1. Tsui, D. C., Stormer, H. L. \& Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).

Article 
ADS 
Google Scholar
2. Willett, R. et al. Observation of an even-denominator quantum number in the fractional quantum Hall effect. Phys. Rev. Lett. 59, 1776–1779 (1987).

Article 
ADS 
PubMed 
Google Scholar
3. Neupert, T., Santos, L., Chamon, C. \& Mudry, C. Fractional quantum Hall states at zero magnetic field. Phys. Rev. Lett. 106, 236804 (2011).

Article 
ADS 
PubMed 
Google Scholar
4. Tang, E., Mei, J.-W. \& Wen, X.-G. High-temperature fractional quantum Hall states. Phys. Rev. Lett. 106, 236802 (2011).

Article 
ADS 
PubMed 
Google Scholar
5. Sun, K., Gu, Z., Katsura, H. \& Das Sarma, S. Nearly flatbands with nontrivial topology. Phys. Rev. Lett. 106, 236803 (2011).

Article 
ADS 
PubMed 
Google Scholar
6. Sheng, D. N., Gu, Z.-C., Sun, K. \& Sheng, L. Fractional quantum Hall effect in the absence of Landau levels. Nat. Commun. 2, 389 (2011).

Article 
ADS 
PubMed 
PubMed Central 
Google Scholar
7. Regnault, N. \& Bernevig, B. A. Fractional Chern insulator. Phys. Rev. X 1, 021014 (2011).

Google Scholar
8. Arovas, D., Schrieffer, J. R. \& Wilczek, F. Fractional statistics and the quantum Hall effect. Phys. Rev. Lett. 53, 722–723 (1984).

Article 
ADS 
Google Scholar
9. Wen, X. G. Non-Abelian statistics in the fractional quantum Hall states. Phys. Rev. Lett. 66, 802–805 (1991).

Article 
ADS 
MathSciNet 
PubMed 
Google Scholar
10. Bartolomei, H. et al. Fractional statistics in anyon collisions. Science 368, 173–177 (2020).

[Article](https://doi.org/10.1126%2Fscience.aaz5601) 
[ADS](http://adsabs.harvard.edu/cgi-bin/nph-data_query?link_type=ABSTRACT&bibcode=2020Sci...368..173B) 
[MathSciNet](http://www.ams.org/mathscinet-getitem?mr=4265161) 
[PubMed](http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Abstract&list_uids=32273465) 
[Google Scholar](http://scholar.google.com/scholar_lookup?&title=Fractional%20statistics%20in%20anyon%20collisions&journal=Science&doi=10.1126%2Fscience.aaz5601&volume=368&pages=173-177&publication_year=2020&author=Bartolomei%2CH)
  1. Nakamura, J., Liang, S., Gardner, G. C. \& Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).

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

    Article 
    ADS 
    PubMed 
    Google Scholar
    13. Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023).

    Article 
    ADS 
    PubMed 
    Google Scholar
    14. Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).

    Article 
    ADS 
    PubMed 
    Google Scholar
    15. Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. X 13, 031037 (2023).

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

    Article 
    ADS 
    PubMed 
    Google Scholar
    17. Lu, Z. et al. Extended quantum anomalous Hall states in graphene/hBN moiré superlattices. Nature 637, 1090–1095 (2025).

    Article 
    ADS 
    PubMed 
    Google Scholar
    18. Waters, D. et al. Chern insulators at integer and fractional filling in moiré pentalayer graphene. Phys. Rev. X 15, 011045 (2025).

    Google Scholar
    19. Choi, Y. et al. Superconductivity and quantized anomalous Hall effect in rhombohedral graphene. Nature 639, 342–347 (2025).

    Article 
    ADS 
    PubMed 
    Google Scholar
    20. Xie, J. et al. Tunable fractional Chern insulators in rhombohedral graphene superlattices. Nat. Mater. 24, 1042–1048 (2025).

    Article 
    PubMed 
    Google Scholar
    21. Liu, Z., Bergholtz, E. J., Fan, H. \& Läuchli, A. M. Fractional Chern insulators in topological flat bands with higher Chern number. Phys. Rev. Lett. 109, 186805 (2012).

    Article 
    ADS 
    PubMed 
    Google Scholar
    22. Yang, S., Gu, Z.-C., Sun, K. \& Das Sarma, S. Topological flat band models with arbitrary Chern numbers. Phys. Rev. B 86, 241112 (2012).

    Article 
    ADS 
    Google Scholar
    23. Sterdyniak, A., Repellin, C., Bernevig, B. A. \& Regnault, N. Series of Abelian and non-Abelian states in C > 1 fractional Chern insulators. Phys. Rev. B 87, 205137 (2013).

    Article 
    ADS 
    Google Scholar
    24. Möller, G. \& Cooper, N. R. Fractional Chern insulators in Harper–Hofstadter bands with higher Chern number. Phys. Rev. Lett. 115, 126401 (2015).

    Article 
    ADS 
    PubMed 
    Google Scholar
    25. Wang, J. \& Liu, Z. Hierarchy of ideal flatbands in chiral twisted multilayer graphene models. Phys. Rev. Lett. 128, 176403 (2022).

    Article 
    ADS 
    PubMed 
    Google Scholar
    26. Zhang, Y.-H., Mao, D., Cao, Y., Jarillo-Herrero, P. \& Senthil, T. Nearly flat Chern bands in moiré superlattices. Phys. Rev. B 99, 075127 (2019).

    Article 
    ADS 
    Google Scholar
    27. Ledwith, P. J., Vishwanath, A. \& Khalaf, E. Family of ideal Chern flatbands with arbitrary Chern number in chiral twisted graphene multilayers. Phys. Rev. Lett. 128, 176404 (2022).

    Article 
    ADS 
    MathSciNet 
    PubMed 
    Google Scholar
    28. Repellin, C. \& Senthil, T. Chern bands of twisted bilayer graphene: fractional Chern insulators and spin phase transition. Phys. Rev. Res. 2, 023238 (2020).

    Article 
    Google Scholar
    29. Ledwith, P. J., Tarnopolsky, G., Khalaf, E. \& Vishwanath, A. Fractional Chern insulator states in twisted bilayer graphene: an analytical approach. Phys. Rev. Res. 2, 023237 (2020).

    Article 
    Google Scholar
    30. Aronson, S. H. et al. Displacement field-controlled fractional chern insulators and charge density waves in a graphene/hBN moiré superlattice. Phys. Rev. X 15, 031026 (2025).

    Google Scholar
    31. Xie, J. et al. Unconventional orbital magnetism in graphene-based fractional Chern insulators. Preprint at https://arxiv.org/abs/2506.01485 (2025).
    32. Huo, Z. et al. Does moire matter? Critical moire dependence with quantum fluctuations in graphene based integer and fractional Chern insulators. Preprint at https://arxiv.org/abs/2510.15309 (2025).
    33. Dong, J. et al. Observation of integer and fractional Chern insulators in high Chern number flatbands. Preprint at https://arxiv.org/abs/2507.09908 (2025).
    34. Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).

    Article 
    ADS 
    PubMed 
    Google Scholar
    35. Han, T. et al. Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene. Nat. Nanotechnol. 19, 181–187 (2024).

    Article 
    ADS 
    PubMed 
    Google Scholar
    36. Han, T. et al. Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene. Science 384, 647–651 (2024).

    Article 
    ADS 
    PubMed 
    Google Scholar
    37. Sha, Y. et al. Observation of a Chern insulator in crystalline ABCA-tetralayer graphene with spin–orbit coupling. Science 384, 414–419 (2024).

    Article 
    ADS 
    PubMed 
    Google Scholar
    38. Wang, W. et al. Programmable quantum anomalous Hall insulator in twisted crystalline flatbands. Phys. Rev. X 16, 011015 (2026).

    Google Scholar
    39. Liu, N. et al. Diverse high-Chern-number quantum anomalous Hall insulators in twisted rhombohedral graphene. Preprint at https://arxiv.org/abs/2507.11347 (2025).
    40. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    Article 
    ADS 
    PubMed 
    Google Scholar
    41. Chen, S. et al. Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene. Nat. Phys. 17, 374–380 (2021).

    Article 
    Google Scholar
    42. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    Article 
    ADS 
    PubMed 
    Google Scholar
    43. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

    Article 
    ADS 
    PubMed 
    Google Scholar
    44. Bultinck, N., Chatterjee, S. \& Zaletel, M. P. Mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene. Phys. Rev. Lett. 124, 166601 (2020).

    Article 
    ADS 
    MathSciNet 
    PubMed 
    Google Scholar
    45. Zhu, J., Su, J.-J. \& MacDonald, A. H. Voltage-controlled magnetic reversal in orbital Chern insulators. Phys. Rev. Lett. 125, 227702 (2020).

    Article 
    ADS 
    PubMed 
    Google Scholar
    46. Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).

    Article 
    ADS 
    PubMed 
    Google Scholar
    47. Dong, Z., Patri, A. S. \& Senthil, T. Stability of anomalous Hall crystals in multilayer rhombohedral graphene. Phys. Rev. B 110, 205130 (2024).

    Article 
    ADS 
    Google Scholar
    48. Zhou, B., Yang, H. \& Zhang, Y.-H. Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene in the moiréless limit. Phys. Rev. Lett. 133, 206504 (2024).

    Article 
    ADS 
    PubMed 
    Google Scholar
    49. Dong, J. et al. Anomalous Hall crystals in rhombohedral multilayer graphene. I. Interaction-driven Chern bands and fractional quantum Hall states at zero magnetic field. Phys. Rev. Lett. 133, 206503 (2024).

    Article 
    ADS 
    PubMed 
    Google Scholar
    50. Soejima, T. et al. Anomalous Hall crystals in rhombohedral multilayer graphene. II. General mechanism and a minimal model. Phys. Rev. B 110, 205124 (2024).

    Article 
    ADS 
    Google Scholar
    51. Xie, Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021).

    Article 
    ADS 
    PubMed 
    PubMed Central 
    Google Scholar
    52. Dong, J., Ledwith, P. J., Khalaf, E., Lee, J. Y. \& Vishwanath, A. Many-body ground states from decomposition of ideal higher Chern bands: applications to chirally twisted graphene multilayers. Phys. Rev. Res. 5, 023166 (2023).

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

    Article 
    Google Scholar
    54. Barkeshli, M. \& Qi, X.-L. Topological nematic states and non-Abelian lattice dislocations. Phys. Rev. X 2, 031013 (2012).

    Google Scholar
    55. Wang, J., Klevtsov, S. \& Liu, Z. Origin of model fractional Chern insulators in all topological ideal flatbands: explicit color-entangled wave function and exact density algebra. Phys. Rev. Res. 5, 023167 (2023).

    Article 
    Google Scholar
    56. Feng, Z. et al. Rapid infrared imaging of rhombohedral graphene. Phys. Rev. Appl. 23, 034012 (2025).

    Article 
    ADS 
    Google Scholar
    57. Zhang, H. et al. Moiré enhanced flat band in rhombohedral graphene. Nat. Mater. 25, 566–572 (2026).