Ultrasteep Slope Cryogenic FETs Based on Bilayer GrapheneClick to copy article linkArticle link copied!
- Eike IckingEike IckingJARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, GermanyPeter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, GermanyMore by Eike Icking
- David EmmerichDavid EmmerichJARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, GermanyPeter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, GermanyMore by David Emmerich
- Kenji WatanabeKenji WatanabeResearch Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, JapanMore by Kenji Watanabe
- Takashi TaniguchiTakashi TaniguchiResearch Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, JapanMore by Takashi Taniguchi
- Bernd BeschotenBernd BeschotenJARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, GermanyMore by Bernd Beschoten
- Max C. LemmeMax C. LemmeChair of Electronic Devices, RWTH Aachen University, 52074 Aachen, GermanyAMO GmbH, 52074 Aachen, GermanyMore by Max C. Lemme
- Joachim Knoch
- Christoph Stampfer*Christoph Stampfer*E-mail: [email protected]JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, GermanyPeter Grünberg Institute (PGI-9), Forschungszentrum Jülich, 52425 Jülich, GermanyMore by Christoph Stampfer
Abstract
Cryogenic field-effect transistors (FETs) offer great potential for applications, the most notable example being classical control electronics for quantum information processors. For the latter, on-chip FETs with low power consumption are crucial. This requires operating voltages in the millivolt range, which are only achievable in devices with ultrasteep subthreshold slopes. However, in conventional cryogenic metal-oxide-semiconductor (MOS)FETs based on bulk material, the experimentally achieved inverse subthreshold slopes saturate around a few mV/dec due to disorder and charged defects at the MOS interface. FETs based on two-dimensional materials offer a promising alternative. Here, we show that FETs based on Bernal stacked bilayer graphene encapsulated in hexagonal boron nitride and graphite gates exhibit inverse subthreshold slopes of down to 250 μV/dec at 0.1 K, approaching the Boltzmann limit. This result indicates an effective suppression of band tailing in van der Waals heterostructures without bulk interfaces, leading to superior device performance at cryogenic temperature.
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Field-effect transistors operable at cryogenic temperatures are an ongoing area of research with potential applications in outer space electronic devices, (1−5) semiconductor-superconducting coupled systems, (6) scientific instruments such as infrared sensors, (5,7,8) and notably control electronics in quantum computing. (9−14) The distinct advantages of operating at cryogenic temperatures include reduced power dissipation, minimized thermal noise, and faster signal transmission. (1,15,16) The significance of cryogenic control electronics is especially apparent in the context of quantum information processing, where the availability of control electronics in close proximity to the qubits is seen as a necessary condition for operating large quantum processors with thousands of qubits. (11,14,17−20) However, developing cryogenic electronics for quantum computing applications poses significant challenges due to the limited cooling power of dilution refrigerators. One of the requirements is to reduce the operational voltage range of the FETs into the mV range, (21) which, in turn, requires devices with ultrasteep subthreshold slopes. Temperature broadening effects impose a lower limit–the so-called Boltzmann limit–to the inverse subthreshold slope (SS) given by SSBL = kBT/e · ln(10), where T is the operating temperature and kB the Boltzmann constant. Thus, the inverse SS is expected to decrease from 60 mV/dec at room temperature to as low as, e.g., 20 μV/dec at 0.1 K. However, experiments with conventional FET devices optimized for low-temperature operation have shown that the inverse SS saturates at considerably higher values in the order of 10 mV/dec at cryogenic temperature. (22−25) This saturation originates mainly from static disorder at the metal-oxide-semiconductor (MOS) interface (due to, e.g., surface roughness, charged defects,etc.). (23,24,24−27) This contributes to the formation of a finite density of states (DOS) near the band edges, which decays exponentially into the band gap. (28) This so-called band-tailing leads to deteriorated off-state behavior and limits the achievable SS. This effect is further enhanced by dopants, which could either freeze out or become partially ionized. (21,29) Interface engineering can improve the MOS interface, (30) but in MOSFETs based on bulk materials, inherent disorder at the interfaces and charged defects within bulk dielectrics cannot be fully eliminated.
FETs based entirely on van der Waals (vdW) materials are a promising alternative because these materials offer atomically clean interfaces, as there are no dangling bonds in the vertical direction. Particularly promising for cryogenic applications are vdW-heterostructures based on Bernal stacked bilayer graphene (BLG). (34) Indeed, it has been shown that by encapsulating BLG into hexagonal boron nitride (hBN) and by placing it on graphite (Gr), it is possible to open a tunable, ultraclean, and spatially homogeneous band gap in BLG by applying an out-of-plane electric displacement field. (31,35,36) Such BLG-based heterostructures can be seen as an electrostatically tunable semiconductor. (32,37,38) The high device quality allowed the realization of BLG-based quantum point contacts (38,39) and quantum dot devices. (40−42) Further incorporating graphite top gates (tg) instead of state-of-the-art gold top gates in the BLG heterostructures promises a further reduction of disorder as recent publications reported magnetic and even superconducting phases hosted in the valence and conduction bands of BLG. (43−45) In this work, we demonstrate the enhanced device quality of dual graphite-gated BLG, evident in ultraclean band gaps and ultrasmall inverse subthreshold slopes, establishing vdW-material-based heterostructures as an ideal platform for cryogenic FETs. We use finite bias spectroscopy to show that the band gap tunability is enhanced in pure vdW BLG heterostructures with almost no residual disorder. By extracting the inverse subthreshold slopes, we obtain values as low as 250 μV/dec at T = 0.1 K, which is only an order of magnitude larger than the Boltzmann limit of 20 μV/dec at this temperature. These results demonstrate the effective suppression of band tailing, leading to superior cryogenic device behavior of FETs based on vdW materials compared to conventional FETs.
The studied devices are fabricated by a standard dry van-der-Waals transfer technique. (46,47) The process involves the sequential stacking of hBN, graphite and BLG flakes produced by mechanical exfoliation. (48) First, a large hBN flake is selected to completely cover the top graphite gate, which is picked up in the second step. The (top) graphite gate is encapsulated in another hBN flake which acts as the top gate dielectric. We then pick up the BLG, a third hBN flake (bottom gate dielectric), and the bottom graphite gate and transfer the vdW heterostructure to a Si++/SiO2 substrate. The exact thicknesses of the used hBN dielectric layers (mainly ≈20 nm) can be found in the Table S1. Complete encapsulation of the BLG in hBN is essential to prevent degradation and short circuits to the graphite gates. One-dimensional side contacts are then fabricated using electron-beam lithography, CF4-based reactive ion etching and metal evaporation followed by lift-off. (46) A schematic of the final device, including the gating and contacting scheme, is shown in Figure 1a (an optical image can be found in the Figure S1). If not stated otherwise, all measurements were performed at T = 0.1 K in a dilution refrigerator with a two-terminal configuration, where we applied the drain-source voltage symmetrically (for more information on the measurement setup, see ref (32)).
As a first electrical characterization, we measure the drain current Id as a function of top and bottom gate voltage by applying a small drain-source voltage Vds = 100 μV. Figure 1b shows the resulting map of the BLG resistance R = Vds/Id. Here, we observe a diagonal feature of increased resistance with a slope β = 1.22, which gives us directly the relative gate lever arm β = αbg/αtg, where αbg and αtg denote the gate lever-arms of the top and bottom gate and can be extracted from quantum Hall measurements (49−51) (for more information, see Supporting Information). The increasing width of the region of maximum resistance with increasing gate voltages is direct evidence for the formation and tuning of the BLG band gap with increasing out-of-plane displacement field D (see also band structure calculations in Figure 1c). The displacement field in the dual-gated BLG-based vdW heterostructure is given by D = eαtg[β(Vbg – Vbg0) – (Vtg – Vtg0)]/2, and the effective gate voltage is given by Vg = [β(Vbg – Vbg0) + (Vtg – Vtg0)]/(1 + β), which tunes the electrochemical potential in the band gap of the BLG, μ ≈ eVg. (32) Here, ε0 is the vacuum permittivity, and the parameters Vtg0 and Vbg0 account for the offsets of the charge neutrality point from Vtg = Vbg = 0.
To study the band gap opening in our devices as a function of the displacement field D, we perform finite bias spectroscopy measurements and investigate the differential conductance dI/dVds as a function of the effective gating potential Vg and the applied drain-source voltage Vds for different fixed displacement fields D, see Figure 1d. A distinct diamond-shaped region of suppressed conductance emerges, which has a high degree of symmetry and sharp edges and scales well with the applied displacement field. The outlines of the diamonds (black dashed lines in Figure 1d) show a slope of ≈2, highlighting that Vg directly tunes the electrochemical potential μ within the band gap and indicating that the band gap is as good as free of any trap states. (32) In the Supporting Information. we show that the slope of the diamond outlines is indeed constant (≈ 2) for all displacement fields D/ε0 ≳ 0.2 V/nm.
From the extension of the diamonds on the Vds axis, we can directly extract the size of the band gap Eg, (32) which are shown in Figure 1e for positive (filled triangles) and negative displacement fields (empty triangles). They agree reasonably well with the theoretical prediction assuming an effective dielectric constant of BLG of εBLG = 1 (blue line, for more information, see Supporting Information.) except for a small offset of 5 meV (gray dashed line), which might be due to some residual disorder or interaction effects. Measurements on a second graphite top-gated device reveal the same behavior (see Figure S9).
In Figure 1e we also report the results of measurements performed on a similar BLG device but with the top gate made of gold instead of graphite (see ref (32)). It is noteworthy that the extracted band gap for the device with graphite gates is almost 20 meV higher than that extracted for the device with a gold top gate for the same displacement fields, highlighting the importance of clean vdW-interfaces. Furthermore, the observed extracted band gap Eg persists down to lower displacement fields D/ε0 ≈ 50 mV/nm compared to devices with a gold top gate.
The high tuning efficiency of the band gap in graphite dual-gated BLG combined with the high symmetry of the diamonds from the bias spectroscopy measurements demonstrates that BLG heterostructures built entirely from vdW materials, including top and bottom gates, outperform BLG devices with non-vdW materials thanks to much cleaner interfaces, allowing them to achieve unprecedented levels of device quality.
The finite bias spectroscopy measurements show that the edges of the diamonds are sharply defined, which promises excellent switching efficiency of FETs based on dual graphite-gated BLG when using Vg as the tuning parameter. To extract the inverse subthreshold slope, we measure the drain current Id as a function of Vg for fixed D-field and Vds ≈ 0.1 mV at both band edges, see Figures 2a and 2b. From the linear fits of the slopes (black dashed lines), we extract the inverse subthreshold slope SS = (∂(log10(Id)/∂Vg)−1. The resulting values for the valence and conduction band are plotted in Figure 2c.
At the valence band edge, we extract record low values of SS ≈ 270–500 μV/dec, roughly 1 order of magnitude above the Boltzmann limit SSBL(0.1 K) = 20 μV/dec. For comparison, the saturation limit of conventional FETs based on non-vdW materials at T ≈ 0.1 K is in the order of a few mV/dec. (25) We repeat similar measurements for slightly higher drain-source voltages Vds ≈ 0.5 mV. The results are also shown in Figure 2c as upward-pointing triangles. They agree overall with the values from the measurements at Vds = 0.1 mV, with inverse subthreshold slopes at the valence band around SS ≈ 250 to 500 μV/dec. The very low SS value indicates that band tailing is suppressed for devices with only vdW interfaces. This is also supported by the fact that samples with a gold top gate (i.e., an interface between a vdW and a bulk material) show significantly higher SS values for comparable D-fields at the valence band edge (see the cross and gray upward-pointing triangles in Figure 2c).
It is remarkable to observe that while the SS extracted at the valence band edge does not show a significant dependency on the applied displacement field D, the values extracted at the conduction band edge show a considerable increase from SS ≈ 500 μV/dec up to SS ≈ 2.8 mV/dec with increasing D. This displacement field-dependent asymmetry of the SS values is related to the electron–hole asymmetry of the BLG band structure. In principle, this asymmetry could also be due to a top-bottom asymmetry of (weak) interface disorder in the vdW heterostructure, since transport near the band edges is dominated by orbitals in only one of the two graphene layers. For example, for a positive D-field, transport at the conductance (valence) band edge is carried only by the top (bottom) layer of the BLG. (32) Changing the D-field direction reverses the band-edge to layer assignment. This allows us to experimentally exclude such a possible nonuniformity of the interface disorder, as we observe the same asymmetry in the SS values for the conductance and valence band edge also for negative D-fields (see downward pointing triangles in Figure 2c), in good agreement with the values for positive D-fields, thus strongly emphasizing the importance of the asymmetry in the BLG band structure. In Figure 2d we show the calculated band structure as a function of the onsite potential difference between the layers Δ(D), which can be directly tuned with the applied displacement field D (for more information on the calculations, see Supporting Information). With increasing Δ(D), the bands undergo an increasingly asymmetric deformation due to the trigonal-warping effect. (33,52) As a consequence, the bands change from a hyperbolic shape at low Δ(D) to an asymmetric Mexican-hat shape for high Δ(D), (31) see Figure 2d. With increasing band deformation, parts of the bands close to the K and K′ points of the Brillouin zone become flat. Recent studies have shown that these flat bands give rise to a rich phase diagram in BLG, where magnetic and superconducting phases emerge. (43−45) The emerging phases could act phenomenologically similar to the interface-induced disorder, resulting in effective tail states at the band edges and degradation of the SS. The flat parts of the bands are right at the conduction band edge, but slightly deeper in the valence band: for example, for Δ = 100 meV in Figure 2d, the local valence band maximum is much more pronounced than the local conduction band minimum (see gray shaded areas). Consequently, the resulting phase diagrams also exhibit an asymmetry similar to our SS values, (45) which suggests that the asymmetric band deformation could cause the SS asymmetry in our measurements. We observed the same behavior for a second device, although at slightly different D-fields (see Figure S10), most likely due to sample-to-sample variations. Regardless, we would like to emphasize that this consistent asymmetry is in itself an indicator of the overall low disorder in our devices.
While our device presents excellent SS values, the measured on–off ratio in Figure 2a and b is only about 104 to 105, which is a direct consequence of the low on-current of about Id ≈ 10–8 A. This low current level is partially due to the small size of the device contacts, which are circularly etched vias through the hBN, with a diameter of just 1 μm. However, it is mainly because the measured current is limited by our measurement setup, which is optimized for low-noise, small-current measurements but also imposes a sharp limit of about 10–8 A, see Figure 3a. In a different setup at higher temperatures T = 1.5 K, we observe on-currents of up to 1 μA in the very same device for large Vds = 30 mV, see Figure 3b, indicating that higher currents are possible also with the contact geometry used. This is also confirmed by measurements in a second device of similar design, where we measure currents up to 1 μA even at T = 0.1 K in a different low-temperature setup (see Figure S11).
The measurements presented in Figure 3 also show that the threshold voltage shifts to lower values of Vg with increasing Vds, without significantly affecting SS, see Figure 3a (more data are provided in Sec. 3 in the Supporting Information). This implies that–despite the small on-current–the device presented in this manuscript could be operated at T = 0.1 K as a FET with an on–off ratio of at least 105 and an operational voltage range of only 3–4 mV by suitably choosing the drain-source voltage Vds, thanks to the small SS ≈ 250 μV/dec At T = 1.5 K, reaching an on–off ratio of 105 will require operational voltages of 6–7 mV due to a slightly higher noise level and slightly higher SS ≈ 500 μV/dec.
Finally, we summarize in Figure 4 the minimum inverse SS for different transistor device architectures reported in the literature (empty dots) as a function of temperature for low T ≤ 6 K. The best performing conventional FET devices, based on silicon-on-insulator (18) or nanowires, (53) allow to reach SS ≈ 2 mV/dec. These values are almost an order of magnitude higher than the 250 μV/dec of the BLG-based devices reported in this work (red dots). The theoretical Boltzmann limit is included as a solid line. At T = 1.5 K, the Boltzmann limit is SSBL ≈ 300 μV/dec, only slightly less than the inverse subthreshold slope of our device (SS ≈ 500 μV/dec). We attribute this improvement in SS directly to the reduced interface disorder in devices based on pure vdW heterostructures, i.e., without bulk interfaces to metal or oxides. The detrimental effect of bulk interfaces is well illustrated by the much higher SS values of BLG devices, where the top gate was made of gold instead of graphite (blue triangles in Figure 4). A BLG device with an additional Al2O3 between the metal top gate and the top hBN performed even worse (green triangle).
In summary, we have demonstrated that BLG devices based on pure vdW materials exhibit excellent band gap tunability and have provided evidence that 2D material-based FETs offer superior device behavior at cryogenic temperatures, with SS in the order of 250 μV/dec, only 1 order of magnitude above the Boltzmann limit of SSBL ≈ 20 μV/dec at T = 0.1 K. The ability to also electrostatically confine carriers in BLG (38,40,42) and the excellent performance as a field-effect transistor make this type of device an ideal platform for cryogenic applications and calls for further device design improvements that allow for down-scaling and circuit integration. Moreover, we expect this work to trigger the exploration of pure vdW heterostructure FETs based on true 2D semiconductors, such as the transition metal dichalcogenides MoS2 and WSe2.
Data Availability
The data supporting the findings are available in a Zenodo repository under accession code 10.5281/zenodo.10526847.
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.4c02463.
Equations used to calculate the band gap and band structure in bilayer graphene as a function of the displacement field, additional information for the first sample, comparable data for a second device, and the drain-current traces for the BLG devices with Au top gate and additional Al2O3 dielectric (PDF)
Terms & Conditions
Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.
Acknowledgments
The authors thank S. Trellenkamp and F. Lentz for their support in device fabrication. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 881603 (Graphene Flagship), from the European Research Council (ERC) under grant agreement No. 820254, the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1–390534769, by the FLAG-ERA grant PhotoTBG, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 471733165, by the FLAG-ERA grant TATTOOS, by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 437214324, from the EU project ATTOSWITCH under grant No. 101135571, and by the Helmholtz Nano Facility. (62) K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant Numbers 20H00354, 21H05233 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan.
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- 25Beckers, A.; Jazaeri, F.; Enz, C. Theoretical Limit of Low Temperature Subthreshold Swing in Field-Effect Transistors. IEEE Electron Device Lett. 2020, 41, 276– 279, DOI: 10.1109/LED.2019.2963379Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhslCitbfL&md5=194933f084b92cc8786e2e113b2c8095Theoretical limit of low temperature subthreshold swing in field-effect transistorsBeckers, Arnout; Jazaeri, Farzan; Enz, ChristianIEEE Electron Device Letters (2020), 41 (2), 276-279CODEN: EDLEDZ; ISSN:1558-0563. (Institute of Electrical and Electronics Engineers)This letter reports a temp.-dependent limit for the subthreshold swing in MOSFETs that deviates from the Boltzmann limit at deep-cryogenic temps. Below a crit. temp., the derived limit sats. to a value that is independent of temp. and proportional to the characteristic decay of a band tail. The proposed expression tends to the Boltzmann limit when the decay of the band tail tends to zero. Since the saturationis universally obsd. in different types of MOSFETs (regardless of dimension or semiconductor material), this suggests that an intrinsic mechanism is responsible for the band tail.
- 26Kamgar, A. Subthreshold behavior of silicon MOSFETs at 4.2 K. Solid-State Electron. 1982, 25, 537– 539, DOI: 10.1016/0038-1101(82)90052-1Google ScholarThere is no corresponding record for this reference.
- 27Ghibaudo, G.; Aouad, M.; Casse, M.; Martinie, S.; Poiroux, T.; Balestra, F. On the modelling of temperature dependence of subthreshold swing in MOSFETs down to cryogenic temperature. Solid-State Electron. 2020, 170, 107820, DOI: 10.1016/j.sse.2020.107820Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXotVCrsLY%253D&md5=61779f21f47b7d1287cad425e51edaeeOn the modelling of temperature dependence of subthreshold swing in MOSFETs down to cryogenic temperatureGhibaudo, G.; Aouad, M.; Casse, M.; Martinie, S.; Poiroux, T.; Balestra, F.Solid-State Electronics (2020), 170 (), 107820CODEN: SSELA5; ISSN:0038-1101. (Elsevier Ltd.)A comprehensive anal. of the MOSFET subthreshold swing for a 2D subband with exponential band tail of states is first proposed. Then, a compact anal. expression for the subthreshold swing as a function of temp. is derived, well accounting for both its cryogenic temp. satn. and classical higher temp. increase. Moreover, a generalized subthreshold swing calcn. applicable to the situation where the MOSFET drain current should be evaluated from the cond. function within the Kubo-Greenwood formalism is developed.
- 28Hill, R. M. Charge transport in band tails. Thin Solid Films 1978, 51, 133– 140, DOI: 10.1016/0040-6090(78)90347-4Google ScholarThere is no corresponding record for this reference.
- 29Beckers, A.; Jazaeri, F.; Enz, C. Cryogenic MOSFET Threshold Voltage Model. In ESSDERC 2019 - 49th European Solid-State Device Research Conference (ESSDERC) , 2019; pp 94– 97. DOI: 10.1109/ESSDERC.2019.8901806Google ScholarThere is no corresponding record for this reference.
- 30Richstein, B.; Han, Y.; Zhao, Q.; Hellmich, L.; Klos, J.; Scholz, S.; Schreiber, L. R.; Knoch, J. Interface Engineering for Steep Slope Cryogenic MOSFETs. IEEE Electron Device Lett. 2022, 43, 2149– 2152, DOI: 10.1109/LED.2022.3217314Google ScholarThere is no corresponding record for this reference.
- 31McCann, E.; Koshino, M. The electronic properties of bilayer graphene. Rep. Prog. Phys. 2013, 76, 056503, DOI: 10.1088/0034-4885/76/5/056503Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhsVOgurzN&md5=f765883278ab44bbd61386a0db3f3421The electronic properties of bilayer grapheneMcCann, Edward; Koshino, MikitoReports on Progress in Physics (2013), 76 (5), 056503/1-056503/28CODEN: RPPHAG; ISSN:0034-4885. (IOP Publishing Ltd.)We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between at. sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.
- 32Icking, E.; Banszerus, L.; Wörtche, F.; Volmer, F.; Schmidt, P.; Steiner, C.; Engels, S.; Hesselmann, J.; Goldsche, M.; Watanabe, K.; Taniguchi, T.; Volk, C.; Beschoten, B.; Stampfer, C. Transport Spectroscopy of Ultraclean Tunable Band Gaps in Bilayer Graphene. Advanced Electronic Materials 2022, 8, 2200510, DOI: 10.1002/aelm.202200510Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhvFyhsLjF&md5=c05aefdf53ca0481f5cc318883033779Transport Spectroscopy of Ultraclean Tunable Band Gaps in Bilayer GrapheneIcking, Eike; Banszerus, Luca; Wortche, Frederike; Volmer, Frank; Schmidt, Philipp; Steiner, Corinne; Engels, Stephan; Hesselmann, Jonas; Goldsche, Matthias; Watanabe, Kenji; Taniguchi, Takashi; Volk, Christian; Beschoten, Bernd; Stampfer, ChristophAdvanced Electronic Materials (2022), 8 (11), 2200510CODEN: AEMDBW; ISSN:2199-160X. (Wiley-VCH Verlag GmbH & Co. KGaA)The importance of controlling both the charge carrier d. and the band gap of a semiconductor cannot be overstated, as it opens the doors to a wide range of applications, including, for example, highly-tunable transistors, photodetectors, and lasers. Bernal-stacked bilayer graphene is a unique van-der-Waals material that allows tuning of the band gap by an out-of-plane elec. field. Although the first evidence of the tunable gap is already found 10 years ago, it took until recent to fabricate sufficiently clean heterostructures where the elec. induced gap can be used to fully suppress transport or confine charge carriers. Here, a detailed study of the tunable band gap in gated bilayer graphene characterized by temp.-activated transport and finite-bias spectroscopy measurements is presented. The latter method allows comparing different gate materials and device technologies, which directly affects the disorder potential in bilayer graphene. It is shown that graphite-gated bilayer graphene exhibits extremely low disorder and as good as no subgap states resulting in ultraclean tunable band gaps up to 120 meV. The size of the band gaps are in good agreement with theory and allow complete current suppression making a wide range of semiconductor applications possible.
- 33Varlet, A.; Bischoff, D.; Simonet, P.; Watanabe, K.; Taniguchi, T.; Ihn, T.; Ensslin, K.; Mucha-Kruczyński, M.; Fal’ko, V. I. Anomalous Sequence of Quantum Hall Liquids Revealing a Tunable Lifshitz Transition in Bilayer Graphene. Phys. Rev. Lett. 2014, 113, 116602, DOI: 10.1103/PhysRevLett.113.116602Google Scholar33https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhvVWgsb3F&md5=c29e67b741660b7e6fd9edf7dc0859fdAnomalous sequence of quantum Hall liquids revealing a tunable Lifshitz transition in bilayer grapheneVarlet, Anastasia; Bischoff, Dominik; Simonet, Pauline; Watanabe, Kenji; Taniguchi, Takashi; Ihn, Thomas; Ensslin, Klaus; Mucha-Kruczynski, Marcin; Fal'ko, Vladimir I.Physical Review Letters (2014), 113 (11), 116602/1-116602/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Bilayer graphene is a unique system where both the Fermi energy and the low-energy electron dispersion can be tuned. This is brought about by an interplay between trigonal warping and the band gap opened by a transverse elec. field. Here, we drive the Lifshitz transition in bilayer graphene to exptl. controllable carrier densities by applying a large transverse elec. field to a h-BN-encapsulated bilayer graphene structure. We perform magnetotransport measurements and investigate the different degeneracies in the Landau level spectrum. At low magnetic fields, the observation of filling factors -3 and -6 quantum Hall states reflects the existence of three maxima at the top of the valence-band dispersion. At high magnetic fields, all integer quantum Hall states are obsd., indicating that deeper in the valence band the const. energy contours are singly connected. The fact that we observe ferromagnetic quantum Hall states at odd-integer filling factors testifies to the high quality of our sample. This enables us to identify several phase transitions between correlated quantum Hall states at intermediate magnetic fields, in agreement with the calcd. evolution of the Landau level spectrum. The obsd. evolution of the degeneracies, therefore, reveals the presence of a Lifshitz transition in our system.
- 34Knoch, J.; Richstein, B.; Han, Y.; Jungemann, C.; Icking, E.; Schreiber, L.; Xue, R.; Tu, J.-S.; Gökcel, T.; Neugebauer, J.; Stampfer, C.; Zhao, Q. On the Performance of Low Power Cryogenic Electronics for Scalable Quantum Information Processors. In 2023 IEEE Nanotechnology Materials and Devices Conference (NMDC) , 2023; pp 440– 445. DOI: 10.1109/NMDC57951.2023.10343713Google ScholarThere is no corresponding record for this reference.
- 35McCann, E.; Fal’ko, V. I. Landau-Level Degeneracy and Quantum Hall Effect in a Graphite Bilayer. Phys. Rev. Lett. 2006, 96, 086805, DOI: 10.1103/PhysRevLett.96.086805Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XitVGqsLw%253D&md5=6274e974dfa7c5e911bfac0a3246f953Landau-Level Degeneracy and Quantum Hall Effect in a Graphite BilayerMcCann, Edward; Fal'ko, Vladimir I.Physical Review Letters (2006), 96 (8), 086805/1-086805/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We derive an effective two-dimensional Hamiltonian to describe the low-energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase 2π. Its high-magnetic-field Landau-level spectrum consists of almost equidistant groups of fourfold degenerate states at finite energy and eight zero-energy states. This can be translated into the Hall cond. dependence on carrier d., σxy(N), which exhibits plateaus at integer values of 4e2/h and has a double 8e2/h step between the hole and electron gases across zero d., in contrast to (4n+2)e2/h sequencing in a monolayer.
- 36Jung, J.; MacDonald, A. H. Accurate tight-binding models for the π bands of bilayer graphene. Phys. Rev. B 2014, 89, 035405, DOI: 10.1103/PhysRevB.89.035405Google ScholarThere is no corresponding record for this reference.
- 37Li, J.; Wang, K.; McFaul, K. J.; Zern, Z.; Ren, Y.; Watanabe, K.; Taniguchi, T.; Qiao, Z.; Zhu, J. Gate-controlled topological conducting channels in bilayer graphene - Nature Nanotechnology. Nat. Nanotechnol. 2016, 11, 1060– 1065, DOI: 10.1038/nnano.2016.158Google ScholarThere is no corresponding record for this reference.
- 38Overweg, H.; Knothe, A.; Fabian, T.; Linhart, L.; Rickhaus, P.; Wernli, L.; Watanabe, K.; Taniguchi, T.; Sánchez, D.; Burgdörfer, J.; Libisch, F.; Fal’ko, V. I.; Ensslin, K.; Ihn, T. Topologically Nontrivial Valley States in Bilayer Graphene Quantum Point Contacts. Phys. Rev. Lett. 2018, 121, 257702, DOI: 10.1103/PhysRevLett.121.257702Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltFWgtLs%253D&md5=18b13328df726742b3f2783bcfd62f5dTopologically Nontrivial Valley States in Bilayer Graphene Quantum Point ContactsOverweg, Hiske; Knothe, Angelika; Fabian, Thomas; Linhart, Lukas; Rickhaus, Peter; Wernli, Lucien; Watanabe, Kenji; Taniguchi, Takashi; Sanchez, David; Burgdorfer, Joachim; Libisch, Florian; Fal'ko, Vladimir I.; Ensslin, Klaus; Ihn, ThomasPhysical Review Letters (2018), 121 (25), 257702CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies with increasing field: at zero magnetic field the degeneracy of quantized one-dimensional subbands is four, because of a twofold spin and a twofold valley degeneracy. By switching on the magnetic field, the valley degeneracy is lifted. Because of the Berry curvature, states from different valleys split linearly in magnetic field. In the quantum Hall regime fourfold degenerate conductance plateaus reemerge. During the adiabatic transition to the quantum Hall regime, levels from one valley shift by two in quantum no. with respect to the other valley, forming an interweaving pattern that can be reproduced by numerical calcns.
- 39Banszerus, L.; Frohn, B.; Fabian, T.; Somanchi, S.; Epping, A.; Müller, M.; Neumaier, D.; Watanabe, K.; Taniguchi, T.; Libisch, F.; Beschoten, B.; Hassler, F.; Stampfer, C. Observation of the Spin-Orbit Gap in Bilayer Graphene by One-Dimensional Ballistic Transport. Phys. Rev. Lett. 2020, 124, 177701, DOI: 10.1103/PhysRevLett.124.177701Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtVaktrjL&md5=1ec69c1874733b6a462e24ed12552c68Observation of the Spin-Orbit Gap in Bilayer Graphene by One-Dimensional Ballistic TransportBanszerus, L.; Frohn, B.; Fabian, T.; Somanchi, S.; Epping, A.; Mueller, M.; Neumaier, D.; Watanabe, K.; Taniguchi, T.; Libisch, F.; Beschoten, B.; Hassler, F.; Stampfer, C.Physical Review Letters (2020), 124 (17), 177701CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We report on measurements of quantized conductance in gate-defined quantum point contacts in bilayer graphene that allow the observation of subband splittings due to spin-orbit coupling. The size of this splitting can be tuned from 40 to 80μeV by the displacement field. We assign this gate-tunable subband splitting to a gap induced by spin-orbit coupling of Kane-Mele type, enhanced by proximity effects due to the substrate. We show that this spin-orbit coupling gives rise to a complex pattern in low perpendicular magnetic fields, increasing the Zeeman splitting in one valley and suppressing it in the other one. In addn., we observe a spin polarized channel of 6e2/h at high in-plane magnetic field and signatures of interaction effects at the crossings of spin-split subbands of opposite spins at finite magnetic field.
- 40Eich, M.; Pisoni, R.; Pally, A.; Overweg, H.; Kurzmann, A.; Lee, Y.; Rickhaus, P.; Watanabe, K.; Taniguchi, T.; Ensslin, K.; Ihn, T. Coupled Quantum Dots in Bilayer Graphene. Nano Lett. 2018, 18, 5042– 5048, DOI: 10.1021/acs.nanolett.8b01859Google Scholar40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXht1Ois7jP&md5=3cbe22df7f36e9bc26a956f0c45ebff5Coupled Quantum Dots in Bilayer GrapheneEich, Marius; Pisoni, Riccardo; Pally, Alessia; Overweg, Hiske; Kurzmann, Annika; Lee, Yongjin; Rickhaus, Peter; Watanabe, Kenji; Taniguchi, Takashi; Ensslin, Klaus; Ihn, ThomasNano Letters (2018), 18 (8), 5042-5048CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)Electrostatic confinement of charge carriers in bilayer graphene provides a unique platform for carbon-based spin, charge, or exchange qubits. By exploiting the possibility to induce a band gap with electrostatic gating, the authors form a versatile and widely tunable multiquantum dot system. The authors demonstrate the formation of single, double and triple quantum dots that are free of any sign of disorder. In bilayer graphene, the authors have the possibility to form tunnel barriers using different mechanisms. The authors can exploit the ambipolar nature of bilayer graphene where pn-junctions form natural tunnel barriers. Alternatively, the authors can use gates to form tunnel barriers, where the authors can vary the tunnel coupling by >2 orders of magnitude tuning between a deeply Coulomb blockaded system and a Fabry-P´erot-like cavity. Demonstrating such tunability is an important step toward graphene-based quantum computation.
- 41Banszerus, L.; Frohn, B.; Epping, A.; Neumaier, D.; Watanabe, K.; Taniguchi, T.; Stampfer, C. Gate-Defined Electron–Hole Double Dots in Bilayer Graphene. Nano Lett. 2018, 18, 4785– 4790, DOI: 10.1021/acs.nanolett.8b01303Google Scholar41https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXht1SrtrrP&md5=d757b1265e5dc8b6a9d02b5863ed6684Gate-defined electron-hole double dots in bilayer grapheneBanszerus, L.; Frohn, B.; Epping, A.; Neumaier, D.; Watanabe, K.; Taniguchi, T.; Stampfer, C.Nano Letters (2018), 18 (8), 4785-4790CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)The authors present gate-controlled single-, double-, and triple-dot operation in electrostatically gapped bilayer graphene. Thanks to the recent advancements in sample fabrication, which include the encapsulation of bilayer graphene in hexagonal boron nitride and the use of graphite gates, it has become possible to electrostatically confine carriers in bilayer graphene and to completely pinch-off current through quantum dot devices. Here, they discuss the operation and characterization of electron-hole double dots. They show a remarkable degree of control of their device, which allows the implementation of two different gate-defined electron-hole double-dot systems with very similar energy scales. In the single-dot regime, they ext. excited state energies and investigate their evolution in a parallel magnetic field, which is in agreement with a Zeeman-spin-splitting expected for a g-factor of 2.
- 42Banszerus, L.; Möller, S.; Hecker, K.; Icking, E.; Watanabe, K.; Taniguchi, T.; Hassler, F.; Volk, C.; Stampfer, C. Particle–hole symmetry protects spin-valley blockade in graphene quantum dots. Nature 2023, 618, 51– 56, DOI: 10.1038/s41586-023-05953-5Google ScholarThere is no corresponding record for this reference.
- 43Zhou, H.; Holleis, L.; Saito, Y.; Cohen, L.; Huynh, W.; Patterson, C. L.; Yang, F.; Taniguchi, T.; Watanabe, K.; Young, A. F. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 2022, 375, 774– 778, DOI: 10.1126/science.abm8386Google Scholar43https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XkvFyhur0%253D&md5=4a71351373832812ddcff0de4ffa51c6Isospin magnetism and spin-polarized superconductivity in Bernal bilayer grapheneZhou, Haoxin; Holleis, Ludwig; Saito, Yu; Cohen, Liam; Huynh, William; Patterson, Caitlin L.; Yang, Fangyuan; Taniguchi, Takashi; Watanabe, Kenji; Young, Andrea F.Science (Washington, DC, United States) (2022), 375 (6582), 774-778CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)In conventional superconductors, Cooper pairing occurs between electrons of opposite spin. We observe spin-polarized supercond. in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by a large applied perpendicular elec. field. We observe a cascade of electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within the isospin space defined by the combination of the spin and momentum-space valley degrees of freedom. Although all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite magnetic field B‖ ≈ 150 milliteslas applied parallel to the two-dimensional sheet. Supercond. occurs near a symmetry-breaking transition and exists exclusively above the B‖ limit expected of a paramagnetic superconductor with the obsd. transition crit. temp. TC ≈ 30 mK, consistent with a spin-triplet order parameter.
- 44Seiler, A. M.; Geisenhof, F. R.; Winterer, F.; Watanabe, K.; Taniguchi, T.; Xu, T.; Zhang, F.; Weitz, R. T. Quantum cascade of correlated phases in trigonally warped bilayer graphene. Nature 2022, 608, 298– 302, DOI: 10.1038/s41586-022-04937-1Google Scholar44https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitFSjtbfI&md5=ae7d6865b3b069a27bfccef44d5bfc08Quantum cascade of correlated phases in trigonally warped bilayer grapheneSeiler, Anna M.; Geisenhof, Fabian R.; Winterer, Felix; Watanabe, Kenji; Taniguchi, Takashi; Xu, Tianyi; Zhang, Fan; Weitz, R. ThomasNature (London, United Kingdom) (2022), 608 (7922), 298-302CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Divergent d. of states offers an opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultraflat bands of magic-angle twisted bilayer graphene, the band touching points of few-layer rhombohedral graphite and the lightly doped rhombohedral trilayer graphene. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism at charge neutrality leading to layer antiferromagnetic states or quantum anomalous Hall states. Here we report the observation of a cascade of correlated phases in the vicinity of elec.-field-controlled Lifshitz transitions and van Hove singularities in Bernal bilayer graphene. We provide evidence for the observation of Stoner ferromagnets in the form of half and quarter metals. Furthermore, we identify signatures consistent with a topol. non-trivial Wigner-Hall crystal at zero magnetic field and its transition to a trivial Wigner crystal, as well as two correlated metals whose behavior deviates from that of std. Fermi liqs. Our results in this reproducible, tunable, simple system open up new horizons for studying strongly correlated electrons.
- 45de la Barrera, S. C.; Aronson, S.; Zheng, Z.; Watanabe, K.; Taniguchi, T.; Ma, Q.; Jarillo-Herrero, P.; Ashoori, R. Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field. Nat. Phys. 2022, 18, 771– 775, DOI: 10.1038/s41567-022-01616-wGoogle Scholar45https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsVGgsbjK&md5=40473d72081abec5779f9c8febfdd553Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic fieldde la Barrera, Sergio C.; Aronson, Samuel; Zheng, Zhiren; Watanabe, Kenji; Taniguchi, Takashi; Ma, Qiong; Jarillo-Herrero, Pablo; Ashoori, RaymondNature Physics (2022), 18 (7), 771-775CODEN: NPAHAX; ISSN:1745-2473. (Nature Portfolio)Abstr.: Emergent phenomena arising from the collective behavior of electrons is expected when Coulomb interactions dominate over the kinetic energy, and one way to create this situation is to reduce the electronic bandwidth. Bernal-stacked bilayer graphene intrinsically supports saddle points in the band structure that are predicted to host a variety of spontaneous symmetry-broken states. Here we show that bilayer graphene displays a cascade of symmetry-broken states with spontaneous spin and valley isospin ordering at zero magnetic field. We independently tune the carrier d. and elec. displacement field to explore the phase space of isospin order. Itinerant ferromagnetic states emerge near the conduction and valence band edges with complete spin and valley polarization. At larger hole densities, twofold degenerate quantum oscillations manifest in an addnl. symmetry-broken state that is enhanced by the application of an in-plane magnetic field. Both symmetry-broken states display enhanced layer polarization, suggesting a coupling to the layer degree of freedom. These states occur in the absence of a moire superlattice and are intrinsic to natural graphene bilayers. Therefore, we demonstrate that bilayer graphene represents a related but distinct approach to produce collective behavior from flat dispersion, complementary to engineered moire structures.
- 46Wang, L.; Meric, I.; Huang, P. Y.; Gao, Q.; Gao, Y.; Tran, H.; Taniguchi, T.; Watanabe, K.; Campos, L. M.; Muller, D. A.; Guo, J.; Kim, P.; Hone, J.; Shepard, K. L.; Dean, C. R. One-Dimensional Electrical Contact to a Two-Dimensional Material. Science 2013, 342, 614– 617, DOI: 10.1126/science.1244358Google Scholar46https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhs1yrs7fJ&md5=de354f7f8a0425d61230545f9afd5e80One-Dimensional Electrical Contact to a Two-Dimensional MaterialWang, L.; Meric, I.; Huang, P. Y.; Gao, Q.; Gao, Y.; Tran, H.; Taniguchi, T.; Watanabe, K.; Campos, L. M.; Muller, D. A.; Guo, J.; Kim, P.; Hone, J.; Shepard, K. L.; Dean, C. R.Science (Washington, DC, United States) (2013), 342 (6158), 614-617CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)Heterostructures based on layering of two-dimensional (2D) materials such as graphene and hexagonal B nitride represent a new class of electronic devices. Realizing this potential, however, depends critically on the ability to make high-quality elec. contact. Here, the authors report a contact geometry in which the authors metalize only the 1-dimensional edge of a 2-dimensional graphene layer. In addn. to outperforming conventional surface contacts, the edge-contact geometry allows a complete sepn. of the layer assembly and contact metalization processes. In graphene heterostructures, this enables high electronic performance, including low-temp. ballistic transport over distances longer than 15 μm, and room-temp. mobility comparable to the theor. phonon-scattering limit. The edge-contact geometry provides new design possibilities for multilayered structures of complimentary 2-dimensional materials.
- 47Purdie, D. G.; Pugno, N. M.; Taniguchi, T.; Watanabe, K.; Ferrari, A. C.; Lombardo, A. Cleaning interfaces in layered materials heterostructures. Nat. Commun. 2018, 9, 1– 12, DOI: 10.1038/s41467-018-07558-3Google Scholar47https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhslWju7nJ&md5=37facaed110c8ff3ee8b61ae6d412c37The genomic landscape of cutaneous SCC reveals drivers and a novel azathioprine associated mutational signatureInman, Gareth J.; Wang, Jun; Nagano, Ai; Alexandrov, Ludmil B.; Purdie, Karin J.; Taylor, Richard G.; Sherwood, Victoria; Thomson, Jason; Hogan, Sarah; Spender, Lindsay C.; South, Andrew P.; Stratton, Michael; Chelala, Claude; Harwood, Catherine A.; Proby, Charlotte M.; Leigh, Irene M.Nature Communications (2018), 9 (1), 1-14CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)Cutaneous squamous cell carcinoma (cSCC) has a high tumor mutational burden (50 mutations per megabase DNA pair). Here, we combine whole-exome analyses from 40 primary cSCC tumors, comprising 20 well-differentiated and 20 moderately/poorly differentiated tumors, with accompanying clin. data from a longitudinal study of immunosuppressed and immunocompetent patients and integrate this anal. with independent gene expression studies. We identify commonly mutated genes, copy no. changes and altered pathways and processes. Comparisons with tumor differentiation status suggest events which may drive disease progression. Mutational signature anal. reveals the presence of a novel signature (signature 32), whose incidence correlates with chronic exposure to the immunosuppressive drug azathioprine. Characterization of a panel of 15 cSCC tumor-derived cell lines reveals that they accurately reflect the mutational signatures and genomic alterations of primary tumors and provide a valuable resource for the validation of tumor drivers and therapeutic targets.
- 48Novoselov, K. S.; Geim, A. K.; Morozov, S.; Jiang, D.; Zhang, Y.; Dubonos, S.; Grigorieva, I.; Firsov, A. Electric field effect in atomically thin carbon films. Science 2004, 306, 666– 669, DOI: 10.1126/science.1102896Google Scholar48https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXos1Kqt70%253D&md5=488da13500bf24e8fc419052dc1a9e84Electric Field Effect in Atomically Thin Carbon FilmsNovoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A.Science (Washington, DC, United States) (2004), 306 (5696), 666-669CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)The authors describe monocryst. graphitic films, which are a few atoms thick but are nonetheless stable under ambient conditions, metallic, and of remarkably high quality. The films are a two-dimensional semimetal with a tiny overlap between valence and conductance bands, and they exhibit a strong ambipolar elec. field effect such that electrons and holes in concns. up to 1013 per square centimeter and with room-temp. mobilities of ∼10,000 square centimeters per V-second can be induced by applying gate voltage.
- 49Zhao, Y.; Cadden-Zimansky, P.; Jiang, Z.; Kim, P. Symmetry Breaking in the Zero-Energy Landau Level in Bilayer Graphene. Phys. Rev. Lett. 2010, 104, 066801, DOI: 10.1103/PhysRevLett.104.066801Google Scholar49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXisFOhsrk%253D&md5=9053c258add9d6a1d3cd553ba0c5653eSymmetry Breaking in the Zero-Energy Landau Level in Bilayer GrapheneZhao, Y.; Cadden-Zimansky, P.; Jiang, Z.; Kim, P.Physical Review Letters (2010), 104 (6), 066801/1-066801/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high-field regime, the eightfold degeneracy in the zero-energy Landau level is completely lifted, exhibiting new quantum Hall states corresponding to filling factors ν=0, 1, 2, and 3. Measurements of the activation energy gaps for the ν=2 and 3 filling factors in tilted magnetic fields exhibit no appreciable dependence on the in-plane magnetic field, suggesting that these Landau level splittings are independent of spin. In addn., measurements taken at the ν=0 charge neutral point show that, similar to single layer graphene, the bilayer becomes insulating at high fields.
- 50Sonntag, J.; Reichardt, S.; Wirtz, L.; Beschoten, B.; Katsnelson, M. I.; Libisch, F.; Stampfer, C. Impact of Many-Body Effects on Landau Levels in Graphene. Phys. Rev. Lett. 2018, 120, 187701, DOI: 10.1103/PhysRevLett.120.187701Google Scholar50https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltV2jur0%253D&md5=351198c4e10e15d11b74eef91b600e67Impact of Many-Body Effects on Landau Levels in GrapheneSonntag, J.; Reichardt, S.; Wirtz, L.; Beschoten, B.; Katsnelson, M. I.; Libisch, F.; Stampfer, C.Physical Review Letters (2018), 120 (18), 187701CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier d.-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magnetophonon resonances, we ext. the charge carrier d. dependence of the Landau level transition energies and the assocd. effective Fermi velocity vF. In contrast to the logarithmic divergence of vF at zero magnetic field, we find a piecewise linear scaling of vF as a function of the charge carrier d., due to a magnetic-field-induced suppression of the long-range Coulomb interaction. We quant. confirm our exptl. findings by performing tight-binding calcns. on the level of the Hartree-Fock approxn., which also allow us to est. an excitonic binding energy of ≈6 meV contained in the exptl. extd. Landau level transitions energies.
- 51Schmitz, M.; Ouaj, T.; Winter, Z.; Rubi, K.; Watanabe, K.; Taniguchi, T.; Zeitler, U.; Beschoten, B.; Stampfer, C. Fractional quantum Hall effect in CVD-grown graphene. 2D Mater. 2020, 7, 041007, DOI: 10.1088/2053-1583/abae7bGoogle Scholar51https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXit1Sqs73N&md5=a873725d115bc9f1fc490a278ea3f841Fractional quantum Hall effect in CVD-grown grapheneSchmitz, M.; Ouaj, T.; Winter, Z.; Rubi, K.; Watanabe, K.; Taniguchi, T.; Zeitler, U.; Beschoten, B.; Stampfer, C.2D Materials (2020), 7 (4), 041007CODEN: DMATB7; ISSN:2053-1583. (IOP Publishing Ltd.)A review. We show the emergence of fractional quantum Hall states in graphene grown by chem. vapor deposition (CVD) for magnetic fields from below 3 T to 35 T where the CVD-graphene was dry-transferred. Effective composite-fermion filling factors up to ν* = 4 are visible and higher order composite-fermion states (with four flux quanta attached) start to emerge at the highest fields. Our results show that the quantum mobility of CVD-grown graphene is comparable to that of exfoliated graphene and, more specifically, that the p/3 fractional quantum Hall states have energy gaps of up to 30 K, well comparable to those obsd. in other silicon-gated devices based on exfoliated graphene.
- 52Varlet, A.; Mucha-Kruczyński, M.; Bischoff, D.; Simonet, P.; Taniguchi, T.; Watanabe, K.; Fal’ko, V.; Ihn, T.; Ensslin, K. Tunable Fermi surface topology and Lifshitz transition in bilayer graphene. Synth. Met. 2015, 210, 19– 31, DOI: 10.1016/j.synthmet.2015.07.006Google Scholar52https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXht1Omt7nF&md5=adc2bdb8b5b2aea90eb7a1f93350c39dTunable Fermi surface topology and Lifshitz transition in bilayer grapheneVarlet, Anastasia; Mucha-Kruczynski, Marcin; Bischoff, Dominik; Simonet, Pauline; Taniguchi, Takashi; Watanabe, Kenji; Fal'ko, Vladimir; Ihn, Thomas; Ensslin, KlausSynthetic Metals (2015), 210 (Part_A), 19-31CODEN: SYMEDZ; ISSN:0379-6779. (Elsevier B.V.)Bilayer graphene is a highly tunable material: not only can one tune the Fermi energy using std. gates, as in single-layer graphene, but the band structure can also be modified by external perturbations such as transverse elec. fields or strain. We review the theor. basics of the band structure of bilayer graphene and study the evolution of the band structure under the influence of these two external parameters. We highlight their key role concerning the ease to exptl. probe the presence of a Lifshitz transition, which consists in a change of Fermi contour topol. as a function of energy close to the edges of the conduction and valence bands. Using a device geometry that allows the application of exceptionally high displacement fields, we then illustrate in detail the way to probe the topol. changes exptl. using quantum Hall effect measurements in a gapped bilayer graphene system.
- 53Han, Y.; Sun, J.; Bae, J.-H.; Grützmacher, D.; Knoch, J.; Zhao, Q.-T. High Performance 5 nm Si Nanowire FETs with a Record Small SS = 2.3 mV/dec and High Transconductance at 5.5 K Enabled by Dopant Segregated Silicide Source/Drain. In 2023 IEEE Symposium on VLSI Technology and Circuits (VLSI Technology and Circuits) , 2023; pp 1– 2. DOI: 10.23919/VLSITechnologyandCir57934.2023.10185373Google ScholarThere is no corresponding record for this reference.
- 54Han, Y.; Sun, J.; Richstein, B.; Allibert, F.; Radu, I.; Bae, J.-H.; Grützmacher, D.; Knoch, J.; Zhao, Q.-T. Steep Switching Si Nanowire p-FETs With Dopant Segregated Silicide Source/Drain at Cryogenic Temperature. IEEE Electron Device Lett. 2022, 43, 1187– 1190, DOI: 10.1109/LED.2022.3185781Google ScholarThere is no corresponding record for this reference.
- 55Beckers, A.; Jazaeri, F.; Enz, C. Characterization and Modeling of 28-nm Bulk CMOS Technology Down to 4.2 K. IEEE Journal of the Electron Devices Society 2018, 6, 1007– 1018, DOI: 10.1109/JEDS.2018.2817458Google ScholarThere is no corresponding record for this reference.
- 56Singh, N.; Lim, F. Y.; Fang, W. W.; Rustagi, S. C.; Bera, L. K.; Agarwal, A.; Tung, C. H.; Hoe, K. M.; Omampuliyur, S. R.; Tripathi, D.; Adeyeye, A. O.; Lo, G. Q.; Balasubramanian, N.; Kwong, D. L. Ultra-Narrow Silicon Nanowire Gate-All-Around CMOS Devices: Impact of Diameter, Channel-Orientation and Low Temperature on Device Performance. In 2006 International Electron Devices Meeting , 2006; pp 1– 4. DOI: 10.1109/IEDM.2006.346840Google ScholarThere is no corresponding record for this reference.
- 57Paz, B. C. Variability Evaluation of 28nm FD-SOI Technology at Cryogenic Temperatures down to 100mK for Quantum Computing. In 2020 IEEE Symposium on VLSI Technology , 2020; pp 1– 2. DOI: 10.1109/VLSITechnology18217.2020.9265034Google ScholarThere is no corresponding record for this reference.
- 58Han, H.-C.; Jazaeri, F.; D’Amico, A.; Baschirotto, A.; Charbon, E.; Enz, C. Cryogenic Characterization of 16 nm FinFET Technology for Quantum Computing. In ESSDERC 2021 - IEEE 51st European Solid-State Device Research Conference (ESSDERC) , 2021; pp 71– 74. DOI: 10.1109/ESSDERC53440.2021.9631805Google ScholarThere is no corresponding record for this reference.
- 59Habicht, S.; Feste, S.; Zhao, Q.-T.; Buca, D.; Mantl, S. Electrical characterization of Ω-gated uniaxial tensile strained Si nanowire-array metal-oxide-semiconductor field effect transistors with < 100>- and < 110> channel orientations. Thin Solid Films 2012, 520, 3332– 3336, DOI: 10.1016/j.tsf.2011.08.034Google ScholarThere is no corresponding record for this reference.
- 60Sekiguchi, S.; Ahn, M.-J.; Mizutani, T.; Saraya, T.; Kobayashi, M.; Hiramoto, T. Subthreshold Swing in Silicon Gate-All-Around Nanowire and Fully Depleted SOI MOSFETs at Cryogenic Temperature. IEEE Journal of the Electron Devices Society 2021, 9, 1151– 1154, DOI: 10.1109/JEDS.2021.3108854Google ScholarThere is no corresponding record for this reference.
- 61Paz, B. C.; Cassé, M.; Haendler, S.; Juge, A.; Vincent, E.; Galy, P.; Arnaud, F.; Ghibaudo, G.; Vinet, M.; de Franceschi, S.; Meunier, T.; Gaillard, F. Front and back channels coupling and transport on 28 nm FD-SOI MOSFETs down to liquid-He temperature. Solid-State Electron. 2021, 186, 108071, DOI: 10.1016/j.sse.2021.108071Google ScholarThere is no corresponding record for this reference.
- 62Albrecht, W.; Moers, J.; Hermanns, B. HNF - Helmholtz Nano Facility. Journal of Large-Scale Research Facilities 2017, 3, A112, DOI: 10.17815/jlsrf-3-158Google ScholarThere is no corresponding record for this reference.
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- 29Beckers, A.; Jazaeri, F.; Enz, C. Cryogenic MOSFET Threshold Voltage Model. In ESSDERC 2019 - 49th European Solid-State Device Research Conference (ESSDERC) , 2019; pp 94– 97. DOI: 10.1109/ESSDERC.2019.8901806There is no corresponding record for this reference.
- 30Richstein, B.; Han, Y.; Zhao, Q.; Hellmich, L.; Klos, J.; Scholz, S.; Schreiber, L. R.; Knoch, J. Interface Engineering for Steep Slope Cryogenic MOSFETs. IEEE Electron Device Lett. 2022, 43, 2149– 2152, DOI: 10.1109/LED.2022.3217314There is no corresponding record for this reference.
- 31McCann, E.; Koshino, M. The electronic properties of bilayer graphene. Rep. Prog. Phys. 2013, 76, 056503, DOI: 10.1088/0034-4885/76/5/05650331https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhsVOgurzN&md5=f765883278ab44bbd61386a0db3f3421The electronic properties of bilayer grapheneMcCann, Edward; Koshino, MikitoReports on Progress in Physics (2013), 76 (5), 056503/1-056503/28CODEN: RPPHAG; ISSN:0034-4885. (IOP Publishing Ltd.)We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between at. sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.
- 32Icking, E.; Banszerus, L.; Wörtche, F.; Volmer, F.; Schmidt, P.; Steiner, C.; Engels, S.; Hesselmann, J.; Goldsche, M.; Watanabe, K.; Taniguchi, T.; Volk, C.; Beschoten, B.; Stampfer, C. Transport Spectroscopy of Ultraclean Tunable Band Gaps in Bilayer Graphene. Advanced Electronic Materials 2022, 8, 2200510, DOI: 10.1002/aelm.20220051032https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhvFyhsLjF&md5=c05aefdf53ca0481f5cc318883033779Transport Spectroscopy of Ultraclean Tunable Band Gaps in Bilayer GrapheneIcking, Eike; Banszerus, Luca; Wortche, Frederike; Volmer, Frank; Schmidt, Philipp; Steiner, Corinne; Engels, Stephan; Hesselmann, Jonas; Goldsche, Matthias; Watanabe, Kenji; Taniguchi, Takashi; Volk, Christian; Beschoten, Bernd; Stampfer, ChristophAdvanced Electronic Materials (2022), 8 (11), 2200510CODEN: AEMDBW; ISSN:2199-160X. (Wiley-VCH Verlag GmbH & Co. KGaA)The importance of controlling both the charge carrier d. and the band gap of a semiconductor cannot be overstated, as it opens the doors to a wide range of applications, including, for example, highly-tunable transistors, photodetectors, and lasers. Bernal-stacked bilayer graphene is a unique van-der-Waals material that allows tuning of the band gap by an out-of-plane elec. field. Although the first evidence of the tunable gap is already found 10 years ago, it took until recent to fabricate sufficiently clean heterostructures where the elec. induced gap can be used to fully suppress transport or confine charge carriers. Here, a detailed study of the tunable band gap in gated bilayer graphene characterized by temp.-activated transport and finite-bias spectroscopy measurements is presented. The latter method allows comparing different gate materials and device technologies, which directly affects the disorder potential in bilayer graphene. It is shown that graphite-gated bilayer graphene exhibits extremely low disorder and as good as no subgap states resulting in ultraclean tunable band gaps up to 120 meV. The size of the band gaps are in good agreement with theory and allow complete current suppression making a wide range of semiconductor applications possible.
- 33Varlet, A.; Bischoff, D.; Simonet, P.; Watanabe, K.; Taniguchi, T.; Ihn, T.; Ensslin, K.; Mucha-Kruczyński, M.; Fal’ko, V. I. Anomalous Sequence of Quantum Hall Liquids Revealing a Tunable Lifshitz Transition in Bilayer Graphene. Phys. Rev. Lett. 2014, 113, 116602, DOI: 10.1103/PhysRevLett.113.11660233https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhvVWgsb3F&md5=c29e67b741660b7e6fd9edf7dc0859fdAnomalous sequence of quantum Hall liquids revealing a tunable Lifshitz transition in bilayer grapheneVarlet, Anastasia; Bischoff, Dominik; Simonet, Pauline; Watanabe, Kenji; Taniguchi, Takashi; Ihn, Thomas; Ensslin, Klaus; Mucha-Kruczynski, Marcin; Fal'ko, Vladimir I.Physical Review Letters (2014), 113 (11), 116602/1-116602/5, 5 pp.CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Bilayer graphene is a unique system where both the Fermi energy and the low-energy electron dispersion can be tuned. This is brought about by an interplay between trigonal warping and the band gap opened by a transverse elec. field. Here, we drive the Lifshitz transition in bilayer graphene to exptl. controllable carrier densities by applying a large transverse elec. field to a h-BN-encapsulated bilayer graphene structure. We perform magnetotransport measurements and investigate the different degeneracies in the Landau level spectrum. At low magnetic fields, the observation of filling factors -3 and -6 quantum Hall states reflects the existence of three maxima at the top of the valence-band dispersion. At high magnetic fields, all integer quantum Hall states are obsd., indicating that deeper in the valence band the const. energy contours are singly connected. The fact that we observe ferromagnetic quantum Hall states at odd-integer filling factors testifies to the high quality of our sample. This enables us to identify several phase transitions between correlated quantum Hall states at intermediate magnetic fields, in agreement with the calcd. evolution of the Landau level spectrum. The obsd. evolution of the degeneracies, therefore, reveals the presence of a Lifshitz transition in our system.
- 34Knoch, J.; Richstein, B.; Han, Y.; Jungemann, C.; Icking, E.; Schreiber, L.; Xue, R.; Tu, J.-S.; Gökcel, T.; Neugebauer, J.; Stampfer, C.; Zhao, Q. On the Performance of Low Power Cryogenic Electronics for Scalable Quantum Information Processors. In 2023 IEEE Nanotechnology Materials and Devices Conference (NMDC) , 2023; pp 440– 445. DOI: 10.1109/NMDC57951.2023.10343713There is no corresponding record for this reference.
- 35McCann, E.; Fal’ko, V. I. Landau-Level Degeneracy and Quantum Hall Effect in a Graphite Bilayer. Phys. Rev. Lett. 2006, 96, 086805, DOI: 10.1103/PhysRevLett.96.08680535https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28XitVGqsLw%253D&md5=6274e974dfa7c5e911bfac0a3246f953Landau-Level Degeneracy and Quantum Hall Effect in a Graphite BilayerMcCann, Edward; Fal'ko, Vladimir I.Physical Review Letters (2006), 96 (8), 086805/1-086805/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)We derive an effective two-dimensional Hamiltonian to describe the low-energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase 2π. Its high-magnetic-field Landau-level spectrum consists of almost equidistant groups of fourfold degenerate states at finite energy and eight zero-energy states. This can be translated into the Hall cond. dependence on carrier d., σxy(N), which exhibits plateaus at integer values of 4e2/h and has a double 8e2/h step between the hole and electron gases across zero d., in contrast to (4n+2)e2/h sequencing in a monolayer.
- 36Jung, J.; MacDonald, A. H. Accurate tight-binding models for the π bands of bilayer graphene. Phys. Rev. B 2014, 89, 035405, DOI: 10.1103/PhysRevB.89.035405There is no corresponding record for this reference.
- 37Li, J.; Wang, K.; McFaul, K. J.; Zern, Z.; Ren, Y.; Watanabe, K.; Taniguchi, T.; Qiao, Z.; Zhu, J. Gate-controlled topological conducting channels in bilayer graphene - Nature Nanotechnology. Nat. Nanotechnol. 2016, 11, 1060– 1065, DOI: 10.1038/nnano.2016.158There is no corresponding record for this reference.
- 38Overweg, H.; Knothe, A.; Fabian, T.; Linhart, L.; Rickhaus, P.; Wernli, L.; Watanabe, K.; Taniguchi, T.; Sánchez, D.; Burgdörfer, J.; Libisch, F.; Fal’ko, V. I.; Ensslin, K.; Ihn, T. Topologically Nontrivial Valley States in Bilayer Graphene Quantum Point Contacts. Phys. Rev. Lett. 2018, 121, 257702, DOI: 10.1103/PhysRevLett.121.25770238https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltFWgtLs%253D&md5=18b13328df726742b3f2783bcfd62f5dTopologically Nontrivial Valley States in Bilayer Graphene Quantum Point ContactsOverweg, Hiske; Knothe, Angelika; Fabian, Thomas; Linhart, Lukas; Rickhaus, Peter; Wernli, Lucien; Watanabe, Kenji; Taniguchi, Takashi; Sanchez, David; Burgdorfer, Joachim; Libisch, Florian; Fal'ko, Vladimir I.; Ensslin, Klaus; Ihn, ThomasPhysical Review Letters (2018), 121 (25), 257702CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies with increasing field: at zero magnetic field the degeneracy of quantized one-dimensional subbands is four, because of a twofold spin and a twofold valley degeneracy. By switching on the magnetic field, the valley degeneracy is lifted. Because of the Berry curvature, states from different valleys split linearly in magnetic field. In the quantum Hall regime fourfold degenerate conductance plateaus reemerge. During the adiabatic transition to the quantum Hall regime, levels from one valley shift by two in quantum no. with respect to the other valley, forming an interweaving pattern that can be reproduced by numerical calcns.
- 39Banszerus, L.; Frohn, B.; Fabian, T.; Somanchi, S.; Epping, A.; Müller, M.; Neumaier, D.; Watanabe, K.; Taniguchi, T.; Libisch, F.; Beschoten, B.; Hassler, F.; Stampfer, C. Observation of the Spin-Orbit Gap in Bilayer Graphene by One-Dimensional Ballistic Transport. Phys. Rev. Lett. 2020, 124, 177701, DOI: 10.1103/PhysRevLett.124.17770139https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtVaktrjL&md5=1ec69c1874733b6a462e24ed12552c68Observation of the Spin-Orbit Gap in Bilayer Graphene by One-Dimensional Ballistic TransportBanszerus, L.; Frohn, B.; Fabian, T.; Somanchi, S.; Epping, A.; Mueller, M.; Neumaier, D.; Watanabe, K.; Taniguchi, T.; Libisch, F.; Beschoten, B.; Hassler, F.; Stampfer, C.Physical Review Letters (2020), 124 (17), 177701CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We report on measurements of quantized conductance in gate-defined quantum point contacts in bilayer graphene that allow the observation of subband splittings due to spin-orbit coupling. The size of this splitting can be tuned from 40 to 80μeV by the displacement field. We assign this gate-tunable subband splitting to a gap induced by spin-orbit coupling of Kane-Mele type, enhanced by proximity effects due to the substrate. We show that this spin-orbit coupling gives rise to a complex pattern in low perpendicular magnetic fields, increasing the Zeeman splitting in one valley and suppressing it in the other one. In addn., we observe a spin polarized channel of 6e2/h at high in-plane magnetic field and signatures of interaction effects at the crossings of spin-split subbands of opposite spins at finite magnetic field.
- 40Eich, M.; Pisoni, R.; Pally, A.; Overweg, H.; Kurzmann, A.; Lee, Y.; Rickhaus, P.; Watanabe, K.; Taniguchi, T.; Ensslin, K.; Ihn, T. Coupled Quantum Dots in Bilayer Graphene. Nano Lett. 2018, 18, 5042– 5048, DOI: 10.1021/acs.nanolett.8b0185940https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXht1Ois7jP&md5=3cbe22df7f36e9bc26a956f0c45ebff5Coupled Quantum Dots in Bilayer GrapheneEich, Marius; Pisoni, Riccardo; Pally, Alessia; Overweg, Hiske; Kurzmann, Annika; Lee, Yongjin; Rickhaus, Peter; Watanabe, Kenji; Taniguchi, Takashi; Ensslin, Klaus; Ihn, ThomasNano Letters (2018), 18 (8), 5042-5048CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)Electrostatic confinement of charge carriers in bilayer graphene provides a unique platform for carbon-based spin, charge, or exchange qubits. By exploiting the possibility to induce a band gap with electrostatic gating, the authors form a versatile and widely tunable multiquantum dot system. The authors demonstrate the formation of single, double and triple quantum dots that are free of any sign of disorder. In bilayer graphene, the authors have the possibility to form tunnel barriers using different mechanisms. The authors can exploit the ambipolar nature of bilayer graphene where pn-junctions form natural tunnel barriers. Alternatively, the authors can use gates to form tunnel barriers, where the authors can vary the tunnel coupling by >2 orders of magnitude tuning between a deeply Coulomb blockaded system and a Fabry-P´erot-like cavity. Demonstrating such tunability is an important step toward graphene-based quantum computation.
- 41Banszerus, L.; Frohn, B.; Epping, A.; Neumaier, D.; Watanabe, K.; Taniguchi, T.; Stampfer, C. Gate-Defined Electron–Hole Double Dots in Bilayer Graphene. Nano Lett. 2018, 18, 4785– 4790, DOI: 10.1021/acs.nanolett.8b0130341https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXht1SrtrrP&md5=d757b1265e5dc8b6a9d02b5863ed6684Gate-defined electron-hole double dots in bilayer grapheneBanszerus, L.; Frohn, B.; Epping, A.; Neumaier, D.; Watanabe, K.; Taniguchi, T.; Stampfer, C.Nano Letters (2018), 18 (8), 4785-4790CODEN: NALEFD; ISSN:1530-6984. (American Chemical Society)The authors present gate-controlled single-, double-, and triple-dot operation in electrostatically gapped bilayer graphene. Thanks to the recent advancements in sample fabrication, which include the encapsulation of bilayer graphene in hexagonal boron nitride and the use of graphite gates, it has become possible to electrostatically confine carriers in bilayer graphene and to completely pinch-off current through quantum dot devices. Here, they discuss the operation and characterization of electron-hole double dots. They show a remarkable degree of control of their device, which allows the implementation of two different gate-defined electron-hole double-dot systems with very similar energy scales. In the single-dot regime, they ext. excited state energies and investigate their evolution in a parallel magnetic field, which is in agreement with a Zeeman-spin-splitting expected for a g-factor of 2.
- 42Banszerus, L.; Möller, S.; Hecker, K.; Icking, E.; Watanabe, K.; Taniguchi, T.; Hassler, F.; Volk, C.; Stampfer, C. Particle–hole symmetry protects spin-valley blockade in graphene quantum dots. Nature 2023, 618, 51– 56, DOI: 10.1038/s41586-023-05953-5There is no corresponding record for this reference.
- 43Zhou, H.; Holleis, L.; Saito, Y.; Cohen, L.; Huynh, W.; Patterson, C. L.; Yang, F.; Taniguchi, T.; Watanabe, K.; Young, A. F. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 2022, 375, 774– 778, DOI: 10.1126/science.abm838643https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XkvFyhur0%253D&md5=4a71351373832812ddcff0de4ffa51c6Isospin magnetism and spin-polarized superconductivity in Bernal bilayer grapheneZhou, Haoxin; Holleis, Ludwig; Saito, Yu; Cohen, Liam; Huynh, William; Patterson, Caitlin L.; Yang, Fangyuan; Taniguchi, Takashi; Watanabe, Kenji; Young, Andrea F.Science (Washington, DC, United States) (2022), 375 (6582), 774-778CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)In conventional superconductors, Cooper pairing occurs between electrons of opposite spin. We observe spin-polarized supercond. in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by a large applied perpendicular elec. field. We observe a cascade of electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within the isospin space defined by the combination of the spin and momentum-space valley degrees of freedom. Although all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite magnetic field B‖ ≈ 150 milliteslas applied parallel to the two-dimensional sheet. Supercond. occurs near a symmetry-breaking transition and exists exclusively above the B‖ limit expected of a paramagnetic superconductor with the obsd. transition crit. temp. TC ≈ 30 mK, consistent with a spin-triplet order parameter.
- 44Seiler, A. M.; Geisenhof, F. R.; Winterer, F.; Watanabe, K.; Taniguchi, T.; Xu, T.; Zhang, F.; Weitz, R. T. Quantum cascade of correlated phases in trigonally warped bilayer graphene. Nature 2022, 608, 298– 302, DOI: 10.1038/s41586-022-04937-144https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XitFSjtbfI&md5=ae7d6865b3b069a27bfccef44d5bfc08Quantum cascade of correlated phases in trigonally warped bilayer grapheneSeiler, Anna M.; Geisenhof, Fabian R.; Winterer, Felix; Watanabe, Kenji; Taniguchi, Takashi; Xu, Tianyi; Zhang, Fan; Weitz, R. ThomasNature (London, United Kingdom) (2022), 608 (7922), 298-302CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Divergent d. of states offers an opportunity to explore a wide variety of correlated electron physics. In the thinnest limit, this has been predicted and verified in the ultraflat bands of magic-angle twisted bilayer graphene, the band touching points of few-layer rhombohedral graphite and the lightly doped rhombohedral trilayer graphene. The simpler and seemingly better understood Bernal bilayer graphene is also susceptible to orbital magnetism at charge neutrality leading to layer antiferromagnetic states or quantum anomalous Hall states. Here we report the observation of a cascade of correlated phases in the vicinity of elec.-field-controlled Lifshitz transitions and van Hove singularities in Bernal bilayer graphene. We provide evidence for the observation of Stoner ferromagnets in the form of half and quarter metals. Furthermore, we identify signatures consistent with a topol. non-trivial Wigner-Hall crystal at zero magnetic field and its transition to a trivial Wigner crystal, as well as two correlated metals whose behavior deviates from that of std. Fermi liqs. Our results in this reproducible, tunable, simple system open up new horizons for studying strongly correlated electrons.
- 45de la Barrera, S. C.; Aronson, S.; Zheng, Z.; Watanabe, K.; Taniguchi, T.; Ma, Q.; Jarillo-Herrero, P.; Ashoori, R. Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field. Nat. Phys. 2022, 18, 771– 775, DOI: 10.1038/s41567-022-01616-w45https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhsVGgsbjK&md5=40473d72081abec5779f9c8febfdd553Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic fieldde la Barrera, Sergio C.; Aronson, Samuel; Zheng, Zhiren; Watanabe, Kenji; Taniguchi, Takashi; Ma, Qiong; Jarillo-Herrero, Pablo; Ashoori, RaymondNature Physics (2022), 18 (7), 771-775CODEN: NPAHAX; ISSN:1745-2473. (Nature Portfolio)Abstr.: Emergent phenomena arising from the collective behavior of electrons is expected when Coulomb interactions dominate over the kinetic energy, and one way to create this situation is to reduce the electronic bandwidth. Bernal-stacked bilayer graphene intrinsically supports saddle points in the band structure that are predicted to host a variety of spontaneous symmetry-broken states. Here we show that bilayer graphene displays a cascade of symmetry-broken states with spontaneous spin and valley isospin ordering at zero magnetic field. We independently tune the carrier d. and elec. displacement field to explore the phase space of isospin order. Itinerant ferromagnetic states emerge near the conduction and valence band edges with complete spin and valley polarization. At larger hole densities, twofold degenerate quantum oscillations manifest in an addnl. symmetry-broken state that is enhanced by the application of an in-plane magnetic field. Both symmetry-broken states display enhanced layer polarization, suggesting a coupling to the layer degree of freedom. These states occur in the absence of a moire superlattice and are intrinsic to natural graphene bilayers. Therefore, we demonstrate that bilayer graphene represents a related but distinct approach to produce collective behavior from flat dispersion, complementary to engineered moire structures.
- 46Wang, L.; Meric, I.; Huang, P. Y.; Gao, Q.; Gao, Y.; Tran, H.; Taniguchi, T.; Watanabe, K.; Campos, L. M.; Muller, D. A.; Guo, J.; Kim, P.; Hone, J.; Shepard, K. L.; Dean, C. R. One-Dimensional Electrical Contact to a Two-Dimensional Material. Science 2013, 342, 614– 617, DOI: 10.1126/science.124435846https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXhs1yrs7fJ&md5=de354f7f8a0425d61230545f9afd5e80One-Dimensional Electrical Contact to a Two-Dimensional MaterialWang, L.; Meric, I.; Huang, P. Y.; Gao, Q.; Gao, Y.; Tran, H.; Taniguchi, T.; Watanabe, K.; Campos, L. M.; Muller, D. A.; Guo, J.; Kim, P.; Hone, J.; Shepard, K. L.; Dean, C. R.Science (Washington, DC, United States) (2013), 342 (6158), 614-617CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)Heterostructures based on layering of two-dimensional (2D) materials such as graphene and hexagonal B nitride represent a new class of electronic devices. Realizing this potential, however, depends critically on the ability to make high-quality elec. contact. Here, the authors report a contact geometry in which the authors metalize only the 1-dimensional edge of a 2-dimensional graphene layer. In addn. to outperforming conventional surface contacts, the edge-contact geometry allows a complete sepn. of the layer assembly and contact metalization processes. In graphene heterostructures, this enables high electronic performance, including low-temp. ballistic transport over distances longer than 15 μm, and room-temp. mobility comparable to the theor. phonon-scattering limit. The edge-contact geometry provides new design possibilities for multilayered structures of complimentary 2-dimensional materials.
- 47Purdie, D. G.; Pugno, N. M.; Taniguchi, T.; Watanabe, K.; Ferrari, A. C.; Lombardo, A. Cleaning interfaces in layered materials heterostructures. Nat. Commun. 2018, 9, 1– 12, DOI: 10.1038/s41467-018-07558-347https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhslWju7nJ&md5=37facaed110c8ff3ee8b61ae6d412c37The genomic landscape of cutaneous SCC reveals drivers and a novel azathioprine associated mutational signatureInman, Gareth J.; Wang, Jun; Nagano, Ai; Alexandrov, Ludmil B.; Purdie, Karin J.; Taylor, Richard G.; Sherwood, Victoria; Thomson, Jason; Hogan, Sarah; Spender, Lindsay C.; South, Andrew P.; Stratton, Michael; Chelala, Claude; Harwood, Catherine A.; Proby, Charlotte M.; Leigh, Irene M.Nature Communications (2018), 9 (1), 1-14CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)Cutaneous squamous cell carcinoma (cSCC) has a high tumor mutational burden (50 mutations per megabase DNA pair). Here, we combine whole-exome analyses from 40 primary cSCC tumors, comprising 20 well-differentiated and 20 moderately/poorly differentiated tumors, with accompanying clin. data from a longitudinal study of immunosuppressed and immunocompetent patients and integrate this anal. with independent gene expression studies. We identify commonly mutated genes, copy no. changes and altered pathways and processes. Comparisons with tumor differentiation status suggest events which may drive disease progression. Mutational signature anal. reveals the presence of a novel signature (signature 32), whose incidence correlates with chronic exposure to the immunosuppressive drug azathioprine. Characterization of a panel of 15 cSCC tumor-derived cell lines reveals that they accurately reflect the mutational signatures and genomic alterations of primary tumors and provide a valuable resource for the validation of tumor drivers and therapeutic targets.
- 48Novoselov, K. S.; Geim, A. K.; Morozov, S.; Jiang, D.; Zhang, Y.; Dubonos, S.; Grigorieva, I.; Firsov, A. Electric field effect in atomically thin carbon films. Science 2004, 306, 666– 669, DOI: 10.1126/science.110289648https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXos1Kqt70%253D&md5=488da13500bf24e8fc419052dc1a9e84Electric Field Effect in Atomically Thin Carbon FilmsNovoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A.Science (Washington, DC, United States) (2004), 306 (5696), 666-669CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)The authors describe monocryst. graphitic films, which are a few atoms thick but are nonetheless stable under ambient conditions, metallic, and of remarkably high quality. The films are a two-dimensional semimetal with a tiny overlap between valence and conductance bands, and they exhibit a strong ambipolar elec. field effect such that electrons and holes in concns. up to 1013 per square centimeter and with room-temp. mobilities of ∼10,000 square centimeters per V-second can be induced by applying gate voltage.
- 49Zhao, Y.; Cadden-Zimansky, P.; Jiang, Z.; Kim, P. Symmetry Breaking in the Zero-Energy Landau Level in Bilayer Graphene. Phys. Rev. Lett. 2010, 104, 066801, DOI: 10.1103/PhysRevLett.104.06680149https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXisFOhsrk%253D&md5=9053c258add9d6a1d3cd553ba0c5653eSymmetry Breaking in the Zero-Energy Landau Level in Bilayer GrapheneZhao, Y.; Cadden-Zimansky, P.; Jiang, Z.; Kim, P.Physical Review Letters (2010), 104 (6), 066801/1-066801/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)The quantum Hall effect near the charge neutrality point in bilayer graphene is investigated in high magnetic fields of up to 35 T using electronic transport measurements. In the high-field regime, the eightfold degeneracy in the zero-energy Landau level is completely lifted, exhibiting new quantum Hall states corresponding to filling factors ν=0, 1, 2, and 3. Measurements of the activation energy gaps for the ν=2 and 3 filling factors in tilted magnetic fields exhibit no appreciable dependence on the in-plane magnetic field, suggesting that these Landau level splittings are independent of spin. In addn., measurements taken at the ν=0 charge neutral point show that, similar to single layer graphene, the bilayer becomes insulating at high fields.
- 50Sonntag, J.; Reichardt, S.; Wirtz, L.; Beschoten, B.; Katsnelson, M. I.; Libisch, F.; Stampfer, C. Impact of Many-Body Effects on Landau Levels in Graphene. Phys. Rev. Lett. 2018, 120, 187701, DOI: 10.1103/PhysRevLett.120.18770150https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltV2jur0%253D&md5=351198c4e10e15d11b74eef91b600e67Impact of Many-Body Effects on Landau Levels in GrapheneSonntag, J.; Reichardt, S.; Wirtz, L.; Beschoten, B.; Katsnelson, M. I.; Libisch, F.; Stampfer, C.Physical Review Letters (2018), 120 (18), 187701CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier d.-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magnetophonon resonances, we ext. the charge carrier d. dependence of the Landau level transition energies and the assocd. effective Fermi velocity vF. In contrast to the logarithmic divergence of vF at zero magnetic field, we find a piecewise linear scaling of vF as a function of the charge carrier d., due to a magnetic-field-induced suppression of the long-range Coulomb interaction. We quant. confirm our exptl. findings by performing tight-binding calcns. on the level of the Hartree-Fock approxn., which also allow us to est. an excitonic binding energy of ≈6 meV contained in the exptl. extd. Landau level transitions energies.
- 51Schmitz, M.; Ouaj, T.; Winter, Z.; Rubi, K.; Watanabe, K.; Taniguchi, T.; Zeitler, U.; Beschoten, B.; Stampfer, C. Fractional quantum Hall effect in CVD-grown graphene. 2D Mater. 2020, 7, 041007, DOI: 10.1088/2053-1583/abae7b51https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXit1Sqs73N&md5=a873725d115bc9f1fc490a278ea3f841Fractional quantum Hall effect in CVD-grown grapheneSchmitz, M.; Ouaj, T.; Winter, Z.; Rubi, K.; Watanabe, K.; Taniguchi, T.; Zeitler, U.; Beschoten, B.; Stampfer, C.2D Materials (2020), 7 (4), 041007CODEN: DMATB7; ISSN:2053-1583. (IOP Publishing Ltd.)A review. We show the emergence of fractional quantum Hall states in graphene grown by chem. vapor deposition (CVD) for magnetic fields from below 3 T to 35 T where the CVD-graphene was dry-transferred. Effective composite-fermion filling factors up to ν* = 4 are visible and higher order composite-fermion states (with four flux quanta attached) start to emerge at the highest fields. Our results show that the quantum mobility of CVD-grown graphene is comparable to that of exfoliated graphene and, more specifically, that the p/3 fractional quantum Hall states have energy gaps of up to 30 K, well comparable to those obsd. in other silicon-gated devices based on exfoliated graphene.
- 52Varlet, A.; Mucha-Kruczyński, M.; Bischoff, D.; Simonet, P.; Taniguchi, T.; Watanabe, K.; Fal’ko, V.; Ihn, T.; Ensslin, K. Tunable Fermi surface topology and Lifshitz transition in bilayer graphene. Synth. Met. 2015, 210, 19– 31, DOI: 10.1016/j.synthmet.2015.07.00652https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXht1Omt7nF&md5=adc2bdb8b5b2aea90eb7a1f93350c39dTunable Fermi surface topology and Lifshitz transition in bilayer grapheneVarlet, Anastasia; Mucha-Kruczynski, Marcin; Bischoff, Dominik; Simonet, Pauline; Taniguchi, Takashi; Watanabe, Kenji; Fal'ko, Vladimir; Ihn, Thomas; Ensslin, KlausSynthetic Metals (2015), 210 (Part_A), 19-31CODEN: SYMEDZ; ISSN:0379-6779. (Elsevier B.V.)Bilayer graphene is a highly tunable material: not only can one tune the Fermi energy using std. gates, as in single-layer graphene, but the band structure can also be modified by external perturbations such as transverse elec. fields or strain. We review the theor. basics of the band structure of bilayer graphene and study the evolution of the band structure under the influence of these two external parameters. We highlight their key role concerning the ease to exptl. probe the presence of a Lifshitz transition, which consists in a change of Fermi contour topol. as a function of energy close to the edges of the conduction and valence bands. Using a device geometry that allows the application of exceptionally high displacement fields, we then illustrate in detail the way to probe the topol. changes exptl. using quantum Hall effect measurements in a gapped bilayer graphene system.
- 53Han, Y.; Sun, J.; Bae, J.-H.; Grützmacher, D.; Knoch, J.; Zhao, Q.-T. High Performance 5 nm Si Nanowire FETs with a Record Small SS = 2.3 mV/dec and High Transconductance at 5.5 K Enabled by Dopant Segregated Silicide Source/Drain. In 2023 IEEE Symposium on VLSI Technology and Circuits (VLSI Technology and Circuits) , 2023; pp 1– 2. DOI: 10.23919/VLSITechnologyandCir57934.2023.10185373There is no corresponding record for this reference.
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Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.4c02463.
Equations used to calculate the band gap and band structure in bilayer graphene as a function of the displacement field, additional information for the first sample, comparable data for a second device, and the drain-current traces for the BLG devices with Au top gate and additional Al2O3 dielectric (PDF)
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