3299CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Al(110) has been studied for temps. up to 900 K via ensemble d.-functional mol. dynamics. The strong anharmonicity displayed by this surface results in a neg. coeff. of thermal expansion, where the first interlayer distance decreases with increasing temp. Very shallow channels of oscillation for the second-layer atoms in the direction perpendicular to the surface support this anomalous contraction, and provide a novel mechanism for the formation of adatom-vacancy pairs, preliminary to the disordering and premelting transition. Such characteristic behavior originates in the free-electron-gas bonding at a loosely packed surface.
    34. 34
      Baroni, S.; de Gironcoli, S.; Dal Corso, A.; Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 2001, 73, 515– 562,  DOI: 10.1103/RevModPhys.73.515
      34
      Phonons and related crystal properties from density-functional perturbation theory
      Baroni, Stefano; De Gironcoli, Stefano; Dal Corso, Andrea; Giannozzi, Paolo
      Reviews of Modern Physics (2001), 73 (2), 515-562CODEN: RMPHAT; ISSN:0034-6861. (American Physical Society)
      This article reviews with many refs. the current status of lattice-dynamical calcns. in crystals, using d.-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calcn. of the response to macroscopic elec. fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodol. is demonstrated with a no. of applications existing in the literature.
    35. 35
      Kokalj, A. Computer graphics and graphical user interfaces as tools in simulations of matter at the atomic scale. Computational Materials Science. Proceedings of the Symposium on Software Development for Process and Materials Design 2003, 28, 155– 168,  DOI: 10.1016/S0927-0256(03)00104-6
      35
      Computer graphics and graphical user interfaces as tools in simulations of matter at the atomic scale
      Kokalj, Anton
      Computational Materials Science (2003), 28 (2), 155-168CODEN: CMMSEM; ISSN:0927-0256. (Elsevier Science B.V.)
      The role of computer graphics in different aspects of simulating matter on the at. scale is discussed. Computer graphics is useful in specifying and examg. chem. structures, since it is nowadays possible to study, with d. functional theory, complex systems contg. up to a few hundreds in-equiv. atoms. Furthermore, computer graphics is also an indispensable tool in analyzing computed data and facilitates interpretation of results. In this context (http://www.xcrysden.org/) is presented, a cryst. and mol. structure visualization program, which aims at display of isosurfaces and contours, which can be superimposed on cryst. structures and interactively rotated and manipulated. Another aspect of computer utilization in simulations that takes advantage of the computer's graphics capabilities, is that it provides intuitive graphical user interfaces for the simulation setup. A demonstration of how such interfaces are easily built using the developed software can be found at : (http://www-k3.ijs.si/kokalj/guib/).
    36. 36
      Momma, K.; Izumi, F. VESTA3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 2011, 44, 1272– 1276,  DOI: 10.1107/S0021889811038970
      36
      VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data
      Momma, Koichi; Izumi, Fujio
      Journal of Applied Crystallography (2011), 44 (6), 1272-1276CODEN: JACGAR; ISSN:0021-8898. (International Union of Crystallography)
      VESTA is a 3D visualization system for crystallog. studies and electronic state calcns. It was upgraded to the latest version, VESTA 3, implementing new features including drawing the external morphpol. of crysals; superimposing multiple structural models, volumetric data and crystal faces; calcn. of electron and nuclear densities from structure parameters; calcn. of Patterson functions from the structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels, detn. of the best plane for selected atoms; an extended bond-search algorithm to enable more sophisticated searches in complex mols. and cage-like structures; undo and redo is graphical user interface operations; and significant performance improvements in rendering isosurfaces and calcg. slices.
    37. 37
      Bansal, D.; Hong, J.; Li, C. W.; May, A. F.; Porter, W.; Hu, M. Y.; Abernathy, D. L.; Delaire, O. Phonon anharmonicity and negative thermal expansion in SnSe. Phys. Rev. B 2016, 94, 054307,  DOI: 10.1103/PhysRevB.94.054307
      37
      Phonon anharmonicity and negative thermal expansion in SnSe
      Bansal, Dipanshu; Hong, Jiawang; Li, Chen W.; May, Andrew F.; Porter, Wallace; Hu, Michael Y.; Abernathy, Douglas L.; Delaire, Olivier
      Physical Review B (2016), 94 (5), 054307/1-054307/13CODEN: PRBHB7; ISSN:2469-9950. (American Physical Society)
      The anharmonic phonon properties of SnSe in the Pnma phase were investigated with a combination of expts. and first-principles simulations. Using inelastic neutron scattering (INS) and nuclear resonant inelastic X-ray scattering (NRIXS), we have measured the phonon dispersions and d. of states (DOS) and their temp. dependence, which revealed a strong, inhomogeneous shift and broadening of the spectrum on warming. First-principles simulations were performed to rationalize these measurements, and to explain the previously reported anisotropic thermal expansion, in particular the neg. thermal expansion within the Sn-Se bilayers. Including the anisotropic strain dependence of the phonon free energy, in addn. to the electronic ground state energy, is essential to reproduce the neg. thermal expansion. From the phonon DOS obtained with INS and addnl. calorimetry measurements, we quantify the harmonic, dilational, and anharmonic components of the phonon entropy, heat capacity, and free energy. The origin of the anharmonic phonon thermodn. is linked to the electronic structure.
    38. 38
      Li, C. W.; Hong, J.; May, A. F.; Bansal, D.; Chi, S.; Hong, T.; Ehlers, G.; Delaire, O. Orbitally driven giant phonon anharmonicity in SnSe. Nat. Phys. 2015, 11, 1063– 1069,  DOI: 10.1038/nphys3492
      38
      Orbitally driven giant phonon anharmonicity in SnSe
      Li, C. W.; Hong, J.; May, A. F.; Bansal, D.; Chi, S.; Hong, T.; Ehlers, G.; Delaire, O.
      Nature Physics (2015), 11 (12), 1063-1069CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)
      Understanding elementary excitations and their couplings in condensed matter systems is crit. for developing better energy-conversion devices. In thermoelec. materials, the heat-to-electricity conversion efficiency is directly improved by suppressing the propagation of phonon quasiparticles responsible for macroscopic thermal transport. The current record material for thermoelec. conversion efficiency, SnSe, has an ultralow thermal cond., but the mechanism behind the strong phonon scattering remains largely unknown. From inelastic neutron scattering measurements and first-principles simulations, we mapped the four-dimensional phonon dispersion surfaces of SnSe, and found the origin of the ionic-potential anharmonicity responsible for the unique properties of SnSe. We show that the giant phonon scattering arises from an unstable electronic structure, with orbital interactions leading to a ferroelec.-like lattice instability. The present results provide a microscopic picture connecting electronic structure and phonon anharmonicity in SnSe, and offers new insights on how electron-phonon and phonon-phonon interactions may lead to the realization of ultralow thermal cond.
    39. 39
      Gong, X.; Wu, H.; Yang, D.; Zhang, B.; Peng, K.; Zou, H.; Guo, L.; Lu, X.; Chai, Y.; Wang, G. Temperature dependence of Raman scattering in single crystal SnSe. Vib. Spectrosc. 2020, 107, 103034,  DOI: 10.1016/j.vibspec.2020.103034
      39
      Temperature dependence of Raman scattering in single crystal SnSe
      Gong, Xiangnan; Wu, Hong; Yang, Dingfeng; Zhang, Bin; Peng, Kunling; Zou, Hanjun; Guo, Lijie; Lu, Xu; Chai, Yisheng; Wang, Guoyu; Zhou, Xiaoyuan
      Vibrational Spectroscopy (2020), 107 (), 103034CODEN: VISPEK; ISSN:0924-2031. (Elsevier B.V.)
      We report on the temp.-dependence Raman modes of in-plane B3g, A2g and out-of-plane A1g, A3g in single crystals of tin selenide that grown by a modified home-made Bridgeman method. The samples are characterized by single crystal X-ray diffraction and high-resoln. transmission electron microscopy to confirm their crystal structure. The temp.-dependence of Raman spectroscopy illustrates that A1g, B3g, A2g and A3g modes are red-shifted and softened with increasing temp. from 77 K to 400 K. Large temp. coeffs. for in-plane Raman modes are obsd., say -4.13 × 10-2 cm-1/K and -5.20 × 10-2 cm-1/K for B3g and A2g modes, resp. The result indicates intrinsic anisotropic Gruneisen parameter β in SnSe, revealing the strong anisotropic lattice anharmonicity. Besides, coeffs. of optical-phonon frequency with incident laser-power were (-0.87, -2.77, -2.18 and -1.08) cm-1/mW for A1g, B3g, A2g and A3g, resp. for the laser-power dependent Raman spectroscopy expts. Our work offers a new insight to understand the lattice anharmonicity via Raman spectroscopy and is conductive to search the new thermoelec. materials with intrinsic low lattice thermal cond.
    40. 40
      Shi, G.; Kioupakis, E. Quasiparticle band structures and thermoelectric transport properties of p-type SnSe. J. Appl. Phys. 2015, 117, 065103,  DOI: 10.1063/1.4907805
      40
      Quasiparticle band structures and thermoelectric transport properties of p-type SnSe
      Shi, Guangsha; Kioupakis, Emmanouil
      Journal of Applied Physics (Melville, NY, United States) (2015), 117 (6), 065103/1-065103/10CODEN: JAPIAU; ISSN:0021-8979. (American Institute of Physics)
      We used d. functional and many-body perturbation theory to calc. the quasiparticle band structures and electronic transport parameters of p-type SnSe both for the low-temp. Pnma and high-temp. Cmcm phases. The Pnma phase has an indirect band gap of 0.829 eV, while the Cmcm has a direct band gap of 0.464 eV. Both phases exhibit multiple local band extrema within an energy range comparable to the thermal energy of carriers from the global extrema. We calcd. the electronic transport coeffs. as a function of doping concn. and temp. for single-crystal and polycryst. materials to understand the previous exptl. measurements. The electronic transport coeffs. are highly anisotropic and are strongly affected by bipolar transport effects at high temp. Our results indicate that SnSe exhibits optimal thermoelec. performance at high temp. when doped in the 1019-1020 cm-3 range. (c) 2015 American Institute of Physics.
    41. 41
      Blöchl, P. E.; Jepsen, O.; Andersen, O. K. Improved tetrahedron method for Brillouin-zone integrations. Phys. Rev. B 1994, 49, 16223– 16233,  DOI: 10.1103/PhysRevB.49.16223
      41
      Improved tetrahedron method for Brillouin-zone integrations
      Blochl, Peter E.; Jepsen, O.; Andersen, O. K.
      Physical Review B: Condensed Matter and Materials Physics (1994), 49 (23), 16223-33CODEN: PRBMDO; ISSN:0163-1829.
      Several improvements of the tetrahedron method for Brillouin-zone integrations are presented. (1) A translational grid of k points and tetrahedra is suggested that renders the results for insulators identical to those obtained with special-point methods with the same no. of k points. (2) A simple correction formula goes beyond the linear approxn. of matrix elements within the tetrahedra and also improves the results for metals significantly. For a required accuracy this reduces the no. of k points by orders of magnitude. (3) Irreducible k points and tetrahedra are selected by a fully automated procedure, requiring as input only the space-group operations. (4) The integration is formulated as a weighted sum over irreducible k points with integration wts. calcd. using the tetrahedron method once for a given band structure. This allows an efficient use of the tetrahedron method also in plane-wave-based electronic-structure methods.
    42. 42
      Nikolić, P. M.; Milković, L.; Mihajlović, P.; Lavrenčić, B. Raman scattering in snse. Czech. J. Phys. 1978, 28, 456– 459,  DOI: 10.1007/BF01594258
      There is no corresponding record for this reference.
    43. 43
      Huang, Y.; Teitelbaum, S.; Yang, S.; na, G. D. l. P.; Chollet, T. S. M.; Zhu, D.; Niedziela, J. L.; Bansal, D.; May, A. F.; Lindenberg, A. M. Determination of nonthermal bonding origin of a novel photoexcited lattice instability in SnSe. arXiv 2023, 2301.08955,  DOI: 10.48550/arXiv.2301.08955
      There is no corresponding record for this reference.
    44. 44
      Reis, D. A.; Lindenberg, A. M. Ultrafast X-ray scattering in solids. Topics in Applied Physics 2006, 108, 371– 422,  DOI: 10.1007/978-3-540-34436-0_6
      There is no corresponding record for this reference.
    45. 45
      Tangney, P.; Fahy, S. Density-functional theory approach to ultrafast laser excitation of semiconductors: Application to the A1 phonon in tellurium. Phys. Rev. B 2002, 65, 054302,  DOI: 10.1103/PhysRevB.65.054302
      45
      Density-functional theory approach to ultrafast laser excitation of semiconductors: Application to the A1 phonon in tellurium
      Tangney, P.; Fahy, S.
      Physical Review B: Condensed Matter and Materials Physics (2002), 65 (5), 054302/1-054302/13CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
      Calcns. of the A1 phonon frequency in photoexcited Te are presented. The phonon frequency as a function of photoexcited carrier d. and phonon amplitude is detd., including anharmonic effects. The sensitivity of the A1 mode to photoexcitation is related to the Peierls mechanism for stabilizing the α-Te structure. The assumptions of slow and fast carrier recombination were studied and the two regimes give qual. different predictions for the excitation dependence of the phonon frequency. Recent pump-probe expts. are compared with the calcns. The predictions based on fast carrier recombination are not in agreement with expt. The reflectivity oscillations expected to occur in pump-probe expts. are simulated, including the coupled effects of optical absorption, carrier diffusion, and phonon dynamics. Using the calcd. dependence of phonon frequency on carrier d. (assuming slow carrier recombination) and exptl. values for the optical dielec. consts., the deriv. of the frequency peak for reflectivity oscillations with respect to pump fluence is -0.085 THz per mJ/cm2, compared to an exptl. value of -0.07 THz per mJ/cm2 in the low-fluence regime. The ambipolar diffusion const. for the optically excited carriers is 10 cm2/s, substantially smaller than its equil. value. The effects of carrier diffusion are more important than phonon anharmonicity in the obsd. changes of phonon frequency within the 1st few cycles of motion after laser excitation. Greatly increased damping of the reflectivity oscillations at high pump fluences, which is reported in recent expts., is not found in the simulations.
    46. 46
      Hu, J.; Vanacore, G. M.; Yang, Z.; Miao, X.; Zewail, A. H. Transient Structures and Possible Limits of Data Recording in Phase-Change Materials. ACS Nano 2015, 9, 6728– 6737,  DOI: 10.1021/acsnano.5b01965
      46
      Transient Structures and Possible Limits of Data Recording in Phase-Change Materials
      Hu, Jianbo; Vanacore, Giovanni M.; Yang, Zhe; Miao, Xiangshui; Zewail, Ahmed H.
      ACS Nano (2015), 9 (7), 6728-6737CODEN: ANCAC3; ISSN:1936-0851. (American Chemical Society)
      Phase-change materials (PCMs) represent the leading candidates for universal data storage devices, which exploit the large difference in the phys. properties of their transitional lattice structures. On a nanoscale, it is fundamental to det. their performance, which is ultimately controlled by the speed limit of transformation among the different structures involved. Here, we report observation with at.-scale resoln. of transient structures of nanofilms of cryst. germanium telluride, a prototypical PCM, using ultrafast electron crystallog. A nonthermal transformation from the initial rhombohedral phase to the cubic structure was found to occur in 12 ps. On a much longer time scale, hundreds of picoseconds, equil. heating of the nanofilm is reached, driving the system toward amorphization, provided that high excitation energy is invoked. These results elucidate the elementary steps defining the structural pathway in the transformation of cryst.-to-amorphous phase transitions and describe the essential at. motions involved when driven by an ultrafast excitation. The establishment of the time scales of the different transient structures, as reported here, permits detn. of the possible limit of performance, which is crucial for high-speed recording applications of PCMs.
    47. 47
      Cavalleri, A.; Tóth, C.; Siders, C. W.; Squier, J. A.; Ráksi, F.; Forget, P.; Kieffer, J. C. Femtosecond Structural Dynamics in VO2 during an Ultrafast Solid-Solid Phase Transition. Phys. Rev. Lett. 2001, 87, 237401,  DOI: 10.1103/PhysRevLett.87.237401
      47
      Femtosecond structural dynamics in VO2 during an ultrafast solid-solid phase transition
      Cavalleri, A.; Toth, Cs.; Siders, C. W.; Squier, J. A.; Raksi, F.; Forget, P.; Kieffer, J. C.
      Physical Review Letters (2001), 87 (23), 237401/1-237401/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
      Femtosecond x-ray and visible pulses were used to probe structural and electronic dynamics during an optically driven, solid-solid phase transition in VO2. For high interband electronic excitation (∼5 × 1021 cm-3), a subpicosecond transformation into the high-T, rutile phase of the material is obsd., simultaneous with an insulator-to-metal transition. The fast time scale obsd. suggests that, in this regime, the structural transition may not be thermally initiated.
    48. 48
      Wall, S.; Yang, S.; Vidas, L.; Chollet, M.; Glownia, J. M.; Kozina, M.; Katayama, T.; Henighan, T.; Jiang, M.; Miller, T. A. Ultrafast disordering of vanadium dimers in photoexcited VO2. Science 2018, 362, 572– 576,  DOI: 10.1126/science.aau3873
      48
      Ultrafast disordering of vanadium dimers in photoexcited VO2
      Wall, Simon; Yang, Shan; Vidas, Luciana; Chollet, Matthieu; Glownia, James M.; Kozina, Michael; Katayama, Tetsuo; Henighan, Thomas; Jiang, Mason; Miller, Timothy A.; Reis, David A.; Boatner, Lynn A.; Delaire, Olivier; Trigo, Mariano
      Science (Washington, DC, United States) (2018), 362 (6414), 572-576CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      Many ultrafast solid phase transitions are treated as chem. reactions that transform the structures between two different unit cells along a reaction coordinate, but this neglects the role of disorder. Although ultrafast diffraction provides insights into at. dynamics during such transformations, diffraction alone probes an averaged unit cell and is less sensitive to randomness in the transition pathway. Using total scattering of femtosecond x-ray pulses, we show that at. disordering in photoexcited vanadium dioxide (VO2) is central to the transition mechanism and that, after photoexcitation, the system explores a large vol. of phase space on a time scale comparable to that of a single phonon oscillation. These results overturn the current understanding of an archetypal ultrafast phase transition and provide new microscopic insights into rapid evolution toward equil. in photoexcited matter.
    49. 49
      Behnia, K. Finding merit in dividing neighbors. Science 2016, 351, 124– 124,  DOI: 10.1126/science.aad8688
      49
      Finding merit in dividing neighbors
      Behnia, Kamran
      Science (Washington, DC, United States) (2016), 351 (6269), 124CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
      There is no expanded citation for this reference.

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