Pith. sign in

REVIEW 5 major objections 4 minor 75 references

Pressure-Driven Moir\'e Potential Enhancement and Tertiary Gap Opening in Graphene/h-BN Heterostructure

T0 review · 5 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Pressure up to 9 GPa doubles the moiré gap and opens a third

desk verdict A real technical advance: DAC transport in encapsulated moiré devices to ~9 GPa, with the first evidence for a pressure-induced tertiary gap; the bandwidth-suppression claim leans on a constant-tau assumption that needs checking. read the letter →

arxiv 2507.20637 v1 pith:DYJTSZJ6 submitted 2025-07-28 cond-mat.str-el cond-mat.mes-hall

Yupeng Wang , Jiaqi An , Chunhui Ye , Xiangqi Wang , Di Mai , Hongze Zhao , Yang Zhang , Chiyu Peng
show 8 more authors
Kenji Watanabe Takashi Taniguchi Xiaoyu Sun Rucheng Dai Zhongping Wang Wei Qin Zhenhua Qiao Zengming Zhang
This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hall PACS 73.22.Pr73.63.-b62.50.-p
keywords moirésuperlatticegraphene/h-BNheterostructurehydrostaticpressurediamondanvilcellband-gaptuningtertiaryDiracpointflatbandsvanderWaals
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that hydrostatic pressure can serve as a continuous, in situ knob for the moiré potential in graphene/hexagonal boron nitride devices, reaching roughly 9 GPa—pressures previously inaccessible for encapsulated moiré devices. In aligned graphene/h-BN, pressure strengthens the moiré potential: the first valence band narrows, and the primary gap at charge neutrality nearly doubles, from about 25 meV at 0.4 GPa to about 49 meV at 5.1 GPa. The paper also reports the first observation of a gap at the tertiary Dirac point, emerging above roughly 5–6 GPa, in agreement with its fully relaxed tight-binding calculation. If correct, this gives moiré systems a new tuning axis—pressure—that changes potential strength without changing twist angle, and it opens a route to flat-band and correlation physics in alignment regimes that are otherwise too dispersive.

What carries the argument

The experimental load-bearing piece is a diamond-anvil-cell platform that combines a transfer-after-fabrication method—prefabricated encapsulated devices are placed onto the diamond anvil—with transferred gold electrodes, enabling four-terminal transport at up to roughly 9 GPa, below 2 K, and in magnetic fields above 9 T. The theoretical load-bearing piece is a two-stage calculation: a large-scale atomistic relaxation simulation with registry-dependent interlayer potentials gives the pressure-dependent out-of-plane corrugation and in-plane strain, and a tight-binding model on the relaxed structure produces the moiré bands. The quantities that carry the argument are the primary, secondary, and tertiary Dirac points—the carrier densities where resistance peaks mark superlattice gaps—and the widths of the first three moiré valence bands. Pressure reduces interlayer spacing, which enhances interlayer coupling and strain, narrowing the first valence bandwidth from about 140 meV to 50 meV and lifting the overlap between the second and third valence bands to open the tertiary gap.

What would settle it

Measure the quantum oscillation (Shubnikov–de Haas) amplitude or Dingle temperature as a function of pressure in the same device: if the effective mass extracted from the oscillation envelope does not rise with the resistance, the bandwidth-suppression interpretation fails. For the tertiary gap, look for an activated conductivity plateau and a Landau fan that pins the gap to the tertiary Dirac point at a fixed density across different magnetic fields and gate configurations; a resistance peak without a corresponding activated gap or Hall signature would rule it out.

Watch

Extended reading notes

Core claim

On its own terms, the paper demonstrates that pressure substantially enhances the moiré potential strength in aligned graphene/h-BN heterostructures. The evidence is threefold: the resistance at fixed carrier density grows with pressure, which the authors read through the Drude relation as an increasing effective mass and hence a narrower first valence band; the primary Dirac gap measured by activated transport rises from about 25 meV at 0.4 GPa to about 49 meV at 5.1 GPa; and a new resistance peak appears at a hole density near $-5.6\times10^{12}\,\mathrm{cm}^{-2}$ above roughly 5–6 GPa, which the authors identify as a gap at the tertiary Dirac point. A fully relaxed tight-binding calculation reproduces the pressure evolution of the primary and secondary gaps and shows that the tertiary gap appears when the second and third moiré valence bands stop overlapping. The paper claims this is the first observation of the tertiary gap and the first quantum transport study of a moiré device at pressures up to the structural phase-transition threshold of the h-BN encapsulation layers.

Load-bearing premise

The central inference assumes that the scattering time stays constant under pressure, so a pressure-induced rise in resistance directly means a heavier carrier and a narrower band; it also assumes the resistance peak at the tertiary density is a genuine bulk band gap rather than a gating or contact artifact.

Editorial extensions

If this is right

  • Within a single device, pressure can sweep the moiré potential strength continuously, avoiding the cross-sample disorder that limits twist-angle comparisons.
  • The primary gap nearly doubles by about 5 GPa, so pressure can strengthen the inversion-symmetry-breaking gap without rebuilding the stack.
  • A gap opens at the tertiary Dirac point above roughly 5–6 GPa, with size about 8–12 meV at 6.4–7.6 GPa, confirming the theoretical prediction that band overlap between the second and third valence bands is lifted.
  • The calculation predicts the tertiary gap appears only for twist angles from 0° to 0.7°, with the critical pressure rising from about 3 GPa at 0° to about 9 GPa at 0.7°, giving a pressure–twist phase diagram.
  • At 8.2 GPa the third valence band flattens to about 15 meV while the tertiary gap is open, so the same device hosts both a gap and an ultraflat band, a promising setting for correlated states.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct test of the constant-scattering-time assumption would be to extract the effective mass from Shubnikov–de Haas oscillation amplitudes under pressure; if the mass does not track the resistance rise, the strength of the claimed moiré-potential enhancement would need to be revised.
  • The same diamond-anvil platform should transfer to twisted bilayer graphene and twisted transition-metal dichalcogenides, where pressure could tune interlayer tunneling ratios and Berry curvature; the paper leaves those applications as outlook rather than demonstration.
  • The predicted twist-angle window for the tertiary gap suggests a systematic pressure–twist matrix could map where flat coexisting bands appear, which is an interpolation of the paper's phase diagram rather than its data.
  • The near-doubling of the primary gap implies the inversion-breaking mass term grows substantially with pressure; one consequence, hinted at but not measured here, is that the Berry curvature and possibly the topological character of the moiré bands change across this pressure range.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 4 minor

Summary. The manuscript reports high-pressure (up to ~9 GPa) quantum transport measurements on h-BN-encapsulated monolayer graphene aligned to a top h-BN layer, forming a graphene/h-BN moiré superlattice. The authors present a new DAC-based technique with transferred electrodes and claim that pressure continuously tunes the moiré potential: the longitudinal resistance at fixed carrier density rises (interpreted as bandwidth suppression), the primary gap approximately doubles from ~25 meV to ~49 meV, the secondary gap starts to increase above ~2.5 GPa, and a tertiary gap opens at the tertiary Dirac point above 5.1 GPa (Device 2) or 2.8 GPa (Device 3), in agreement with a fully relaxed tight-binding calculation that was not fitted to the experimental gaps.

Significance. If the claims hold, this is a significant experimental advance: it extends pressure-tuned quantum transport in moiré devices to ~9 GPa, demonstrates a reversible in situ knob for moiré band structure without changing twist angle, and reports the first observation of the tertiary gap predicted by Lin, Zhu, and Ni (Ref. [36]). A clear strength is that the theoretical band-structure calculations use a fully relaxed LAMMPS structure and tight-binding parameters from prior literature, so the comparison with experiment is a genuine test of a published prediction rather than a fit. The control device (Device 1) shows that pressure alone does not strongly affect transport in a misaligned monolayer, supporting the methodology. The paper is nevertheless not yet fully convincing because the experimental evidence for bandwidth suppression rests on an unverified constant-τ assumption, the abstract and body disagree on the tertiary-gap pressure threshold, and the raw data and many details are not included in the preprint.

major comments (5)
  1. [After Fig. 2 (Drude argument)] The claim that the pressure-induced increase of Rxx at fixed carrier density demonstrates 'suppression of the first valence bandwidth' rests on the assumption that τ remains unchanged under pressure, stated in the text as 'it is reasonable to assume that τ remains unchanged at different pressures.' This assumption is load-bearing: in an aligned device, pressure modifies interlayer coupling, lattice relaxation, strain, and potentially contact resistance, all of which can alter τ. Device 1 is a helpful control but not dispositive, because the aligned devices undergo exactly the pressure-sensitive structural changes that can affect scattering. A direct measurement of τ (for example, from the temperature dependence of quantum oscillations or from Hall mobility) is needed to support the bandwidth-suppression interpretation; without it, the experimental evidence for moiré potential enhancement should be based on the gap data.
  2. [Abstract vs. main text (Device 2/3 thresholds)] The abstract reports a tertiary gap 'emerging above 6.4 GPa,' while the main text states that the third resistive peak appears 'when the applied pressure exceeds 5.1 GPa' for Device 2 and that Device 3 shows the peak at 2.8 GPa. These statements may refer to different quantities (peak emergence versus Arrhenius gap extraction) and different devices, but as written they conflict. Please reconcile the abstract with the device-specific thresholds and state explicitly which pressure corresponds to the 'first observation' claim.
  3. [Fig. 3(d) and surrounding text] The text says the calculated primary and secondary gaps 'increase monotonically with increasing pressure' and are 'comparable with the experimental findings,' yet the experimental ΔS is reported to remain near 20 meV up to 2.5 GPa before rising. If the theory does not capture the low-pressure plateau, the word 'comparable' is too strong; if it does, the comparison should be shown explicitly in Fig. 3(d). This matters because the claimed consistency between theory and experiment is part of the evidence that the relaxed tight-binding model correctly describes the pressure dependence.
  4. [Supplemental Material [48]] The manuscript repeatedly refers to the Supplemental Material for raw data, capacitive analysis, device fabrication parameters, and details of the theoretical model, but the SM is not included with the preprint. Since the quantitative claims—gap values, vHS positions, and the band-structure comparison—depend on those details, the paper as posted cannot be fully checked. Please make the SM available and ensure it contains the full device parameters, pressure calibration procedure, and raw Arrhenius and Landau-fan data.
  5. [Fig. 2(c) and Fig. 3(c)] The attribution of the third resistive peak to a bulk gap at the tertiary Dirac point is based on the Arrhenius activation gap and the brief statement that the Landau fan 'reveals high-resistivity states at TDP.' Because this is the first observation of the tertiary gap, the Landau-fan evidence should be presented in more detail—for example, with fan diagrams over a wider range of carrier density and magnetic field, and with the high-resistivity state clearly distinguished from nearby Landau-level crossings or contact artifacts. A quantitative fan-index analysis would considerably strengthen the claim.
minor comments (4)
  1. [Pressure medium (Fig. 1 caption)] The pressure-transmitting medium is described only as 'oil'; please specify its composition and the pressure calibration method (e.g., ruby fluorescence), because many oils are not hydrostatic at pressures approaching 9 GPa.
  2. [Fig. 2(c) (vHS positions)] The vHS carrier densities are read from Hall-sign changes at 0.5 T; please state the criterion used to assign the vHS and provide the estimated uncertainty in the quoted values.
  3. [Abstract] The phrase 'achieving the ultimate pressure limit (~9 GPa)' is vague; consider specifying that this approaches the phase-transition threshold of the h-BN encapsulation layers.
  4. [Fig. 4(g) caption] The caption defines red, pink, and blue experimental symbols, but the relationship to Devices 2 and 3 is not given; please identify which symbols correspond to which device and pressure.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the theory is parameter-free with literature inputs, the experimental gaps are measured independently, and the tertiary-gap observation tests an external prediction.

full rationale

The paper's central claims are supported by a derivation chain that is not circular. The experimental gaps at the primary, secondary, and tertiary Dirac points are obtained from Arrhenius activation analysis and Landau-fan measurements, not from the theoretical model. The theoretical band structures are computed from fully relaxed LAMMPS structures using interlayer potentials and tight-binding parameters taken from prior literature, with no fitting to the experimental gap values; the comparison in Fig. 3(d) is therefore a genuine prediction-versus-experiment test. The tertiary gap was predicted in Ref. [36] by different authors, and the present observation tests that external prediction rather than importing it from the present authors' prior work. The main inferential weakness is the assumption that the scattering time τ is pressure-independent when interpreting Rxx increases as effective-mass growth; this is a modeling assumption that could fail under pressure-induced disorder or strain changes, but it is not a circular reduction of the conclusion to its inputs, and the gap data provide independent evidence. No self-citation is load-bearing, and no fitted parameter is renamed as a prediction. The manuscript is self-contained against external benchmarks, so the circularity score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claims rest on standard transport assumptions and established models. The most fragile premise is the pressure independence of the scattering time, which is explicitly stated but not tested. The theory uses force fields and tight-binding parameters from prior literature, so the model is not fully self-contained but is not fitted to the present data. No new physical entities are introduced.

assumptions (5)
  • domain assumption Arrhenius analysis: conductivity at the Dirac point is thermally activated with a single gap, allowing linear fits in ln(sigma) versus 1/T.
    Used to extract primary, secondary, and tertiary gaps in Fig. 3; assumes no variable-range hopping or parallel conduction channel dominates in the fit window.
  • domain assumption The scattering time tau is pressure-independent when resistance increases are interpreted as effective mass increases.
    Explicitly stated after Fig. 2(a); this is load-bearing for the bandwidth-suppression evidence, but it is not directly validated.
  • domain assumption The resistive peak near n = -5.6 x 10^12 cm^-2 corresponds to a bulk band gap at the tertiary Dirac point.
    Used to define Delta_T; supported by high-resistivity states in the Landau fan, but no independent gap probe such as tunneling is reported.
  • domain assumption Classical force fields and the tight-binding model from prior literature correctly describe lattice relaxation and electronic structure up to 9 GPa.
    The theoretical predictions in Figs. 3(d) and 4 depend on Kolmogorov-Crespi, REBO, and other potentials; no in-situ structural validation under pressure is provided.
  • domain assumption The oil pressure medium remains hydrostatic and the pressure calibration is accurate down to 2 K.
    All pressure claims rely on this; it is standard practice in DAC experiments but not independently verified in the main text.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Pressure-Driven Moir\'e Potential Enhancement and Tertiary Gap Opening in Graphene/h-BN Heterostructure." pith.science (2026). https://pith.science/paper/DYJTSZJ6

@misc{pith2026250720637,
  author       = {Pith},
  title        = {Pith review of: Pressure-Driven Moir\'e Potential Enhancement and Tertiary Gap Opening in Graphene/h-BN Heterostructure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DYJTSZJ6}},
  note         = {Machine review of arXiv:2507.20637}
}
read the original abstract

Moir\'e superlattices enable engineering of correlated quantum states through tunable periodic potentials, where twist angle controls periodicity but dynamic potential strength modulation remains challenging. Here, we develop a high-pressure quantum transport technique for van der Waals heterostructures, achieving the ultimate pressure limit (~9 GPa) in encapsulated moir\'e devices. In aligned graphene/h-BN, we demonstrate that pressure induces a substantial enhancement of the moir\'e potential strength, evidenced by the suppression of the first valence bandwidth and the near-doubling of the primary band gap. Moreover, we report the first observation of a tertiary gap emerging above 6.4 GPa, verifying theoretical predictions. Our results establish hydrostatic pressure as a universal parameter to reshape moir\'e band structures. By enabling quantum transport studies at previously inaccessible pressure regimes, this Letter expands the accessible parameter space for exploring correlated phases in moir\'e systems.

Figures

Figures reproduced from arXiv: 2507.20637 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Left: Prefabricated device on a Si/SiO [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Longitudinal resistance [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Arrhenius plots of the conductivity [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Pressure dependence of the interlayer distance, where the color bar denotes the magnitude of the in-plane strain. (b) [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

75 extracted references · 64 canonical work pages

  1. [36]

    X. Lin, H. Zhu, and J. Ni, High pressure induced sec- ondary and tertiary gaps in relaxed graphene on hexago- nal boron nitride, Physical Review B 105, 075424 (2022)

    work page 2022

  2. [1]

    Lopes dos Santos, N

    J. Lopes dos Santos, N. Peres, and A. Castro Neto, Graphene bilayer with a twist: Electronic structure, Physical Review Letters 99, 256802 (2007)

    2007

  3. [2]

    Su´ arez Morell, J

    E. Su´ arez Morell, J. Correa, P. Vargas, M. Pacheco, and Z. Barticevic, Flat bands in slightly twisted bilayer graphene: Tight-binding calculations, Physical Review B 82, 121407 (2010)

    work page 2010

  4. [3]

    Bistritzer and A

    R. Bistritzer and A. H. MacDonald, Moir´ e bands in twisted double-layer graphene, Proceedings of the Na- tional Academy of Sciences 108, 12233 (2011)

    2011

  5. [4]

    J. Jung, A. Raoux, Z. Qiao, and A. H. MacDonald, Ab initio theory of moir´ e superlattice bands in layered two- dimensional materials, Physical Review B 89, 205414 (2014)

    work page 2014

  6. [5]

    Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional super- conductivity in magic-angle graphene superlattices, Na- ture 556, 43 (2018)

    2018

  7. [6]

    Z. Hao, A. Zimmerman, P. Ledwith, E. Khalaf, D. H. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishwanath, and P. Kim, Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene, Science 371, 1133 (2021)

    2021

  8. [7]

    J. M. Park, Y. Cao, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Tunable strongly coupled supercon- ductivity in magic-angle twisted trilayer graphene, Na- ture 590, 249 (2021)

    2021

Show all 75 references
  1. [8]

    H. Kim, Y. Choi, C. Lewandowski, A. Thomson, Y. Zhang, R. Polski, K. Watanabe, T. Taniguchi, J. Al- icea, and S. Nadj-Perge, Evidence for unconventional su- perconductivity in twisted trilayer graphene, Nature606, 6 494 (2022)

    2022

  2. [9]

    J. M. Park, Y. Cao, L.-Q. Xia, S. Sun, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Robust supercon- ductivity in magic-angle multilayer graphene family, Na- ture Materials 21, 877 (2022)

    2022

  3. [10]

    Y. Xia, Z. Han, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Superconductivity in twisted bilayer WSe 2, Nature 637, 833 (2025)

    2025

  4. [11]

    Y. Guo, J. Pack, J. Swann, L. Holtzman, M. Cothrine, K. Watanabe, T. Taniguchi, D. G. Mandrus, K. Barmak, J. Hone, et al., Superconductivity in 5.0 ° twisted bilayer WSe2, Nature 637, 839 (2025)

    2025

  5. [12]

    Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, et al., Correlated insulator be- haviour at half-filling in magic-angle graphene superlat- tices, Nature 556, 80 (2018)

    2018

  6. [13]

    S. Xu, M. M. Al Ezzi, N. Balakrishnan, A. Garcia-Ruiz, B. Tsim, C. Mullan, J. Barrier, N. Xin, B. A. Piot, T. Taniguchi, et al., Tunable van hove singularities and correlated states in twisted monolayer–bilayer graphene, Nature Physics 17, 619 (2021)

    2021

  7. [14]

    C. Shen, Y. Chu, Q. Wu, N. Li, S. Wang, Y. Zhao, J. Tang, J. Liu, J. Tian, K. Watanabe, et al., Corre- lated states in twisted double bilayer graphene, Nature Physics 16, 520 (2020)

    2020

  8. [15]

    M. He, Y. Li, J. Cai, Y. Liu, K. Watanabe, T. Taniguchi, X. Xu, and M. Yankowitz, Symmetry breaking in twisted double bilayer graphene, Nature Physics 17, 26 (2021)

    2021

  9. [16]

    F. Wu, Q. Xu, Q. Wang, Y. Chu, L. Li, J. Tang, J. Liu, J. Tian, Y. Ji, L. Liu,et al., Giant correlated gap and pos- sible room-temperature correlated states in twisted bi- layer MoS2 , Physical Review Letters 131, 256201 (2023)

    2023

  10. [17]

    Huang, T

    X. Huang, T. Wang, S. Miao, C. Wang, Z. Li, Z. Lian, T. Taniguchi, K. Watanabe, S. Okamoto, D. Xiao, et al., Correlated insulating states at fractional fillings of the WS2/WSe2 moir´ e lattice, Nature Physics17, 715 (2021)

    2021

  11. [18]

    Wang, E.-M

    L. Wang, E.-M. Shih, A. Ghiotto, L. Xian, D. A. Rhodes, C. Tan, M. Claassen, D. M. Kennes, Y. Bai, B. Kim, et al., Correlated electronic phases in twisted bilayer transition metal dichalcogenides, Nature Materials 19, 861 (2020)

    2020

  12. [19]

    Ghiotto, E.-M

    A. Ghiotto, E.-M. Shih, G. S. Pereira, D. A. Rhodes, B. Kim, J. Zang, A. J. Millis, K. Watanabe, T. Taniguchi, J. C. Hone, et al., Quantum criticality in twisted transi- tion metal dichalcogenides, Nature 597, 345 (2021)

    2021

  13. [20]

    Y. Tang, L. Li, T. Li, Y. Xu, S. Liu, K. Bar- mak, K. Watanabe, T. Taniguchi, A. H. MacDonald, J. Shan, et al., Simulation of hubbard model physics in WSe2/WS2 moir´ e superlattices, Nature579, 353 (2020)

    2020

  14. [21]

    T. Li, S. Jiang, L. Li, Y. Zhang, K. Kang, J. Zhu, K. Watanabe, T. Taniguchi, D. Chowdhury, L. Fu,et al., Continuous mott transition in semiconductor moir´ e su- perlattices, Nature 597, 350 (2021)

    2021

  15. [22]

    T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. De- vakul, K. Watanabe, T. Taniguchi, L. Fu, et al., Quan- tum anomalous hall effect from intertwined moir´ e bands, Nature 600, 641 (2021)

    2021

  16. [23]

    Serlin, C

    M. Serlin, C. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, and A. Young, Intrinsic quantized anomalous hall effect in a moir´ e het- erostructure, Science 367, 900 (2020)

    2020

  17. [24]

    H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, et al., Observa- tion of fractionally quantized anomalous hall effect, Na- ture 622, 74 (2023)

    2023

  18. [25]

    F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, et al., Observation of integer and fractional quantum anomalous hall effects in twisted bilayer MoTe2, Physical Review X 13, 031037 (2023)

    2023

  19. [26]

    Anderson, F.-R

    E. Anderson, F.-R. Fan, J. Cai, W. Holtzmann, T. Taniguchi, K. Watanabe, D. Xiao, W. Yao, and X. Xu, Programming correlated magnetic states with gate-controlled moir´ e geometry, Science381, 325 (2023)

    2023

  20. [27]

    Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Kn¨ uppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Integer and fractional chern insulators in twisted bilayer MoTe2 , arXiv preprint arXiv:2305.00973 (2023)

    2023 arXiv

  21. [28]

    Z. Ji, H. Park, M. E. Barber, C. Hu, K. Watanabe, T. Taniguchi, J.-H. Chu, X. Xu, and Z.-X. Shen, Lo- cal probe of bulk and edge states in a fractional chern insulator, Nature 635, 578 (2024)

    2024

  22. [29]

    Yankowitz, J

    M. Yankowitz, J. Jung, E. Laksono, N. Leconte, B. L. Chittari, K. Watanabe, T. Taniguchi, S. Adam, D. Graf, and C. R. Dean, Dynamic band-structure tuning of graphene moir´ e superlattices with pressure, Nature557, 404 (2018)

    2018

  23. [30]

    Y. Gao, X. Lin, T. Smart, P. Ci, K. Watanabe, T. Taniguchi, R. Jeanloz, J. Ni, and J. Wu, Band en- gineering of large-twist-angle graphene/h-BN moir´ e su- perlattices with pressure, Physical Review Letters 125, 226403 (2020)

    2020

  24. [31]

    Szentp´ eteri, P

    B. Szentp´ eteri, P. Rickhaus, F. K. de Vries, A. M´ arffy, B. Fulop, E. T´ ov´ ari, K. Watanabe, T. Taniguchi, A. Korm´ anyos, S. Csonka, et al., Tailoring the band structure of twisted double bilayer graphene with pres- sure, Nano Letters 21, 8777 (2021)

    2021

  25. [32]

    Yankowitz, S

    M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watan- abe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Tuning superconductivity in twisted bilayer graphene, Science 363, 1059 (2019)

    2019

  26. [33]

    S. Carr, S. Fang, P. Jarillo-Herrero, and E. Kaxiras, Pres- sure dependence of the magic twist angle in graphene superlattices, Physical Review B 98, 085144 (2018)

    2018

  27. [34]

    B. L. Chittari, N. Leconte, S. Javvaji, and J. Jung, Pres- sure induced compression of flatbands in twisted bilayer graphene, Electronic Structure 1, 015001 (2018)

    2018

  28. [35]

    X. Lin, H. Zhu, and J. Ni, Pressure-induced gap modu- lation and topological transitions in twisted bilayer and twisted double bilayer graphene, Physical Review B 101, 155405 (2020)

    2020

  29. [37]

    Morales-Dur´ an, J

    N. Morales-Dur´ an, J. Wang, G. R. Schleder, M. Angeli, Z. Zhu, E. Kaxiras, C. Repellin, and J. Cano, Pressure- enhanced fractional chern insulators along a magic line in moir´ e transition metal dichalcogenides, Physical Review Research 5, L032022 (2023)

    2023

  30. [38]

    Brzezi´ nska, S

    M. Brzezi´ nska, S. Grytsiuk, M. R¨ osner, M. Gibertini, and L. Rademaker, Pressure-tuned many-body phases through Γ-K valleytronics in moir´ e bilayer WSe2, 2D Ma- terials 12, 015003 (2024)

    2024

  31. [39]

    Y. Gao, Q. Xu, M. U. Farooq, L. Xian, and L. Huang, Switching the moir´ e lattice models in the twisted bi- layer WSe2 by strain or pressure, Nano Letters 23, 7921 (2023). 7

    2023

  32. [40]

    Y. Chen, F. Ke, P. Ci, C. Ko, T. Park, S. Saremi, H. Liu, Y. Lee, J. Suh, L. W. Martin, et al., Pressurizing field- effect transistors of few-layer MoS 2 in a diamond anvil cell, Nano Letters 17, 194 (2017)

    2017

  33. [41]

    S. Saha, D. Muthu, D. Golberg, C. Tang, C. Zhi, Y. Bando, and A. Sood, Comparative high pressure ra- man study of boron nitride nanotubes and hexagonal boron nitride, Chemical Physics Letters 421, 86 (2006)

    2006

  34. [42]

    F. Ke, Y. Chen, K. Yin, J. Yan, H. Zhang, Z. Liu, J. S. Tse, J. Wu, H.-k. Mao, and B. Chen, Large bandgap of pressurized trilayer graphene, Proceedings of the Na- tional Academy of Sciences 116, 9186 (2019)

    2019

  35. [43]

    L. Wang, I. Meric, P. Huang, Q. Gao, Y. Gao, H. Tran, T. Taniguchi, K. Watanabe, L. Campos, D. Muller,et al., One-dimensional electrical contact to a two-dimensional material, Science 342, 614 (2013)

    2013

  36. [44]

    Pizzocchero, L

    F. Pizzocchero, L. Gammelgaard, B. S. Jessen, J. M. Caridad, L. Wang, J. Hone, P. Bøggild, and T. J. Booth, The hot pick-up technique for batch assembly of van der waals heterostructures, Nature Communications7, 11894 (2016)

    2016

  37. [45]

    D. G. Purdie, N. Pugno, T. Taniguchi, K. Watanabe, A. Ferrari, and A. Lombardo, Cleaning interfaces in lay- ered materials heterostructures, Nature Communications 9, 5387 (2018)

    2018

  38. [46]

    Amontree, X

    J. Amontree, X. Yan, C. S. DiMarco, P. L. Levesque, T. Adel, J. Pack, M. Holbrook, C. Cupo, Z. Wang, D. Sun, et al. , Reproducible graphene synthesis by oxygen-free chemical vapour deposition, Nature 630, 636 (2024)

    2024

  39. [47]

    N. Xin, J. Lourembam, P. Kumaravadivel, A. Kazant- sev, Z. Wu, C. Mullan, J. Barrier, A. A. Geim, I. Grig- orieva, A. Mishchenko, et al., Giant magnetoresistance of dirac plasma in high-mobility graphene, Nature 616, 270 (2023)

    2023

  40. [48]

    See Supplemental Material at [url will be inserted by pub- lisher] for device preparation details and full set of ex- perimental and theoretical results, which includes Refs. [49-59]

  41. [49]

    Zomer, M

    P. Zomer, M. Guimar˜ aes, J. Brant, N. Tombros, and B. Van Wees, Fast pick up technique for high quality het- erostructures of bilayer graphene and hexagonal boron nitride, Applied Physics Letters 105 (2014)

    2014

  42. [50]

    Leconte, S

    N. Leconte, S. Javvaji, J. An, A. Samudrala, and J. Jung, Relaxation effects in twisted bilayer graphene: A multi- scale approach, Physical Review B 106, 115410 (2022)

    2022

  43. [51]

    Hermann, Periodic overlayers and moir´ e patterns: theoretical studies of geometric properties, Journal of Physics: Condensed Matter 24, 314210 (2012)

    K. Hermann, Periodic overlayers and moir´ e patterns: theoretical studies of geometric properties, Journal of Physics: Condensed Matter 24, 314210 (2012)

    2012

  44. [52]

    Plimpton, Fast parallel algorithms for short-range molecular dynamics, Journal of Computational Physics 117, 1 (1995)

    S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, Journal of Computational Physics 117, 1 (1995)

    1995

  45. [53]

    M. Wen, S. Carr, S. Fang, E. Kaxiras, and E. B. Tad- mor, Dihedral-angle-corrected registry-dependent inter- layer potential for multilayer graphene structures, Phys- ical Review B 98, 235404 (2018)

    2018

  46. [54]

    Leconte, J

    N. Leconte, J. Jung, S. Leb` egue, and T. Gould, Moir´ e- pattern interlayer potentials in van der waals materials in the random-phase approximation, Physical Review B 96, 195431 (2017)

    2017

  47. [55]

    A. N. Kolmogorov and V. H. Crespi, Registry-dependent interlayer potential for graphitic systems, Physical Re- view B 71, 235415 (2005)

    2005

  48. [56]

    J. H. Los, J. M. H. Kroes, K. Albe, R. M. Gordillo, M. I. Katsnelson, and A. Fasolino, Extended tersoff po- tential for boron nitride: Energetics and elastic proper- ties of pristine and defective h-BN, Physical Review B 96, 184108 (2017)

    2017

  49. [57]

    D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott, A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons, Journal of Physics: Con- densed Matter 14, 783 (2002)

    2002

  50. [58]

    Javvaji, F

    S. Javvaji, F. Li, and J. Jung, Ab initio tight-binding models for mono-and bilayer hexagonal boron nitride (h- BN), Physical Review Materials 9, 024004 (2025)

    2025

  51. [59]

    Jung and A

    J. Jung and A. H. Macdonald, Tight-binding model for graphene π-bands from maximally localized Wannier functions, Physical Review B 87, 1 (2013)

    2013

  52. [60]

    N. R. Finney, M. Yankowitz, L. Muraleetharan, K. Watanabe, T. Taniguchi, C. R. Dean, and J. Hone, Tunable crystal symmetry in graphene–boron nitride het- erostructures with coexisting moir´ e superlattices, Nature Nanotechnology 14, 1029 (2019)

    2019

  53. [61]

    E. Wang, X. Lu, S. Ding, W. Yao, M. Yan, G. Wan, K. Deng, S. Wang, G. Chen, L. Ma, et al., Gaps induced by inversion symmetry breaking and second-generation dirac cones in graphene/hexagonal boron nitride, Nature Physics 12, 1111 (2016)

    2016

  54. [62]

    B. Hunt, J. D. Sanchez-Yamagishi, A. F. Young, M. Yankowitz, B. J. LeRoy, K. Watanabe, T. Taniguchi, P. Moon, M. Koshino, P. Jarillo-Herrero, et al., Massive dirac fermions and hofstadter butterfly in a van der waals heterostructure, Science 340, 1427 (2013)

    2013

  55. [63]

    J. Jung, E. Laksono, A. M. DaSilva, A. H. MacDonald, M. Mucha-Kruczy´ nski, and S. Adam, Moir´ e band model and band gaps of graphene on hexagonal boron nitride, Physical Review B 96, 085442 (2017)

    2017

  56. [64]

    J. Hu, J. Tan, M. M. Al Ezzi, U. Chattopadhyay, J. Gou, Y. Zheng, Z. Wang, J. Chen, R. Thottathil, J. Luo,et al., Controlled alignment of supermoir´ e lattice in double- aligned graphene heterostructures, Nature Communica- tions 14, 4142 (2023)

    2023

  57. [65]

    X. Sun, S. Zhang, Z. Liu, H. Zhu, J. Huang, K. Yuan, Z. Wang, K. Watanabe, T. Taniguchi, X. Li,et al., Corre- lated states in doubly-aligned hBN/graphene/hBN het- erostructures, Nature Communications 12, 7196 (2021)

    2021

  58. [66]

    L. Wang, S. Zihlmann, M.-H. Liu, P. Makk, K. Watan- abe, T. Taniguchi, A. Baumgartner, and C. Schonen- berger, New generation of moir´ e superlattices in doubly aligned hBN/graphene/hBN heterostructures, Nano Let- ters 19, 2371 (2019)

    2019

  59. [67]

    M. M. Al Ezzi, J. Hu, A. Ariando, F. Guinea, and S. Adam, Topological flat bands in graphene super-moir´ e lattices, Physical Review Letters 132, 126401 (2024)

    2024

  60. [68]

    Q. Li, H. Zhang, Y. Wang, W. Chen, C. Bao, Q. Liu, T. Lin, S. Zhang, H. Zhang, K. Watanabe, et al., Evo- lution of the flat band and the role of lattice relaxations in twisted bilayer graphene, Nature Materials 23, 1070 (2024)

    2024

  61. [69]

    Cantele, D

    G. Cantele, D. Alf` e, F. Conte, V. Cataudella, D. Ninno, and P. Lucignano, Structural relaxation and low-energy properties of twisted bilayer graphene, Physical Review Research 2, 043127 (2020)

    2020

  62. [70]

    Lucignano, D

    P. Lucignano, D. Alf` e, V. Cataudella, D. Ninno, and G. Cantele, Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle θ = 1 .08◦, Physical Review B 99, 195419 8 (2019)

    2019

  63. [71]

    Guinea and N

    F. Guinea and N. R. Walet, Continuum models for twisted bilayer graphene: Effect of lattice deformation and hopping parameters, Physical Review B 99, 205134 (2019)

    2019

  64. [72]

    N. N. Nam and M. Koshino, Lattice relaxation and en- ergy band modulation in twisted bilayer graphene, Phys- ical Review B 96, 075311 (2017)

    2017

  65. [73]

    Wang and O

    X. Wang and O. Vafek, Theory of correlated chern in- sulators in twisted bilayer graphene, Physical Review X 14, 021042 (2024)

    2024

  66. [74]

    F. Xie, J. Kang, B. A. Bernevig, O. Vafek, and N. Reg- nault, Phase diagram of twisted bilayer graphene at fill- ing factor ν=±3, Physical Review B 107, 075156 (2023)

    2023

  67. [75]

    Zhang, C

    X.-W. Zhang, C. Wang, X. Liu, Y. Fan, T. Cao, and D. Xiao, Polarization-driven band topology evolution in twisted MoTe2 and WSe 2, Nature Communications 15, 4223 (2024)

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.