Matsukura, F., Tokura, Y. & Ohno, H. Control of magnetism by electric fields. Nat. Nanotechnol. 10, 209–220 (2015).
Jiang, S., Shan, J. & Mak, K. F. Electric-field switching of two-dimensional van der Waals magnets. Nat. Mater. 17, 406–410 (2018).
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).
Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020); correction 581, E3 (2020).
Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
Xie, M. & MacDonald, A. Nature of the correlated insulator states in twisted bilayer graphene. Phys. Rev. Lett. 124, 097601 (2020).
Bultinck, N., Chatterjee, S. & Zaletel, M. P. Mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene. Phys. Rev. Lett. 124, 166601 (2020).
Zhang, Y.-H., Mao, D. & Senthil, T. Twisted bilayer graphene aligned with hexagonal boron nitride: anomalous Hall effect and a lattice model. Phys. Rev. Res. 1, 033126 (2019).
Liu, J. & Dai, X. Theories for the correlated insulating states and quantum anomalous Hall phenomena in twisted bilayer graphene. Preprint at https://arxiv.org/abs/1911.03760 (2020).
Wu, F. & Das Sarma, S. Collective excitations of quantum anomalous Hall ferromagnets in twisted bilayer graphene. Phys. Rev. Lett. 124, 046403 (2020).
Chatterjee, S., Bultinck, N. & Zaletel, M. P. Symmetry breaking and skyrmionic transport in twisted bilayer graphene. Phys. Rev. B 101, 165141 (2020).
Repellin, C., Dong, Z., Zhang, Y.-H. & Senthil, T. Ferromagnetism in narrow bands of moiré superlattices. Phys. Rev. Lett. 124, 187601 (2020).
Alavirad, Y. & Sau, J. D. Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene. Preprint at https://arxiv.org/abs/1907.13633 (2019).
Ma, Z. et al. Topological flat bands in twisted trilayer graphene. Preprint at https://arxiv.org/abs/1905.00622 (2019).
Park, Y., Chittari, B. L. & Jung, J. Gate-tunable topological flat bands in twisted monolayer-bilayer graphene. Phys. Rev. B 102, 035411 (2020).
Rademaker, L., Protopopov, I. V. & Abanin, D. A. Topological flat bands and correlated states in twisted monolayer-bilayer graphene. Phys. Rev. Res. 2, 033150 (2020).
Chang, C.-Z. et al. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340, 167–170 (2013).
Zhu, J., Su, J.-J. & MacDonald, A. H. The curious magnetic properties of orbital Chern insulators. Preprint at https://arxiv.org/abs/2001.05084 (2020).
Haldane, F. D. M. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015–2018 (1988).
Song, J. C. W., Samutpraphoot, P. & Levitov, L. S. Topological Bloch bands in graphene superlattices. Proc. Natl Acad. Sci. USA 112, 10879–10883 (2015).
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).
Liu, J., Ma, Z., Gao, J. & Dai, X. Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems. Phys. Rev. X 9, 031021 (2019).
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).
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); correction 583, E27 (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. https://doi.org/10.1038/s41567-020-1030-6 (2020).
Streda, P. Quantised Hall effect in a two-dimensional periodic potential. J. Phys. C 15, L1299 (1982).
Tschirhart, C. L. et al. Imaging orbital ferromagnetism in a moiré Chern insulator. Preprint at https://arxiv.org/abs/2006.08053 (2020).
Chiba, D. et al. Anomalous Hall effect in field-effect structures of (Ga,Mn)As. Phys. Rev. Lett. 104, 106601 (2010).
Zhang, S. et al. Experimental observation of the gate-controlled reversal of the anomalous Hall effect in the intrinsic magnetic topological insulator MnBi2Te4 device. Nano Lett. 20, 709–714 (2020).
Beekman, M., Heideman, C. L. & Johnson, D. C. Ferecrystals: non-epitaxial layered intergrowths. Semicond. Sci. Technol. 29, 064012 (2014).
Viola, G. & DiVincenzo, D. P. Hall effect gyrators and circulators. Phys. Rev. X 4, 021019 (2014).
Lian, B., Sun, X.-Q., Vaezi, A., Qi, X.-L. & Zhang, S.-C. Topological quantum computation based on chiral Majorana fermions. Proc. Natl Acad. Sci. USA 115, 10938–10942 (2018).