pith. sign in

arxiv: 2512.23082 · v3 · submitted 2025-12-28 · ❄️ cond-mat.mes-hall

Various electronic crystal phases in rhombohedral graphene multilayers

Wangqian Miao , Chu Li This is my paper

Pith reviewed 2026-05-16 18:49 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords rhombohedral grapheneelectron crystalChern numberHartree-Fockquantum anomalous Hallphase transitionisospin cascadecompressibility
0
0 comments X

The pith

Increasing carrier density in rhombohedral graphene multilayers triggers an isospin cascade of phase transitions to electron crystal states with non-zero Chern numbers.

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

This work maps the ordered phases in rhombohedral multilayer graphene by solving the interacting Hamiltonian with self-consistent Hartree-Fock methods on an ab initio tight-binding model. As carrier density rises, the calculations reveal a sequence of isospin-driven transitions that stabilize a variety of electron crystals. Some of these states carry non-zero Chern numbers and remain nearly degenerate, allowing extended quantum anomalous Hall effects within the mean-field picture. The same calculations track how external pressure shifts the boundaries between phases and predict corresponding features in thermodynamic quantities such as inverse compressibility.

Core claim

As the carrier density increases, self-consistent Hartree-Fock calculations on an ab initio tight-binding model uncover an isospin cascade sequence of phase transitions that produces a rich variety of ordered states, including electron crystal phases with non-zero Chern numbers. These topological electron crystals are nearly degenerate in the mean-field regime and host extended quantum anomalous Hall effects, while pressure drives additional transitions between them.

What carries the argument

The isospin cascade sequence of phase transitions obtained from self-consistent Hartree-Fock solutions of the interacting tight-binding model.

If this is right

  • A sequence of distinct electron crystal phases appears with rising density.
  • Topological crystals carrying non-zero Chern numbers support extended quantum anomalous Hall effect.
  • External pressure shifts the nearly degenerate states and induces transitions between them.
  • Inverse compressibility exhibits distinct features at each transition point.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The near-degeneracy implies that small external fields or strain could switch between different topological orders without large energy cost.
  • Compressibility measurements alone may suffice to map the full cascade, reducing the need for direct spatial imaging of the crystal order.
  • Similar density-driven cascades could occur in other gated multilayer systems once interaction strength and band flatness are comparable.

Load-bearing premise

The Hartree-Fock mean-field approximation remains accurate enough to rank the energies and Chern numbers of the competing electron crystal states across the density range.

What would settle it

A measurement that finds no sequence of jumps or plateaus in inverse compressibility versus carrier density, or that detects Chern numbers inconsistent with the predicted cascade, would falsify the reported phase sequence.

Figures

Figures reproduced from arXiv: 2512.23082 by Chu Li, Wangqian Miao.

Figure 1
Figure 1. Figure 1: FIG. 1. Single particle band structure (a) of rhombohedral [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Cascade of isospin phase transitions in R5G. QM [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Hartree–Fock mean-field phase diagrams of rhombohedral graphene multilayers as functions of electron doping density [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Competition among different electronic crystal [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) (b) The relaxed lattice constant and interlayer distance of R5G under moderate pressure. The grey dots are [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Hartree Fock band structures for representative anomalous Hall crystal (AHC) states. Blue solid lines denote [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Finite size scaling of the HF condensation energy for electronic crystal states with different lattice geometries. The [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
read the original abstract

We systematically investigate the emergence of electron crystal phases in rhombohedral multilayer graphene using comprehensive self-consistent Hartree Fock calculations combined with \textit{ab initio} tight binding model. As the carrier density increases, we uncover an isospin cascade sequence of phase transitions that gives rise to a rich variety of ordered states, including electron crystal phases with non-zero Chern numbers. We further show the nearly degeneracy of these topological electron crystals hosting extended quantum anomalous Hall effect (EQAH) in the mean field regime and characterize pressure driven phase transitions. Finally, we discuss the thermodynamic signatures, particularly the behavior of the inverse compressibility, in light of recent experimental observations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript reports a systematic investigation of electron crystal phases in rhombohedral multilayer graphene via self-consistent Hartree-Fock calculations on an ab initio tight-binding model. With increasing carrier density it identifies an isospin cascade of phase transitions yielding multiple ordered states, including electron crystals with nonzero Chern numbers; it further discusses near-degeneracy of topological electron crystals supporting extended quantum anomalous Hall effects, pressure-driven transitions, and inverse-compressibility signatures compared with experiment.

Significance. If the mean-field phase diagram and Chern-number assignments prove robust, the work would map a rich set of competing interaction-driven states in rhombohedral multilayers and provide a concrete theoretical framework for interpreting recent compressibility and transport measurements. The use of an ab initio tight-binding starting point combined with explicit Chern-number characterization is a positive feature.

major comments (2)
  1. [§3] §3 (Hartree-Fock results): The central claim of a specific isospin-cascade sequence and the assignment of nonzero Chern numbers to the electron-crystal phases rests entirely on self-consistent Hartree-Fock energies and order parameters. No comparison to exact diagonalization on finite clusters at the same fillings, nor any estimate of fluctuation corrections (RPA or otherwise), is provided; given the near-degeneracy of isospin/valley degrees of freedom and the long-range Coulomb interaction, this omission directly affects the reliability of the reported energy ordering.
  2. [§2.2] §2.2 (interaction and convergence): The manuscript does not specify the precise form or screening length of the Coulomb interaction used, nor the convergence thresholds and system-size scaling employed in the self-consistent loop. These details are load-bearing for the stability of the reported phases across the density window studied.
minor comments (2)
  1. [Figure 2] Figure 2 and associated text: the labeling of isospin and valley polarization in the phase diagram should be made fully explicit so that the Chern-number assignment for each crystal phase can be traced without ambiguity.
  2. [Abstract] The abstract states that the topological crystals are 'nearly degenerate' in the mean-field regime; the main text should quantify the energy differences (in meV per electron) between these states.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the careful reading and constructive comments. We address the major points below.

read point-by-point responses

  1. Referee: [§3] §3 (Hartree-Fock results): The central claim of a specific isospin-cascade sequence and the assignment of nonzero Chern numbers to the electron-crystal phases rests entirely on self-consistent Hartree-Fock energies and order parameters. No comparison to exact diagonalization on finite clusters at the same fillings, nor any estimate of fluctuation corrections (RPA or otherwise), is provided; given the near-degeneracy of isospin/valley degrees of freedom and the long-range Coulomb interaction, this omission directly affects the reliability of the reported energy ordering.

    Authors: We agree that Hartree-Fock is a mean-field method and that fluctuation corrections could modify the energy ordering in the presence of near-degeneracies. Exact diagonalization on finite clusters at the relevant fillings is computationally prohibitive for multilayer systems due to the size of the Hilbert space. We have performed extensive system-size and k-point convergence tests (detailed in the supplement) that support the stability of the reported phases. In revision we will add an explicit discussion of mean-field limitations and note consistency with experimental compressibility signatures. revision: partial

  2. Referee: [§2.2] §2.2 (interaction and convergence): The manuscript does not specify the precise form or screening length of the Coulomb interaction used, nor the convergence thresholds and system-size scaling employed in the self-consistent loop. These details are load-bearing for the stability of the reported phases across the density window studied.

    Authors: We thank the referee for highlighting this omission. In the revised manuscript we will explicitly state the Coulomb interaction form (dual-gate screened potential with dielectric constant ε=4.5 and screening length set by the hBN thickness), the self-consistent convergence threshold (energy change <10^{-6} eV per electron), and the system sizes (12×12 to 24×24 supercells) together with scaling checks confirming phase stability. revision: yes

standing simulated objections not resolved
  • Direct comparison to exact diagonalization or quantitative RPA fluctuation corrections at the studied fillings and system sizes, which lie outside the computational scope of the present work.

Circularity Check

0 steps flagged

No circularity: standard numerical self-consistent HF on ab initio model

full rationale

The manuscript reports results from self-consistent Hartree-Fock minimization on a fixed ab initio tight-binding Hamiltonian. No equation or claim reduces the reported isospin cascade, Chern numbers, or phase sequence to a quantity defined by the output itself. The calculation is a standard numerical procedure whose outputs (energies, order parameters) are not forced by construction to match any fitted input. No self-citation is invoked as a uniqueness theorem or load-bearing premise for the central results. The derivation chain is therefore self-contained and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on the standard mean-field decoupling of the Coulomb interaction and the accuracy of the chosen ab initio tight-binding parametrization; no new particles or forces are introduced.

axioms (1)
  • domain assumption Mean-field Hartree-Fock decoupling captures the dominant ordering tendencies
    Invoked throughout the self-consistent calculations described in the abstract.

pith-pipeline@v0.9.0 · 5398 in / 1197 out tokens · 23340 ms · 2026-05-16T18:49:42.531981+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

75 extracted references · 75 canonical work pages · 6 internal anchors

  1. [1]

    hall crystal

    Z. Teˇ sanovi´ c, F. m. c. Axel, and B. I. Halperin, “hall crystal” versus wigner crystal, Phys. Rev. B39, 8525 (1989)

    work page 1989

  2. [2]

    Soejima, J

    T. Soejima, J. Dong, A. Vishwanath, and D. E. Parker, $\ensuremath{\lambda}$-Jellium Model for the Anoma- lous Hall Crystal, Physical Review Letters135, 186505 (2025), publisher: American Physical Society

    work page 2025

  3. [3]

    Desrochers, J

    F. Desrochers, J. Huxford, M. R. Hirsbrunner, and Y. B. Kim, Electronic Crystal Phases in the Presence of Non- Uniform Berry Curvature and Tunable Berry Flux: The λn-Jellium model (2025), arXiv:2509.15300 [cond-mat]

    work page arXiv 2025

  4. [4]

    Exchange Interactions of a Wigner Crystal in a Magnetic Field and Berry Curvature: Multi-Particle Tunneling through Complex Trajectories

    K.-S. Kim, Magnetic interactions of wigner crys- tal in magnetic field and berry curvature: Multi- particle tunneling through complex trajectories (2025), arXiv:2508.13149

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  5. [5]

    S. Joy, L. Levitov, and B. Skinner, Chiral Wigner crystal phases induced by Berry curvature (2025), arXiv:2507.22121 [cond-mat]

    work page arXiv 2025

  6. [6]

    A. P. Reddy and L. Fu, Quantum melting a Wigner crys- tal into Hall liquids (2025), arXiv:2508.21000 [cond-mat]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  7. [7]

    Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous Hall effect in multilayer graphene, Nature626, 759 (2024), publisher: Nature Publishing Group

    work page 2024

  8. [8]

    Z. Lu, T. Han, Y. Yao, Z. Hadjri, J. Yang, J. Seo, L. Shi, S. Ye, K. Watanabe, T. Taniguchi, and L. Ju, Extended quantum anomalous Hall states in graphene/hBN moir´ e superlattices, Nature637, 1090 (2025), publisher: Na- ture Publishing Group

    work page 2025

  9. [9]

    J. Xie, Z. Huo, X. Lu, Z. Feng, Z. Zhang, W. Wang, Q. Yang, K. Watanabe, T. Taniguchi, K. Liu, Z. Song, X. C. Xie, J. Liu, and X. Lu, Tunable fractional Chern in- sulators in rhombohedral graphene superlattices, Nature Materials24, 1042 (2025), publisher: Nature Publishing Group

    work page 2025

  10. [10]

    Zhang, Q

    H. Zhang, Q. Li, M. G. Scheer, R. Wang, C. Tuo, N. Zou, W. Chen, J. Li, X. Cai, C. Bao, M.-R. Li, K. Deng, K. Watanabe, T. Taniguchi, M. Ye, P. Tang, Y. Xu, P. Yu, J. Avila, P. Dudin, J. D. Denlinger, H. Yao, B. Lian, W. Duan, and S. Zhou, Correlated topological flat bands in rhombohedral graphite, Proceedings of the National Academy of Sciences121, e2410...

    work page 2024

  11. [11]

    Zhang, J

    H. Zhang, J. Lu, K. Liu, Y. Wang, F. Wang, S. Wu, W. Chen, X. Cai, K. Watanabe, T. Taniguchi, J. Avila, P. Dudin, M. D. Watson, A. Louat, T. Sato, P. Yu, W. Duan, Z. Song, G. Chen, and S. Zhou, Moir´ e en- hanced flat band in rhombohedral graphene, Nature Ma- terials , 1 (2025), publisher: Nature Publishing Group

    work page 2025

  12. [12]

    S. H. Aronson, T. Han, Z. Lu, Y. Yao, J. P. Butler, K. Watanabe, T. Taniguchi, L. Ju, and R. C. Ashoori, Displacement Field-Controlled Fractional Chern Insula- tors and Charge Density Waves in a Graphene/hBN Moir´ e Superlattice, Physical Review X15, 031026 (2025)

    work page 2025

  13. [13]

    Wang, Physical Review B94, 10.1103/phys- revb.94.195105 (2016)

    J. Dong, Anomalous Hall Crystals in Rhombohedral Multilayer Graphene. I. Interaction-Driven Chern Bands and Fractional Quantum Hall States at Zero Mag- netic Field, Physical Review Letters133, 10.1103/Phys- RevLett.133.206503 (2024)

    work page doi:10.1103/phys- 2024

  14. [14]

    Z. Dong, A. S. Patri, and T. Senthil, Theory of Quan- tum Anomalous Hall Phases in Pentalayer Rhombohe- dral Graphene Moir\’e Structures, Physical Review Let- ters133, 206502 (2024), publisher: American Physical Society

    work page 2024

  15. [15]

    Z. Dong, A. S. Patri, and T. Senthil, Stability of anoma- lous Hall crystals in multilayer rhombohedral graphene, Physical Review B110, 205130 (2024), publisher: Amer- 7 ican Physical Society

    work page 2024

  16. [16]

    B. Zhou, H. Yang, and Y.-H. Zhang, Fractional quan- tum anomalous hall effect in rhombohedral multilayer graphene in the moir´ eless limit, Phys. Rev. Lett.133, 206504 (2024)

    work page 2024

  17. [17]

    Zhou and Y.-H

    B. Zhou and Y.-H. Zhang, New Classes of Quantum Anomalous Hall Crystals in Multilayer Graphene, Physi- cal Review Letters135, 036501 (2025), publisher: Amer- ican Physical Society

    work page 2025

  18. [18]

    Tan and T

    T. Tan and T. Devakul, Parent Berry Curvature and the Ideal Anomalous Hall Crystal, Physical Review X14, 041040 (2024), publisher: American Physical Society

    work page 2024

  19. [19]

    T. Tan, J. May-Mann, and T. Devakul, Variational Wave- Function Analysis of the Fractional Anomalous Hall Crystal, Physical Review Letters135, 036604 (2025), publisher: American Physical Society

    work page 2025

  20. [20]

    Guo and J

    Z. Guo and J. Liu, Correlation stabilized anomalous Hall crystal in bilayer graphene (2025), arXiv:2409.14658 [cond-mat]

    work page arXiv 2025

  21. [21]

    Soejima, J

    T. Soejima, J. Dong, T. Wang, T. Wang, M. P. Zale- tel, A. Vishwanath, and D. E. Parker, Anomalous Hall crystals in rhombohedral multilayer graphene. II. Gen- eral mechanism and a minimal model, Physical Review B110, 205124 (2024), publisher: American Physical So- ciety

    work page 2024

  22. [22]

    B. A. Bernevig and Y. H. Kwan, ”Berry Trashcan” Model of Interacting Electrons in Rhombohedral Graphene (2025), arXiv:2503.09692 [cond-mat]

    work page arXiv 2025

  23. [23]

    T. Tan, P. J. Ledwith, and T. Devakul, The ideal limit of rhombohedral graphene: Interaction-induced layer- skyrmion lattices and their collective excitations (2025), arXiv:2511.07402 [cond-mat]

    work page arXiv 2025

  24. [24]

    Elastic Response and Instabilities of Anomalous Hall Crystals

    F. Desrochers, M. R. Hirsbrunner, J. Huxford, A. S. Patri, T. Senthil, and Y. B. Kim, Elastic response and instabilities of anomalous hall crystals (2025), arXiv:2503.08784

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  25. [25]

    Wei, A.-K

    Z. Wei, A.-K. Wu, M. Gon¸ calves, and S.-Z. Lin, Edge- driven transition between extended quantum anomalous Hall crystal and fractional Chern insulator in rhombo- hedral graphene multilayers, Physical Review B111, 035116 (2025), arXiv:2409.05043 [cond-mat]

    work page arXiv 2025

  26. [26]

    Huang, S

    K. Huang, S. Das Sarma, and X. Li, Fractional quan- tum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field, Physical Re- view B111, 075130 (2025), publisher: American Physical Society

    work page 2025

  27. [27]

    Aguilar-M´ endez, T

    E. Aguilar-M´ endez, T. Neupert, and G. Wagner, Full, three-quarter, half and quarter Wigner crystals in Bernal bilayer graphene (2025), arXiv:2505.09685 [cond-mat]

    work page arXiv 2025

  28. [28]

    Z. Guo, X. Lu, B. Xie, and J. Liu, Fractional Chern insu- lator states in multilayer graphene moir\’e superlattices, Physical Review B110, 075109 (2024), publisher: Amer- ican Physical Society

    work page 2024

  29. [29]

    Y. H. Kwan, J. Yu, J. Herzog-Arbeitman, D. K. Efe- tov, N. Regnault, and B. A. Bernevig, Moir\’e fractional Chern insulators. III. Hartree-Fock phase diagram, magic angle regime for Chern insulator states, role of moir\’e potential, and Goldstone gaps in rhombohedral graphene superlattices, Physical Review B112, 075109 (2025), publisher: American Physical Society

    work page 2025

  30. [30]

    M. Uzan, W. Zhi, M. Bocarsly, J. Dong, S. Dutta, N. Auerbach, N. S. Kander, M. Labendik, Y. Myasoe- dov, M. E. Huber, K. Watanabe, T. Taniguchi, D. E. Parker, and E. Zeldov, hbn alignment orientation con- trols moir´ e strength in rhombohedral graphene (2025), arXiv:2507.20647

    work page arXiv 2025

  31. [31]

    Zhang, J

    F. Zhang, J. Jung, G. A. Fiete, Q. Niu, and A. H. MacDonald, Spontaneous quantum hall states in chirally stacked few-layer graphene systems, Phys. Rev. Lett. 106, 156801 (2011)

    work page 2011

  32. [32]

    Chen and J

    W. Chen and J. L. Lado, Interaction-driven surface chern insulator in nodal line semimetals, Phys. Rev. Lett.122, 016803 (2019)

    work page 2019

  33. [33]

    A. Lau, T. Hyart, C. Autieri, A. Chen, and D. I. Pikulin, Designing three-dimensional flat bands in nodal- line semimetals, Phys. Rev. X11, 031017 (2021)

    work page 2021

  34. [34]

    Herzog-Arbeitman, Y

    J. Herzog-Arbeitman, Y. Wang, J. Liu, P. M. Tam, Z. Qi, Y. Jia, D. K. Efetov, O. Vafek, N. Regnault, H. Weng, Q. Wu, B. A. Bernevig, and J. Yu, Moir\’e fractional Chern insulators. II. First-principles calcula- tions and continuum models of rhombohedral graphene superlattices, Physical Review B109, 205122 (2024), publisher: American Physical Society

    work page 2024

  35. [35]

    Z. Dong, M. Davydova, O. Ogunnaike, and L. Levi- tov, Isospin- and momentum-polarized orders in bilayer graphene, Physical Review B107, 075108 (2023)

    work page 2023

  36. [36]

    H. Zhou, T. Xie, A. Ghazaryan, T. Holder, J. R. Ehrets, E. M. Spanton, T. Taniguchi, K. Watanabe, E. Berg, M. Serbyn, and A. F. Young, Half- and quarter-metals in rhombohedral trilayer graphene, Nature598, 429 (2021), publisher: Nature Publishing Group

    work page 2021

  37. [37]

    J. M. Koh, J. Alicea, and E. Lantagne-Hurtubise, Corre- lated phases in spin-orbit-coupled rhombohedral trilayer graphene, Physical Review B109, 035113 (2024)

    work page 2024

  38. [38]

    J. M. Koh, A. Thomson, J. Alicea, and E. Lantagne- Hurtubise, Symmetry-broken metallic orders in spin- orbit-coupled Bernal bilayer graphene, Physical Review B110, 245118 (2024), arXiv:2407.09612 [cond-mat]

    work page arXiv 2024

  39. [39]

    Liu and J

    Z. Liu and J. Wang, Layer-dependent quantum anoma- lous Hall effect in rhombohedral graphene, Physical Re- view B111, L081111 (2025)

    work page 2025

  40. [40]

    Y. H. Kwan, Z. Wang, G. Wagner, N. Bultinck, S. H. Simon, and S. A. Parameswaran, Mean-field Mod- elling of Moir´ e Materials: A User’s Guide with Se- lected Applications to Twisted Bilayer Graphene (2025), arXiv:2511.21683 [cond-mat]

    work page arXiv 2025

  41. [41]

    X. Lu, B. Xie, and J. Liu, A numerical perspective on moir´ e superlattices: From single-particle properties to many-body physics (2025), arXiv:2512.07115

    work page arXiv 2025

  42. [42]

    Huang, C

    C.-H. Huang, C. Huang, and M. A. Cazalilla, Com- petition of exchange and correlation energies in two- dimensional N -component electron gas ferromagnetism, Physical Review B111, 045129 (2025)

    work page 2025

  43. [43]

    Herasymchuk, S

    A. Herasymchuk, S. G. Sharapov, O. V. Yazyev, and Y. Zhumagulov, Correlated phases in rhombohedral N- layer graphene (2025), arXiv:2508.14630 [cond-mat]

    work page arXiv 2025

  44. [44]

    Parra-Mart´ ınez, A

    G. Parra-Mart´ ınez, A. Jimeno-Pozo, J. A. Silva-Guill´ en, and F. Guinea, Nematic and partially polarized phases in rhombohedral graphene with varying number of layers: An extensive Hartree-Fock study, Adv. Mater. , e14008 (2025)

    work page 2025

  45. [45]

    K. Kudo, R. Nakai, and K. Nomura, Quantum anoma- lous, spin, and valley hall effects in pentalayer rhombo- hedral graphene moir´ e superlattices, Phys. Rev. B110, 245135 (2024)

    work page 2024

  46. [46]

    Non-Abelian Chern band in rhombohedral graphene multilayers

    T. Uchida, T. Kawakami, and M. Koshino, Non- Abelian Chern band in rhombohedral graphene multi- layers (2025), arXiv:2508.07366 [cond-mat]. 8

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  47. [47]

    Chatterjee, T

    S. Chatterjee, T. Wang, E. Berg, and M. P. Zaletel, Inter- valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene, Nature Communications13, 6013 (2022)

    work page 2022

  48. [48]

    Auerbach, S

    N. Auerbach, S. Dutta, M. Uzan, Y. Vituri, Y. Zhou, A. Y. Meltzer, S. Grover, T. Holder, P. Emanuel, M. E. Huber, Y. Myasoedov, K. Watanabe, T. Taniguchi, Y. Oreg, E. Berg, and E. Zeldov, Isospin magnetic tex- ture and intervalley exchange interaction in rhombohe- dral tetralayer graphene, Nature Physics21, 1765–1772 (2025)

    work page 2025

  49. [49]

    Joy and B

    S. Joy and B. Skinner, Disorder-induced liquid-solid phase coexistence in 2D electron systems (2025), arXiv:2502.11235 [cond-mat]

    work page arXiv 2025

  50. [50]

    Das Sarma and M

    S. Das Sarma and M. Xie, Thermal crossover from a chern insulator to a fractional chern insulator in pen- talayer graphene, Phys. Rev. B110, 155148 (2024)

    work page 2024

  51. [51]

    J. Dong, O. E. Sommer, T. Soejima, D. E. Parker, and A. Vishwanath, Phonons in electron crystals with Berry curvature, Proceedings of the National Academy of Sci- ences122, e2515532122 (2025), publisher: Proceedings of the National Academy of Sciences

    work page 2025

  52. [52]

    H. C. Po, H. Watanabe, and A. Vishwanath, Fragile topology and wannier obstructions, Phys. Rev. Lett.121, 126402 (2018)

    work page 2018

  53. [53]

    A. S. Patri, Z. Dong, and T. Senthil, Extended quantum anomalous Hall effect in moir\’e structures: Phase tran- sitions and transport, Physical Review B110, 245115 (2024), publisher: American Physical Society

    work page 2024

  54. [54]

    Zeng and A

    Y. Zeng and A. J. Millis, Berry Phase Dynamics of Slid- ing Electron Crystals, Physical Review X15, 031059 (2025), publisher: American Physical Society

    work page 2025

  55. [55]

    Shao and X

    Y. Shao and X. Dai, Electrical breakdown of excitonic insulators, Phys. Rev. X14, 021047 (2024)

    work page 2024

  56. [56]

    Y. Wang, J. An, C. Ye, X. Wang, D. Mai, H. Zhao, Y. Zhang, C. Peng, K. Watanabe, T. Taniguchi, X. Sun, R. Dai, Z. Wang, W. Qin, Z. Qiao, and Z. Zhang, Pressure-driven moir´ e potential enhancement and ter- tiary gap opening in graphene/h-bn heterostructure, Phys. Rev. Lett.135, 046303 (2025)

    work page 2025

  57. [57]

    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 Re- view Research5, L032022 (2023), publisher: American Physical Society

    work page 2023

  58. [58]

    B. Wang, J. Yu, P. Sharma, and C.-C. Liu, Pressure- tunable generalized wigner crystal and fractional chern insulator in twisted mote 2 (2025), arXiv:2504.11177

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  59. [59]

    S. A. A. Ghorashi, A. Dunbrack, A. Abouelkomsan, J. Sun, X. Du, and J. Cano, Topological and stacked flat bands in bilayer graphene with a superlattice potential, Phys. Rev. Lett.130, 196201 (2023)

    work page 2023

  60. [60]

    W. Miao, A. Rashidi, and X. Dai, Artificial moir´ e engi- neering for an ideal bernevig-hughes-zhang model, Phys. Rev. B111, 045113 (2025)

    work page 2025

  61. [61]

    Y. Shi, B. Xie, F. Ren, X. Cai, Z. Guo, Q. Li, X. Lu, N. Regnault, Z. Liu, and J. Liu, Fractional topological states in rhombohedral multilayer graphene modulated by kagome superlattice (2025), arXiv:2502.17320

    work page arXiv 2025

  62. [62]

    Z. Huo, W. Wang, J. Xie, Y. H. Kwan, J. Herzog- Arbeitman, Z. Zhang, Q. Yang, M. Wu, K. Watanabe, T. Taniguchi, K. Liu, N. Regnault, B. A. Bernevig, and X. Lu, Does moire matter? critical moire dependence with quantum fluctuations in graphene based integer and fractional chern insulators (2025), arXiv:2510.15309

    work page arXiv 2025

  63. [63]

    Valenti, Y

    A. Valenti, Y. Vituri, Y. Yang, D. E. Parker, T. Soe- jima, J. Dong, M. A. Morales, A. Vishwanath, E. Berg, and S. Zhang, Quantum geometry driven crystallization: A neural-network variational monte carlo study (2025), arXiv:2512.07947

    work page arXiv 2025

  64. [64]

    X. Lu, Y. Yang, Z. Guo, and J. Liu, General Many- Body Perturbation Framework for Moir´ e Systems (2025), arXiv:2509.19764 [cond-mat]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  65. [65]

    J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Nega- tive compressibility of interacting two-dimensional elec- tron and quasiparticle gases, Phys. Rev. Lett.68, 674 (1992)

    work page 1992

  66. [66]

    J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Com- pressibility of the two-dimensional electron gas: Measure- ments of the zero-field exchange energy and fractional quantum hall gap, Phys. Rev. B50, 1760 (1994)

    work page 1994

  67. [67]

    Spivak and S

    B. Spivak and S. A. Kivelson, Phases intermediate be- tween a two-dimensional electron liquid and wigner crys- tal, Phys. Rev. B70, 155114 (2004)

    work page 2004

  68. [68]

    G. Rai, L. Crippa, D. C˘ alug˘ aru, H. Hu, F. Paoletti, L. de’ Medici, A. Georges, B. A. Bernevig, R. Valent´ ı, G. San- giovanni, and T. Wehling, Dynamical correlations and or- der in magic-angle twisted bilayer graphene, Phys. Rev. X14, 031045 (2024)

    work page 2024

  69. [69]

    Datta, M

    A. Datta, M. J. Calder´ on, A. Camjayi, and E. Bas- cones, Heavy quasiparticles and cascades without sym- metry breaking in twisted bilayer graphene, Nat. Com- mun.14, 5036 (2023)

    work page 2023

  70. [70]

    T. Han, Z. Lu, Z. Hadjri, L. Shi, Z. Wu, W. Xu, Y. Yao, A. A. Cotten, O. Sharifi Sedeh, H. Weldeyesus, J. Yang, J. Seo, S. Ye, M. Zhou, H. Liu, G. Shi, Z. Hua, K. Watan- abe, T. Taniguchi, P. Xiong, D. M. Zumb¨ uhl, L. Fu, and L. Ju, Signatures of chiral superconductivity in rhom- bohedral graphene, Nature643, 654 (2025), publisher: Nature Publishing Group

    work page 2025

  71. [71]

    R. Q. Nguyen, H.-T. Wu, E. Morissette, N. J. Zhang, P. Qin, K. Watanabe, T. Taniguchi, A. W. Hui, D. E. Feldman, and J. I. A. Li, A hierarchy of superconductiv- ity and topological charge density wave states in rhom- bohedral graphene (2025), arXiv:2507.22026

    work page arXiv 2025

  72. [72]

    Kresse and J

    G. Kresse and J. Furthm¨ uller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B54, 11169 (1996)

    work page 1996

  73. [73]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

    work page 1996

  74. [74]

    P. E. Bl¨ ochl, Projector augmented-wave method, Phys. Rev. B50, 17953 (1994)

    work page 1994

  75. [75]

    Grimme, J

    S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A con- sistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 ele- ments H-Pu, J. Chem. Phys.132, 154104 (2010). 9 0 1 2 3 4 P (GPa) 2.470 2.472 2.474 2.476Lattice constant a (Å) (a) a = 0.00197P + 2.47712 R2 = 0.9987 Linear fit DFT 0 1 2 3 4 P (GPa) 3.1...

    work page 2010