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 
CAS 

Google Scholar
 

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 
CAS 
PubMed 

Google Scholar
 

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
 

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
 

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
 

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 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

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


Google Scholar
 

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
 

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

Article 
ADS 
MathSciNet 
CAS 
PubMed 

Google Scholar
 

Bartolomei, H. et al. Fractional statistics in anyon collisions. Science 368, 173–177 (2020).

Article 
ADS 
MathSciNet 
CAS 
PubMed 

Google Scholar
 

Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).

Article 
CAS 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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

CAS 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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

CAS 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Xie, J. et al. Tunable fractional Chern insulators in rhombohedral graphene superlattices. Nat. Mater. 24, 1042–1048 (2025).

Article 
CAS 
PubMed 

Google Scholar
 

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
 

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
 

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
 

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
 

Wang, J. & Liu, Z. Hierarchy of ideal flatbands in chiral twisted multilayer graphene models. Phys. Rev. Lett. 128, 176403 (2022).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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 
CAS 

Google Scholar
 

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 
CAS 
PubMed 

Google Scholar
 

Repellin, C. & Senthil, T. Chern bands of twisted bilayer graphene: fractional Chern insulators and spin phase transition. Phys. Rev. Res. 2, 023238 (2020).

Article 
CAS 

Google Scholar
 

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 
CAS 

Google Scholar
 

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).

CAS 

Google Scholar
 

Xie, J. et al. Unconventional orbital magnetism in graphene-based fractional Chern insulators. Preprint at https://arxiv.org/abs/2506.01485 (2025).

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).

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).

Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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 
CAS 
PubMed 

Google Scholar
 

Wang, W. et al. Programmable quantum anomalous Hall insulator in twisted crystalline flatbands. Phys. Rev. X 16, 011015 (2026).

CAS 

Google Scholar
 

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).

Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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

Article 
CAS 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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 
CAS 
PubMed 

Google Scholar
 

Zhu, J., Su, J.-J. & MacDonald, A. H. Voltage-controlled magnetic reversal in orbital Chern insulators. Phys. Rev. Lett. 125, 227702 (2020).

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 

Google Scholar
 

Dong, Z., Patri, A. S. & Senthil, T. Stability of anomalous Hall crystals in multilayer rhombohedral graphene. Phys. Rev. B 110, 205130 (2024).

Article 
ADS 
CAS 

Google Scholar
 

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 
CAS 
PubMed 

Google Scholar
 

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 
CAS 
PubMed 

Google Scholar
 

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 
CAS 

Google Scholar
 

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

Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar
 

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 
CAS 

Google Scholar
 

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

Article 
CAS 

Google Scholar
 

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


Google Scholar
 

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 
CAS 

Google Scholar
 

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

Article 
ADS 
CAS 

Google Scholar
 

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