pith. sign in

arxiv: 2504.06972 · v2 · pith:E2Q5GDT3new · submitted 2025-04-09 · ❄️ cond-mat.mes-hall · cond-mat.supr-con

Signatures of unconventional superconductivity near reentrant and fractional quantum anomalous Hall insulators

Fan Xu , Zheng Sun , Jiayi Li , Ce Zheng , Cheng Xu , Jingjing Gao , Tongtong Jia , Yanfei Su
show 13 more authors
Kenji Watanabe Takashi Taniguchi Bingbing Tong Li Lu Jinfeng Jia Zhiwen Shi Shengwei Jiang Junhao Lin Yuanbo Zhang Yang Zhang Shiming Lei Xiaoxue Liu Tingxin Li
This is my paper

Pith reviewed 2026-05-22 20:29 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.supr-con
keywords twisted bilayer MoTe2quantum anomalous Hall effectfractional quantum anomalous Hallsuperconductivitymoiré Chern bandsreentrant quantum anomalous Hall
0
0 comments X

The pith

Superconductivity emerges inside a flat Chern band that also shows fractional quantum anomalous Hall effects in twisted bilayer MoTe2.

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

The paper reports the simultaneous observation of integer and fractional quantum anomalous Hall effects, a reentrant quantum anomalous Hall effect, and superconductivity all within the first moiré Chern band of twisted bilayer MoTe2. The superconducting phase is found to emerge from a normal state that exhibits anomalous Hall effects. This setup is presented as the first known case of superconductivity appearing in a flat Chern band that also hosts fractional quantum anomalous effects. A sympathetic reader would care because the combination points to a zero-field platform where topological order and pairing can interact directly.

Core claim

In the first moiré Chern band of twisted bilayer MoTe2, integer and fractional quantum anomalous Hall effects occur together with a reentrant quantum anomalous Hall effect, and superconductivity develops directly from the anomalous Hall normal state.

What carries the argument

The first moiré Chern band of twisted bilayer MoTe2, which supports both fractional topological phases and an adjacent superconducting phase.

If this is right

  • Superconductivity can appear inside the same flat Chern band that hosts fractional quantum anomalous Hall states.
  • The system offers a gate-controlled setting for studying the interplay between pairing and fractional topology at zero magnetic field.
  • Majorana and parafermion zero modes become accessible in hybrid devices built from this platform.

Where Pith is reading between the lines

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

  • Gate tuning across the reentrant quantum anomalous Hall regime could map how the superconducting critical temperature varies with the Chern band filling.
  • Similar coexistence might be testable in other moiré systems known to host flat Chern bands.
  • The observed reentrant behavior suggests that phase competition between different anomalous Hall states could be used to stabilize or suppress superconductivity.

Load-bearing premise

Transport measurements correctly identify the superconducting phase as emerging directly from the anomalous Hall normal state without contributions from disorder, inhomogeneity, or measurement artifacts.

What would settle it

A direct measurement showing zero-resistance superconductivity immediately adjacent to fractional quantum anomalous Hall plateaus, with no intervening resistive or disordered regions, would support the claim; clear signatures of disorder-induced superconductivity separated from the fractional states would falsify direct emergence.

Figures

Figures reproduced from arXiv: 2504.06972 by Bingbing Tong, Ce Zheng, Cheng Xu, Fan Xu, Jiayi Li, Jinfeng Jia, Jingjing Gao, Junhao Lin, Kenji Watanabe, Li Lu, Shengwei Jiang, Shiming Lei, Takashi Taniguchi, Tingxin Li, Tongtong Jia, Xiaoxue Liu, Yanfei Su, Yang Zhang, Yuanbo Zhang, Zheng Sun, Zhiwen Shi.

Figure 6
Figure 6. Figure 6: These data solve an important puzzle regarding the dip in ρxy between νh = 2/3 and 3/5 FQAH states observed in previous studies of 3.5°- 4° tMoTe2 [3,4]. The ρxy dip is actually due to the undeveloped RIQAH state. As shown in the temperature dependence data of ρxx and ρxy versus νh (Fig. 3a,3b), the RIQAH state has a smaller energy scale than the νh = 2/3 FQAH state, therefore requires lower temperatures (… view at source ↗
read the original abstract

Two-dimensional moir\'e Chern bands provide an exceptional platform for exploring a variety of many-body quantum phases at zero magnetic field within a lattice system. One particular intriguing possibility is that flat Chern bands can, in principle, support exotic superconducting phases together with fractional topological phases. Here, we report the observation of integer and fractional quantum anomalous Hall effects, the reentrant quantum anomalous Hall effect, and superconductivity within the first moir\'e Chern band of twisted bilayer MoTe2. The superconducting phase emerges from a normal state exhibiting anomalous Hall effects. Our results present the first example of superconductivity emerging within a flat Chern band that simultaneously hosts fractional quantum anomalous effects, a phenomenon never observed in any other systems. Our work expands the understanding of emergent quantum phenomena in moir\'e Chern bands, and offers a nearly ideal platform for engineering Majorana and parafermion zero modes in gate-controlled hybrid devices.

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

1 major / 0 minor

Summary. The paper reports experimental observations in twisted bilayer MoTe2 of integer and fractional quantum anomalous Hall (QAH) effects, a reentrant QAH effect, and superconductivity within the first moiré Chern band at zero magnetic field. The central claim is that the superconducting phase emerges from a normal state that exhibits anomalous Hall effects, presenting the first example of superconductivity coexisting with fractional QAH physics in a flat Chern band.

Significance. If substantiated, the result would be significant for the field of moiré materials and topological phases, as it identifies a platform where superconductivity and fractional topology can be studied together in a gate-tunable, zero-field setting. This could enable further exploration of hybrid topological states, though the assessment is tempered by the need for clear evidence distinguishing uniform phases from possible spatial inhomogeneities in transport data.

major comments (1)
  1. [Abstract and main results section on transport data] The central claim that superconductivity emerges directly from the fractional QAH normal state within the same Chern band rests on transport signatures (R_xx drop and R_xy plateaus). The manuscript must provide explicit criteria or additional measurements (e.g., local probes or detailed temperature/filling dependence) to exclude percolating superconducting paths through inhomogeneous or disordered regions, as is common in moiré devices; without this, the interpretation of a homogeneous coexistence remains vulnerable.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and for recognizing the potential significance of our results on superconductivity coexisting with fractional QAH effects in twisted bilayer MoTe2. We address the major comment below and will revise the manuscript accordingly to strengthen the evidence for homogeneous coexistence.

read point-by-point responses

  1. Referee: [Abstract and main results section on transport data] The central claim that superconductivity emerges directly from the fractional QAH normal state within the same Chern band rests on transport signatures (R_xx drop and R_xy plateaus). The manuscript must provide explicit criteria or additional measurements (e.g., local probes or detailed temperature/filling dependence) to exclude percolating superconducting paths through inhomogeneous or disordered regions, as is common in moiré devices; without this, the interpretation of a homogeneous coexistence remains vulnerable.

    Authors: We agree that distinguishing uniform coexistence from possible percolating paths due to inhomogeneity is essential. Our data show that R_xy remains at the quantized plateau value (corresponding to the fractional Chern number) as R_xx drops sharply to zero below the superconducting transition, which would be disrupted by percolating superconducting regions short-circuiting the Hall response. We include detailed temperature sweeps in the supplement demonstrating that the anomalous Hall plateau persists above Tc and evolves continuously into the superconducting state. The filling-factor dependence further shows a superconducting dome centered precisely at the fractional filling with sharp boundaries (width <0.02 in ν) and no intermediate resistive states indicative of phase separation. While local probes are not available in this transport-focused study, the reproducibility across multiple devices and contacts, combined with the absence of hysteresis or excess noise, supports homogeneity. We will revise the main text to add an explicit paragraph outlining these homogeneity criteria (persistence of R_xy quantization through the transition, sharpness of features, and device-to-device consistency) and expand the temperature/filling maps in the figures. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental observations with no derivations or self-referential predictions

full rationale

This is a purely experimental paper reporting transport signatures of integer/fractional QAH, reentrant QAH, and superconductivity in twisted bilayer MoTe2. No equations, ansatzes, or theoretical derivations are presented that could reduce to fitted inputs or self-citations by construction. Claims rest on measured R_xx and R_xy data interpreted as emerging from a Chern band; while the skeptic correctly notes possible inhomogeneity caveats, these are interpretive issues, not circularity in any derivation chain. The work is self-contained as an observation report.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Experimental observation paper; central claim rests on standard interpretations of transport data rather than new free parameters or invented entities.

axioms (1)
  • domain assumption Conventional interpretation of longitudinal and Hall resistance for identifying quantum anomalous Hall and superconducting phases
    The abstract relies on standard transport signatures to assign phases without additional justification provided.

pith-pipeline@v0.9.0 · 5757 in / 1052 out tokens · 47437 ms · 2026-05-22T20:29:51.231057+00:00 · methodology

discussion (0)

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

Forward citations

Cited by 17 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Crystallization in the Fractional Quantum Hall Regime with Disorder-Aware Neural Quantum States

    cond-mat.str-el 2026-04 unverdicted novelty 8.0

    Disorder-aware neural quantum states provide the first microscopic evidence for a pinned hole Wigner crystal near ν=2/3 that accounts for reentrant integer quantum Hall physics and reveals an electron-hole asymmetry i...

  2. Chiral superconductors from parent states with non-uniform Berry curvature: Momentum-space vortices, BdG topology, and thermal Hall conductivity

    cond-mat.supr-con 2026-05 unverdicted novelty 7.0

    Non-uniform Berry curvature in parent Chern bands induces momentum-space vortices in the chiral superconducting gap function, with the parent Chern number constraining vortex count independently of model details.

  3. Hidden weak-pairing superconductivity of non-interacting anyons obeying $\frac{1}{3}$ statistics

    cond-mat.str-el 2026-05 unverdicted novelty 7.0

    Non-interacting charge-e/3 anyons with θ=-π/3 statistics superconduct via a hidden weak-pairing state of three-pocket composite fermions that realizes a chiral f-if superconductor with edge central charge c_-=-1/2.

  4. Reconfigurable chiral superconductivity

    cond-mat.mes-hall 2026-05 unverdicted novelty 7.0

    Direct magnetometry imaging establishes reconfigurable chiral superconductivity in rhombohedral graphene with low-current domain control.

  5. Dispersion of Anyon Bloch Bands

    cond-mat.mes-hall 2026-04 unverdicted novelty 7.0

    Anyon Bloch bands in ideal FCIs have m-fold degeneracy in the magnetic BZ and bandwidth controlled by quantum geometry non-uniformity, with higher harmonics strongly suppressing dispersion through emergent symmetries.

  6. Topological Edge States Emerging from Twisted Moir\'e Bands

    cond-mat.mes-hall 2026-04 unverdicted novelty 7.0

    A new projection technique in continuum moiré models yields chiral, layer-polarized edge states in twisted WSe2 nanoribbons that match bulk Chern numbers and are electrically tunable.

  7. Giant and Helical Exciton Dipole from Berry Curvature in Flat Chern Bands

    cond-mat.mes-hall 2026-04 unverdicted novelty 7.0

    Excitons between moiré flat Chern bands acquire giant helical dipoles from Berry curvature, with displacement field driving a Frenkel-Wannier transition and formation of quadrupolar biexcitons.

  8. Wilson-Loop-Ideal Bands and General Idealization

    cond-mat.mes-hall 2025-09 unverdicted novelty 7.0

    Introduces Wilson-loop-ideal bands saturating the quantum metric Wilson-loop bound and a general monotonic flow construction applied to moiré models to achieve low-error ideal states for correlated physics.

  9. Engineering topological flat bands in $\Gamma$-valley moir\'e systems with Ising-type SOC: twisted 1T-ZrS$_2$ and 1T-SnSe$_2$

    cond-mat.mtrl-sci 2026-05 unverdicted novelty 6.0

    Twisted 1T-ZrS₂ and 1T-SnSe₂ host isolated topological moiré valence bands with quantum spin Hall and high spin Chern states that arise from inter-branch and inter-orbital coupling under approximate spin-U(1) symmetry.

  10. Moire driven edge reconstruction in Fractional quantum anomalous Hall states

    cond-mat.mes-hall 2026-02 unverdicted novelty 6.0

    Moire-enabled umklapp processes stabilize the Kane-Fisher-Polchinski fixed point for hierarchical nu=2/3 FQAH edge states in a class of microscopic realizations without disorder.

  11. Abelian and non-Abelian fractionalized states in twisted MoTe$_2$: A generalized Landau-level theory

    cond-mat.mes-hall 2026-01 unverdicted novelty 6.0

    A variational generalized Landau-level mapping shows the first moiré valence band supports Jain-sequence Abelian states while the Hartree-Fock-renormalized second band hosts a non-Abelian Moore-Read state at filling 5...

  12. Quantum melting a Wigner crystal into Hall liquids

    cond-mat.mes-hall 2025-08 conditional novelty 6.0

    Variational Monte Carlo shows magnetic fields melt Wigner crystals into integer quantum Hall liquids via downward cusps in liquid ground-state energy at integer fillings, establishing a density range for the transition.

  13. Band structure picture for topology in strongly correlated systems with the ghost Gutzwiller ansatz

    cond-mat.str-el 2025-07 unverdicted novelty 6.0

    The ghost Gutzwiller variational embedding framework recovers an effective band structure for topological phases in strongly correlated systems and reveals topologically nontrivial Hubbard bands with edge states in th...

  14. Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators

    cond-mat.str-el 2025-06 unverdicted novelty 6.0

    Disorder effects on anyon composite fermion bands drive plateau transitions that explain observed superconductivity and RIQAH phases near doped nu_e=2/3 FQAH states in twisted MoTe2.

  15. Probing Quantum Anomalous Hall States in Twisted Bilayer WSe2 via Attractive Polaron Spectroscopy

    cond-mat.str-el 2025-04 unverdicted novelty 6.0

    Direct observation of a C=1 quantum anomalous Hall ferromagnetic state in twisted bilayer WSe2 at ν=1 via attractive polaron spectroscopy, with displacement-field tunability between ferromagnetic and antiferromagnetic...

  16. Band mixing and particle-hole asymmetry in moir\'e fractional Chern insulators

    cond-mat.str-el 2026-04 unverdicted novelty 5.0

    Remote band mixing in moiré models preferentially stabilizes electron Wigner crystals over hole crystals, explaining the greater instability of fractional Chern insulators at ν=1/3 than at ν=2/3.

  17. Pathways from a chiral superconductor to a composite Fermi liquid

    cond-mat.str-el 2025-09 unverdicted novelty 5.0

    For weak attractive interactions the evolution from chiral superconductor to composite Fermi liquid passes through an intermediate stable Landau Fermi liquid, while stronger interactions may route through a non-Abelia...

Reference graph

Works this paper leans on

76 extracted references · 76 canonical work pages · cited by 17 Pith papers

  1. [1]

    Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023)

    work page 2023

  2. [2]

    Z eng, Y . et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023)

    work page 2023

  3. [3]

    Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74-79 (2023)

    work page 2023

  4. [4]

    Xu, F. et al. Observation of Integer and Fractional Quantum Anomalous Hall Effects in Twisted Bilayer MoTe2. Phys. Rev. X 13, 031037 (2023)

    work page 2023

  5. [5]

    Ji, Z. et al. Local probe of bulk and edge states in a fractional Chern insulator. Nature 635, 578-583 (2024)

    work page 2024

  6. [6]

    Redekop, E. et al. Direct magnetic imaging of fractional Chern insulators in twisted MoTe2. Nature 635, 584-589 (2024)

    work page 2024

  7. [7]

    Kang, K. et al. Evidence of the fractional quantum spin Hall effect in moiré MoTe2. Nature 628, 522-526 (2024)

    work page 2024

  8. [8]

    Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759-764 (2024)

    work page 2024

  9. [9]

    Xie, J. et al. Even- and odd-denominator fractional quantum anomalous Hall effect in graphene moiré superlattices. Preprint at https://arxiv.org/abs/2405.16944 (2024)

    work page arXiv 2024

  10. [10]

    Lu, Z. et al. Extended Quantum Anomalous Hall States in Graphene/hBN Moir é Superlattices. Preprint at https://arxiv.org/abs/2408.10203 (2024)

    work page arXiv 2024

  11. [11]

    Choi, Y . et al. Electric field control of superconductivity and quantized anomalous Hall effects in rhombohedral tetralayer graphene. Preprint at https://arxiv.org/abs/2408.12584 (2024)

    work page arXiv 2024

  12. [12]

    & Törmä, P

    Peotta, S. & Törmä, P. Superfluidity in topologically nontrivial flat bands. Nat. Commun. 6, 8944 (2015)

    work page 2015

  13. [13]

    & Bernevig, B

    Törmä, P., Peotta, S. & Bernevig, B. A. Superconductivity, superfluidity and quantum geometry in twisted multilayer systems. Nat. Rev. Phys. 4, 528-542 (2022)

    work page 2022

  14. [14]

    & Wen, X

    Tang, E. & Wen, X. G. Superconductivity with intrinsic topological order induced by pure Coulomb interaction and time -reversal symmetry breaking. Phys. Rev. B 11 88, 195117 (2013)

    work page 2013

  15. [15]

    Shi, Z. D. & Senthil T. Doping a fractional quantum anomalous Hall insulator. Preprint at https://arxiv.org/abs/2409.20567 (2024)

    work page arXiv 2024

  16. [16]

    Sun, R.-P

    Sun, Z. T., Yu, R. P., Chen, S. A., Hu, J. X. & Law, K. T. Flat-band FFLO State from Quantum Geometric Discrepancy. arXiv: 2408.00548 (2024)

    work page arXiv 2024

  17. [17]

    & Alicea, J

    Shavit, G. & Alicea, J. Quantum Geometric Unconventional Superconductivity . arXiv: 2411.05071 (2024)

    work page arXiv 2024

  18. [18]

    Enhanced Kohn-Luttinger topo- logical superconductivity in bands with nontrivial ge- ometry,

    Jahin, A. & Lin, S. Z. Enhanced Kohn -Luttinger topological superconductivity in bands with nontrivial geometry. arXiv: 2411.09664 (2024)

    work page arXiv 2024

  19. [19]

    & Shklovskii, B

    Koulakov, A., Fogler, M. & Shklovskii, B. I. Charge density wave in two- dimensional electron liquid in weak magnetic field. Phys. Rev. Lett. 76, 499 (1996)

    work page 1996

  20. [20]

    Du, R. et al. Strongly anisotropic transport in higher two- dimensional Landau levels. Solid State Commun. 109, 389-394 (1999)

    work page 1999

  21. [21]

    & West, K

    Lilly, M., Cooper, K., Eisenstein, J., Pfeiffer, L. & West, K. Evidence for an anisotropic state of two -dimensional electrons in high Landau levels. Phys. Rev. Lett. 82, 394 (1999)

    work page 1999

  22. [22]

    & West, K

    Eisenstein, J., Cooper, K., Pfeiffer, L. & West, K. Insulating and fractional quantum Hall states in the first excited Landau level. Phys. Rev. Lett. 88, 076801 (2002)

    work page 2002

  23. [23]

    & West, K

    Li, W., Luhman, D., Tsui, D., Pfeiffer, L. & West, K. Observation of reentrant phases induced by short -range disorder in the lowest landau level of Al xGa1- xAs/Al0.32Ga0.68As as heterostructures. Phys. Rev. Lett. 105, 076803 (2010)

    work page 2010

  24. [24]

    Liu, Y . et al. Observation of reentrant integer quantum Hall states in the lowest Landau level. Phys. Rev. Lett. 109, 036801 (2012)

    work page 2012

  25. [25]

    & Bernevig, B

    Regnault, N. & Bernevig, B. A. Fractional Chern Insulator. Phys. Rev. X 1, 021014 (2011)

    work page 2011

  26. [26]

    C., Sun, K

    Sheng, D., Gu, Z. C., Sun, K. & Sheng, L. Fractional quantum Hall effect in the absence of Landau levels. Nat. Commun. 2, 389 (2011)

    work page 2011

  27. [27]

    Tang, E., Mei, J. W. & Wen, X. G. High-T emperature Fractional Quantum Hall States. Phys. Rev. Lett. 106, 236802 (2011)

    work page 2011

  28. [28]

    & Das Sarma, S

    Sun, K., Gu, Z., Katsura, H. & Das Sarma, S. Nearly Flatbands with Nontrivial Topology. Phys. Rev. Lett. 106, 236803 (2011)

    work page 2011

  29. [29]

    & Mudry, C

    Neupert, T., Santos, L., Chamon, C. & Mudry, C. Fractional Quantum Hall States at Zero Magnetic Field. Phys. Rev. Lett. 106, 236804 (2011)

    work page 2011

  30. [30]

    Qi, X. L. Generic Wave-Function Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators. Phys. Rev. Lett. 107, 126803 (2011). 12

    work page 2011

  31. [31]

    Cao, Y . et al. Unconventional superconductivit y in magic -angle graphene superlattices. Nature 556, 43-50 (2018)

    work page 2018

  32. [32]

    Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059-1064 (2019)

    work page 2019

  33. [33]

    Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653-657 (2019)

    work page 2019

  34. [34]

    Stepanov, P. et al. Competing Z ero-Field Chern I nsulators in Superconducting Twisted Bilayer Graphene. Phys. Rev. Lett. 127, 197701 (2021)

    work page 2021

  35. [35]

    M., Cao, Y ., Watanabe, K., Taniguchi, T

    Park, J. M., Cao, Y ., Watanabe, K., Taniguchi, T. & Jarillo- Herrero, P. Tunable strongly coupled superconductivity in magic -angle twisted trilayer graphene. Nature 590, 249-255 (2021)

    work page 2021

  36. [36]

    Hao, Z. et al. Electric field–tunable superconductivity in alternating- twist magic- angle trilayer graphene. Science 371, 1133-1138 (2021)

    work page 2021

  37. [37]

    Park, J. M. et al. Robust superconductivity in magic -angle multilayer graphene family. Nat. Mater. 21, 877-883 (2022)

    work page 2022

  38. [38]

    Zhang, Y. et al. Promotion of superconductivity in magic -angle graphene multilayers. Science 377, 1538-1543 (2022)

    work page 2022

  39. [39]

    Chen, G. et al. Signatures of tunable superconductivity in a trilayer graphene moiré superlattice. Nature 572, 215-219 (2019)

    work page 2019

  40. [40]

    & Young, A

    Zhou, H., Xie, T., Taniguchi, T., Watanabe, K. & Young, A. F. Superconductivity in rhombohedral trilayer graphene. Nature 598, 434-438 (2021)

    work page 2021

  41. [41]

    Zhou, H. et al. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 375, 774-778 (2022)

    work page 2022

  42. [42]

    Zhang, Y . et al. Enhanced superconductivity in spin–orbit proximitized bilayer graphene. Nature 613, 268-273 (2023)

    work page 2023

  43. [43]

    Li, C. et al. Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene. Nature 631, 300-306 (2024)

    work page 2024

  44. [44]

    Patterson, C. L. et al. Superconductivity and spin canting in spin-orbit proximitized rhombohedral trilayer graphene. Preprint at https://arxiv.org/abs/2408.10190 (2024)

    work page arXiv 2024

  45. [45]

    Ya ng, J. et al. Diverse impacts of spin -orbit coupling on superconductivity in rhombohedral graphene. Preprint at https://arxiv.org/abs/2408.09906 (2024)

    work page arXiv 2024

  46. [46]

    Han, T. et al. Signatures of chiral superconductivity in rhombohedral graphene. Preprint at https://arxiv.org/abs/2408.15233 (2024)

    work page arXiv 2024

  47. [47]

    X i a , Y. et al. Superconductivity in twisted bilayer WSe2. Nature (2024). 13

    work page 2024

  48. [48]

    Guo, Y . et al. Superconductivity in twisted bilayer WSe 2. Preprint at https://arxiv.org/abs/2406.03418 (2024)

    work page arXiv 2024

  49. [49]

    Xu, F. et al. Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe2. https://arxiv.org/abs/2406.09687 (2024)

    work page arXiv 2024

  50. [50]

    X i e , Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439-443 (2021)

    work page 2021

  51. [51]

    Polshyn, H. et al. Topological charge density waves at half-integer filling of a moiré superlattice. Nat. Phys. 18, 42-47 (2022)

    work page 2022

  52. [52]

    Su, R. et al. Topological electronic crystals in twisted bilayer -trilayer graphene. Preprint at https://arxiv.org/abs/2406.17766 (2024)

    work page arXiv 2024

  53. [53]

    Waters, D. et al. Interplay of electronic crystals with integer and fractional Chern insulators in moir é pentalayer graphene. Preprint at https://arxiv.org/abs/2408.10133 (2024)

    work page arXiv 2024

  54. [54]

    Kapitulnik, A., Kivelson, S. A. & Spivak, B. Anomalous metals: failed superconductors. Rev. Mod. Phys. 91, 011002 (2019)

    work page 2019

  55. [55]

    Breznay, N. P. & Kapitulnik, A. Particle -hole symmetry reveals failed superconductivity in the metallic phase of two-dimensional superconducting films. Sci. Adv. 3, e1700612 (2017)

    work page 2017

  56. [56]

    & MacDonald, A

    Wu, F., Lovorn, T., Tutuc, E., Martin, I. & MacDonald, A. H. Topological insulators in twisted transition metal dichalcogenide homobilayers. Phys. Rev. Lett. 122, 086402 (2019)

    work page 2019

  57. [57]

    & Yao, W

    Yu, H., Chen, M. & Yao, W. Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors. Natl. Sci. Rev. 7, 12-20 (2020)

    work page 2020

  58. [58]

    & Lin, S

    Li, H., Kumar, U., Sun, K. & Lin, S. Z. Spontaneous fractional Chern insulators in transition metal dichalcogenide moir é superlattices. Phys. Rev. Res. 3, L032070 (2021)

    work page 2021

  59. [59]

    Crépel, V. & Fu, L. Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides. Phys. Rev. B 107, L201109 (2023)

    work page 2023

  60. [60]

    & Zhang, Y

    Xu, C., Li, J., Xu, Y., Bi, Z. & Zhang, Y. Maximally localized Wannier functions, interaction models, and fractional quantum anomalous Hall effect in twisted bilayer MoTe2. Proc. Natl. Acad. Sci. U.S.A. 121, e2316749121 (2024)

    work page 2024

  61. [61]

    X., Li, B., Luo, X

    Qiu, W. X., Li, B., Luo, X. J., Wu, F. Interaction-Driven Topological Phase Diagram of Twisted Bilayer MoTe2. Phys. Rev. X 13, 041026 (2024)

    work page 2024

  62. [62]

    Anderson, E. et al. Trion sensing of a zero- field composite Fermi liquid . Nature 635, 590-595 (2024)

    work page 2024

  63. [63]

    Knüppel, P. et al. Correlated states controlled by tunable van Hove singularity in moiré WSe2. Preprint at https://arxiv.org/abs/2406.03315 (2024). 14

    work page arXiv 2024

  64. [64]

    Foutty, B. A. et al. Mapping twist -tuned multiband topology in bilayer WSe 2. Science 384, 343-347 (2024)

    work page 2024

  65. [65]

    Jiang, H. et al. Quantum liquid versus electron solid around ν= 1/5 Landau-level filling. Phys. Rev. Lett. 65, 633 (1990)

    work page 1990

  66. [66]

    & Cunningham, J

    Goldman, V ., Santos, M., Shayegan, M. & Cunningham, J. Evidence for two- dimentional quantum Wigner crystal. Phys. Rev. Lett. 65, 2189 (1990)

    work page 1990

  67. [67]

    Santos, M. et al. Observation of a reentrant insulating phase near the 1/3 fractional quantum Hall liquid in a two -dimensional hole system. Phys. Rev. Let t. 68, 1188 (1992)

    work page 1992

  68. [68]

    R. B. Laughlin, Superconducting ground state of noninteracting particles obeying fractional statistics, Phys. Rev. Lett. 60, 2677 (1988)

    work page 1988

  69. [69]

    A. L. Fetter, C. B. Hanna, and R. B. Laughlin, Random-phase approximation in the fractional-statistics gas, Phys. Rev. B 39, 9679 (1989)

    work page 1989

  70. [70]

    Lee and M

    D.-H. Lee and M. P. A. Fisher, Anyon superconductivity and the fractional quantum hall effect, Phys. Rev. Lett. 63, 903 (1989)

    work page 1989

  71. [71]

    Y.-H. Chen, F. Wilczek, E. Witten, and B. I. Halperin, On Anyon Superconductivity, International Journal of Modern Physics A 4, 3983 (1989)

    work page 1989

  72. [72]

    X. G. Wen and A. Zee, Compressibility and superfluidity in the fractional-statistics liquid, Phys. Rev. B 41, 240 (1990). Methods 2H-MoTe2 crystal growth High-purity molybdenum powder (99.997% Mo) and tellurium powder (99.999%) were thoroughly mixed at a molar ratio of 1:30 and loaded into a quartz ampule. The ampule was then sealed under high vacuum (∼10...

    work page 1990

  73. [73]

    Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013)

    work page 2013

  74. [74]

    Mao, N. et al. Transfer learning electronic structure and continuum model for twisted bilayer MoTe2. Commun. Phys. 7, 262 (2024)

    work page 2024

  75. [75]

    Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641-646 (2021)

    work page 2021

  76. [76]

    & Vandenberghe, W.G

    Laturia, A., Van de Put, M.L. & Vandenberghe, W.G. Dielectric properties of hexagonal boron nitride and transition metal dichalcogenides: from monolayer to bulk. npj 2D Mater Appl 2, 6 (2018). 17 Acknowledgement We sincerely thank Rui-Rui Du, Zhao Liu, Xiaoyan Xu, and Xiaoxiang Xi for helpful discussions. This work is supported by the National Key R&D Pro...

    work page 2018