Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002 (1934).
Google Scholar
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).
Google Scholar
Andrei, E. Y. et al. Observation of a magnetically induced Wigner solid. Phys. Rev. Lett. 60, 2765–2768 (1988).
Google Scholar
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).
Google Scholar
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).
Google Scholar
Chang, C.-Z., Liu, C.-X. & MacDonald, A. H. Colloquium: quantum anomalous Hall effect. Rev. Mod. Phys. 95, 011002 (2023).
Google Scholar
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).
Google Scholar
Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959–2007 (2010).
Google Scholar
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Google Scholar
Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).
Google Scholar
Stepanov, P. et al. Competing zero-field Chern insulators in superconducting twisted bilayer graphene. Phys. Rev. Lett. 127, 197701 (2021).
Google Scholar
Polshyn, H. et al. Topological charge density waves at half-integer filling of a moiré superlattice. Nat. Phys. 18, 42–47 (2022).
Google Scholar
Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).
Google Scholar
Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).
Google Scholar
Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).
Google Scholar
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).
Google Scholar
Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023).
Google Scholar
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).
Google Scholar
Tao, Z. et al. Valley-coherent quantum anomalous Hall state in AB-stacked MoTe2/WSe2 bilayers. Phys. Rev. X 14, 011004 (2024).
Google Scholar
Han, T. et al. Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene. Science 384, 647–651 (2024).
Google Scholar
Sha, Y. et al. Observation of Chern insulator in crystalline ABCA-tetralayer graphene with spin-orbit coupling. Science 384, 414–419 (2024).
Google Scholar
Tešanović, Z., Axel, F. & Halperin, B. “Hall crystal” versus Wigner crystal. Phys. Rev. B 39, 8525 (1989).
Google Scholar
Ung, S. F., Lee, J. & Reichman, D. R. Competing generalized Wigner crystal states in moiré heterostructures. Phys. Rev. B 108, 245113 (2023).
Google Scholar
Morales-Durán, N., Potasz, P. & MacDonald, A. H. Magnetism and quantum melting in moiré-material Wigner crystals. Phys. Rev. B 107, 235131 (2023).
Google Scholar
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Google Scholar
Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).
Google Scholar
Wang, L. et al. Evidence for a fractional fractal quantum hall effect in graphene superlattices. Science 350, 1231–1234 (2015).
Google Scholar
Spanton, E. M. et al. Observation of fractional chern insulators in a van der Waals heterostructure. Science 360, 62–66 (2018).
Google Scholar
Saito, Y. et al. Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene. Nat. Phys. 17, 478–481 (2021).
Google Scholar
Xie, Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021).
Google Scholar
He, M. et al. Symmetry-broken Chern insulators in twisted double bilayer graphene. Nano Lett. 23, 11066–11072 (2023).
Google Scholar
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).
Google Scholar
Streda, P. Theory of quantised Hall conductivity in two dimensions. J. Phys. C 15, L717 (1982).
Google Scholar
Zhu, J., Su, J.-J. & MacDonald, A. H. Voltage-controlled magnetic reversal in orbital Chern insulators. Phys. Rev. Lett. 125, 227702 (2020).
Google Scholar
Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).
Google Scholar
Grover, S. et al. Chern mosaic and Berry-curvature magnetism in magic-angle graphene. Nat. Phys. 18, 885–892 (2022).
Google Scholar
Li, H. et al. Electrode-free anodic oxidation nanolithography of low-dimensional materials. Nano Lett. 18, 8011–8015 (2018).
Google Scholar
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Google Scholar
Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015).
Google Scholar
Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).
Google Scholar
Liu, X. et al. Tunable spin-polarized correlated states in twisted double bilayer graphene. Nature 583, 221–225 (2020).
Google Scholar
Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583, 215–220 (2020).
Google Scholar
Burg, G. W. et al. Correlated insulating states in twisted double bilayer graphene. Phys. Rev. Lett. 123, 197702 (2019).
Google Scholar
He, M. et al. Symmetry breaking in twisted double bilayer graphene. Nat. Phys. 17, 26–30 (2021).
Google Scholar
Chen, S. et al. Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene. Nat. Phys. 17, 374–380 (2021).
Google Scholar
Xu, S. et al. Tunable van Hove singularities and correlated states in twisted monolayer–bilayer graphene. Nat. Phys. 17, 619–626 (2021).
Google Scholar
Rickhaus, P. et al. Gap opening in twisted double bilayer graphene by crystal fields. Nano Lett. 19, 8821–8828 (2019).
Google Scholar
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).
Google Scholar
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).
Google Scholar
