Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002 (1934).
Grimes, C. C. & Adams, G. Evidence for a liquid-to-crystal phase transition in a classical, two-dimensional sheet of electrons. Phys. Rev. Lett. 42, 795 (1979).
Andrei, E. Y. et al. Observation of a magnetically induced Wigner solid. Phys. Rev. Lett. 60, 2765–2768 (1988).
Dong, Z., Patri, A. S. & Senthil, T. Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures. Phys. Rev. Lett. 133, 206502 (2024).
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).
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).
Kwan, Y. H. et al. Moiré fractional Chern insulators III: Hartree-Fock phase diagram, magic angle regime for Chern insulator states, the role of the moiré potential and Goldstone gaps in rhombohedral graphene superlattices. Preprint at https://arxiv.org/abs/2312.11617 (2023).
Sheng, D. N., Reddy, A. P., Abouelkomsan, A., Bergholtz, E. J. & Fu, L. Quantum anomalous hall crystal at fractional filling of moiré superlattices. Phys. Rev. Lett. 133, 066601 (2024).
Tan, T. & Devakul, T. Parent Berry curvature and the ideal anomalous Hall crystal. Phys. Rev. X 14, 041040 (2024).
Soejima, T. et al. Anomalous Hall crystals in rhombohedral multilayer graphene. II: General mechanism and a minimal model. Phys. Rev. B 110, 205124 (2024).
Dong, Z., Patri, A. S. & Senthil, T. Stability of anomalous Hall crystals in multilayer rhombohedral graphene. Phys. Rev. B 110, 205130 (2024).
Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015 (1988).
Chang, C.-Z., Liu, C.-X. & MacDonald, A. H. Colloquium: quantum anomalous Hall effect. Rev. Mod. Phys. 95, 011002 (2023).
Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405 (1982).
Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).
Stepanov, P. et al. Competing zero-field Chern insulators in superconducting twisted bilayer graphene. Phys. Rev. Lett. 127, 197701 (2021).
Polshyn, H. et al. Topological charge density waves at half-integer filling of a moiré superlattice. Nat. Phys. 18, 42–47 (2022).
Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).
Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).
Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).
Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023).
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).
Tao, Z. et al. Valley-coherent quantum anomalous Hall state in AB-stacked MoTe2/WSe2 bilayers. Phys. Rev. X 14, 011004 (2024).
Han, T. et al. Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene. Science 384, 647–651 (2024).
Sha, Y. et al. Observation of Chern insulator in crystalline ABCA-tetralayer graphene with spin-orbit coupling. Science 384, 414–419 (2024).
Tešanović, Z., Axel, F. & Halperin, B. “Hall crystal” versus Wigner crystal. Phys. Rev. B 39, 8525 (1989).
Ung, S. F., Lee, J. & Reichman, D. R. Competing generalized Wigner crystal states in moiré heterostructures. Phys. Rev. B 108, 245113 (2023).
Morales-Durán, N., Potasz, P. & MacDonald, A. H. Magnetism and quantum melting in moiré-material Wigner crystals. Phys. Rev. B 107, 235131 (2023).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).
Wang, L. et al. Evidence for a fractional fractal quantum hall effect in graphene superlattices. Science 350, 1231–1234 (2015).
Spanton, E. M. et al. Observation of fractional chern insulators in a van der Waals heterostructure. Science 360, 62–66 (2018).
Saito, Y. et al. Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene. Nat. Phys. 17, 478–481 (2021).
Xie, Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021).
He, M. et al. Symmetry-broken Chern insulators in twisted double bilayer graphene. Nano Lett. 23, 11066–11072 (2023).
Xie, Y. et al. Strong interactions and isospin symmetry breaking in a supermoiré lattice. Preprint at https://arxiv.org/abs/2404.01372 (2024).
Waters, D. et al. Topological flat bands in a family of multilayer graphene moiré lattices. Nat. Commun. 15, 10552 (2024).
Streda, P. Quantised Hall effect in a two-dimensional periodic potential. J. Phys. C 15, L1299 (1982).
Streda, P. Theory of quantised Hall conductivity in two dimensions. J. Phys. C 15, L717 (1982).
Zhu, J., Su, J.-J. & MacDonald, A. H. Voltage-controlled magnetic reversal in orbital Chern insulators. Phys. Rev. Lett. 125, 227702 (2020).
Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).
Grover, S. et al. Chern mosaic and Berry-curvature magnetism in magic-angle graphene. Nat. Phys. 18, 885–892 (2022).
Li, H. et al. Electrode-free anodic oxidation nanolithography of low-dimensional materials. Nano Lett. 18, 8011–8015 (2018).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).
Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).
Liu, X. et al. Tunable spin-polarized correlated states in twisted double bilayer graphene. Nature 583, 221–225 (2020).
Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583, 215–220 (2020).
Burg, G. W. et al. Correlated insulating states in twisted double bilayer graphene. Phys. Rev. Lett. 123, 197702 (2019).
He, M. et al. Symmetry breaking in twisted double bilayer graphene. Nat. Phys. 17, 26–30 (2021).
Chen, S. et al. Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene. Nat. Phys. 17, 374–380 (2021).
Xu, S. et al. Tunable van Hove singularities and correlated states in twisted monolayer–bilayer graphene. Nat. Phys. 17, 619–626 (2021).
Rickhaus, P. et al. Gap opening in twisted double bilayer graphene by crystal fields. Nano Lett. 19, 8821–8828 (2019).
Kolář, K., Zhang, Y., Nadj-Perge, S., von Oppen, F. & Lewandowski, C. Electrostatic fate of N-layer moiré graphene. Phys. Rev. B 108, 195148 (2023).
Fukui, T., Hatsugai, Y. & Suzuki, H. Chern numbers in discretized Brillouin zone: efficient method of computing (spin) Hall conductances. J. Phys. Soc. Jpn 74, 1674–1677 (2005).