Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).
Google Scholar
Kane, C. L. & Mele, E. J. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).
Google Scholar
Bernevig, B. A., Hughes, T. L. & Zhang, S. C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).
Google Scholar
Bernevig, B. A. & Zhang, S.-C. Quantum spin Hall effect. Phys. Rev. Lett. 96, 106802 (2006).
Google Scholar
Sheng, D. N., Weng, Z. Y., Sheng, L. & Haldane, F. D. M. Quantum spin-Hall effect and topologically invariant Chern numbers. Phys. Rev. Lett. 97, 036808 (2006).
Google Scholar
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).
Google Scholar
Konig, M. et al. Quantum spin hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).
Google Scholar
Roth, A. et al. Nonlocal transport in the quantum spin Hall state. Science 325, 294–297 (2009).
Google Scholar
Knez, I., Du, R. R. & Sullivan, G. Evidence for helical edge modes in inverted InAs/GaSb quantum wells. Phys. Rev. Lett. 107, 136603 (2011).
Google Scholar
Young, A. F. et al. Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state. Nature 505, 528–532 (2014).
Google Scholar
Fei, Z. et al. Edge conduction in monolayer WTe2. Nat. Phys. 13, 677–682 (2017).
Google Scholar
Wu, S. F. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018).
Google Scholar
Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).
Google Scholar
Zhao, W. et al. Realization of the Haldane Chern insulator in a moiré lattice. Nat. Phys. 20, 275–280 (2024).
Wu, F. C., Lovorn, T., Tutuc, E., Martin, I. & MacDonald, A. H. Topological insulators in twisted transition metal dichalcogenide homobilayers. Phys. Rev. Lett. 122, 086402 (2019).
Google Scholar
Devakul, T., Crepel, V., Zhang, Y. & Fu, L. Magic in twisted transition metal dichalcogenide bilayers. Nat. Commun. 12, 6730 (2021).
Google Scholar
Andrei, E. Y. et al. The marvels of moiré materials. Nat. Rev. Mater. 6, 201–206 (2021).
Google Scholar
Kennes, D. M. et al. Moire heterostructures as a condensed-matter quantum simulator. Nat. Phys. 17, 155–163 (2021).
Google Scholar
Mak, K. F. & Shan, J. Semiconductor moire materials. Nat. Nanotechnol. 17, 686–695 (2022).
Google Scholar
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Google Scholar
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
Google Scholar
Xiao, D., Liu, G. B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).
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 moire 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
Xu, F. et al. Observation of Integer and Fractional Quantum Anomalous Hall Effects in Twisted Bilayer MoTe2. Phys. Rev. 13, 031037 (2023).
Google Scholar
Reddy, A. P., Alsallom, F. F., Zhang, Y., Devakul, T. & Fu, L. Fractional quantum anomalous Hall states in twisted bilayer MoTe2 and WSe2. Phys. Rev. B 108, 085117 (2023).
Wang, C. et al. Fractional Chern insulator in twisted bilayer MoTe2. Phys. Rev. Lett. 132, 036501 (2024).
Morales-Durán, N., Wei, N., Shi, J. & MacDonald, A. H. Magic angles and fractional Chern insulators in twisted homobilayer TMDs. Preprint at arxiv.org/abs/2308.03143 (2023).
Mao, N. et al. Lattice relaxation, electronic structure and continuum model for twisted bilayer MoTe2. Preprint at arxiv.org/abs/2311.07533 (2023).
Crépel, V., Regnault, N. & Queiroz, R. The chiral limits of moiré semiconductors: origin of flat bands and topology in twisted transition metal dichalcogenides homobilayers. Preprint at https://arxiv.org/abs/2305.10477 (2023).
Jia, Y. et al. Moiré fractional Chern insulators I: first-principles calculations and continuum models of twisted bilayer MoTe2. Preprint at arxiv.org/abs/2311.04958 (2023).
Li, B., Qiu, X-W, Wu, F. Electrically tuned topology and magnetism in twisted bilayer MoTe2 at νh = 1. Phys. Rev. B 109, L041106 (2024).
Mai, P., Feldman, B. E. & Phillips, P. W. Topological Mott insulator at quarter filling in the interacting Haldane model. Phys. Rev. Res. 5, 013162 (2023).
Google Scholar
Morales-Durán, N. et al. Pressure-enhanced fractional Chern insulators along a magic line in moiré transition metal dichalcogenides. Phys. Rev. Research 5, L032022 (2023).
Bai, Y. X. et al. Doubled quantum spin Hall effect with high-spin Chern number in α-antimonene and α-bismuthene. Phys. Rev. B 105, 195142 (2022).
Google Scholar
Levin, M. & Stern, A. Fractional topological insulators. Phys. Rev. Lett. 103, 196803 (2009).
Google Scholar
Maciejko, J. & Fiete, G. A. Fractionalized topological insulators. Nat. Phys. 11, 385–388 (2015).
Google Scholar
Neupert, T., Chamon, C., Iadecola, T., Santos, L. H. & Mudry, C. Fractional (Chern and topological) insulators. Phys. Scr. 2015, 014005 (2015).
Google Scholar
Stern, A. Fractional topological insulators: a pedagogical review. Annu. Rev. Condens. Matter Phys. 7, 349–368 (2016).
Google Scholar
Wu, Y.-M., Shaffer, D., Wu, Z. & Santos, L. H. Time-reversal invariant topological moiré flatband: a platform for the fractional quantum spin Hall effect. Preprint at https://arxiv.org/abs/2309.07222 (2023).
Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).
Google Scholar
Stormer, H. L., Tsui, D. C. & Gossard, A. C. The fractional quantum Hall effect. Rev. Mod. Phys. 71, S298–S305 (1999).
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
Xie, Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021).
Google Scholar
Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).
Xu, Y. et al. A tunable bilayer Hubbard model in twisted WSe2. Nat. Nanotechnol. 17, 934–939 (2022).
Google Scholar
Shi, Q. et al. Odd- and even-denominator fractional quantum Hall states in monolayer WSe2. Nat. Nanotechnol. 15, 569–573 (2020).
Google Scholar
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Google Scholar
Lau, C. N., Bockrath, M. W., Mak, K. F. & Zhang, F. Reproducibility in the fabrication and physics of moiré materials. Nature 602, 41–50 (2022).
Google Scholar
Xia, Z. et al. Optical readout of the chemical potential of two-dimensional electrons. Nat. Photon. 10.1038/s41566-024-01377-3 (2024).
Büttiker, M. Absence of backscattering in the quantum Hall effect in multiprobe conductors. Phys. Rev. B 38, 9375–9389 (1988).
Google Scholar
Pack, J. et al. Charge-transfer contact to a high-mobility monolayer semiconductor. Preprint at arxiv.org/abs/2310.19782 (2023).
Abanin, D. A. et al. Giant nonlocality near the Dirac point in graphene. Science 332, 328–330 (2011).
Google Scholar