Auciello, O., Scott, J. F. & Ramesh, R. The physics of ferroelectric memories. Phys. Today 51, 22–27 (1998).
Chikazumi, S. & Graham, C. D. Physics of Ferromagnetism Vol. 94 (Oxford Univ. Press, 1997).
Liu, J., Wang, H., Fang, C., Fu, L. & Qian, X. Van der Waals stacking-induced topological phase transition in layered ternary transition metal chalcogenides. Nano Lett. 17, 467–475 (2017).
Guo, P.-J., Lu, X.-Q., Ji, W., Liu, K. & Lu, Z.-Y. Quantum spin Hall effect in monolayer and bilayer TaIrTe4. Phys. Rev. B 102, 041109 (2020).
Tang, J. et al. Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe4. Nature 628, 515–521 (2024).
Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).
Ma, Q. et al. Observation of the nonlinear Hall effect under time-reversal-symmetric conditions. Nature 565, 337–342 (2019).
Kang, K., Li, T., Sohn, E., Shan, J. & Mak, K. F. Nonlinear anomalous Hall effect in few-layer WTe2. Nat. Mater. 18, 324–328 (2019).
Xiao, J. et al. Berry curvature memory through electrically driven stacking transitions. Nat. Phys. 16, 1028–1034 (2020).
Gao, A. et al. Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure. Science 381, 181–186 (2023).
Wang, N. et al. Quantum-metric-induced nonlinear transport in a topological antiferromagnet. Nature 621, 487–492 (2023).
Xi, T. et al. Terahertz sensing based on the nonlinear electrodynamics of the two-dimensional correlated topological semimetal TaIrTe4. Nat. Electron. 8, 578–586 (2025).
Jiang, H. et al. Probing interplay of topological properties and electron correlation in TaIrTe4 via nonlinear Hall effect. Nat. Commun. 16, 6351 (2025).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
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).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Andrei, E. Y. et al. The marvels of moiré materials. Nat. Rev. Mater. 6, 201–206 (2021).
Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022).
Wang, P. et al. One-dimensional Luttinger liquids in a two-dimensional moiré lattice. Nature 605, 57–62 (2022).
Kang, K. et al. Switchable moiré potentials in ferroelectric WTe2/WSe2 superlattices. Nat. Nanotechnol. 18, 861–866 (2023).
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).
Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. X 13, 031037 (2023).
Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).
Kang, K. et al. Evidence of the fractional quantum spin Hall effect in moiré MoTe2. Nature 628, 522–526 (2024).
Chen, M. et al. Selective and quasi-continuous switching of ferroelectric Chern insulator devices for neuromorphic computing. Nat. Nanotechnol. 19, 962–969 (2024).
Wang, Y. et al. Structural phase transition in monolayer MoTe2 driven by electrostatic doping. Nature 550, 487–491 (2017).
Forsythe, C. et al. Band structure engineering of 2D materials using patterned dielectric superlattices. Nat. Nanotechnol. 13, 566–571 (2018).
Ribeiro-Palau, R. et al. Twistable electronics with dynamically rotatable heterostructures. Science 361, 690–693 (2018).
Inbar, A. et al. The quantum twisting microscope. Nature 614, 682–687 (2023).
Devarakonda, A. et al. Evidence of striped electronic phases in a structurally modulated superlattice. Nature 631, 526–530 (2024).
Tang, H. et al. On-chip multi-degree-of-freedom control of two-dimensional materials. Nature 632, 1038–1044 (2024).
Kim, D. S. et al. Electrostatic moiré potential from twisted hexagonal boron nitride layers. Nat. Mater. 23, 65–70 (2024).
Porer, M. et al. Non-thermal separation of electronic and structural orders in a persisting charge density wave. Nat. Mater. 13, 857–861 (2014).
Comin, R. & Damascelli, A. Resonant X-ray scattering studies of charge order in cuprates. Annu. Rev. Condens. Matter Phys. 7, 369–405 (2016).
Vaskivskyi, I. et al. Fast electronic resistance switching involving hidden charge density wave states. Nat. Commun. 7, 11442 (2016).
Husremović, S. et al. Encoding multistate charge order and chirality in endotaxial heterostructures. Nat. Commun. 14, 6031 (2023).
Kong, L., Shindou, R. & Sun, Z. Fate of transient order parameter domain walls in ultrafast experiments. npj Quantum Mater. 10, 25 (2025).
Dzsaber, S. et al. Giant spontaneous Hall effect in a nonmagnetic Weyl–Kondo semimetal. Proc. Natl Acad. Sci. USA 118, e2013386118 (2021).
Sinha, S. et al. Berry curvature dipole senses topological transition in a moiré superlattice. Nat. Phys. 18, 765–770 (2022).
Huang, Y.-X., Feng, X., Wang, H., Xiao, C. & Yang, S. A. Intrinsic nonlinear planar Hall effect. Phys. Rev. Lett. 130, 126303 (2023).
Levin, M. & Stern, A. Fractional topological insulators. Phys. Rev. Lett. 103, 196803 (2009).
Maciejko, J. & Fiete, G. A. Fractionalized topological insulators. Nat. Phys. 11, 385–388 (2015).
Stern, A. Fractional topological insulators: a pedagogical review. Annu. Rev. Condens. Matter Phys. 7, 349–368 (2016).
Neupert, T., Denner, M. M., Yin, J.-X., Thomale, R. & Hasan, M. Z. Charge order and superconductivity in kagome materials. Nat. Phys. 18, 137–143 (2022).
Chen, C. et al. Strong electron–phonon coupling in magic-angle twisted bilayer graphene. Nature 636, 342–347 (2024).
Du, Z., Lu, H.-Z. & Xie, X. Nonlinear Hall effects. Nat. Rev. Phys. 3, 744–752 (2021).
Ortix, C. Nonlinear Hall effect with time-reversal symmetry: theory and material realizations. Adv. Quantum Technol. 4, 2100056 (2021).
Adak, P. C., Sinha, S., Agarwal, A. & Deshmukh, M. M. Tunable moiré materials for probing Berry physics and topology. Nat. Rev. Mater. 9, 481–498 (2024).
Tang, J. et al. Quantum spin Hall effects in van der Waals materials. Adv. Quantum Technol. 8, e00327 (2025).
Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558 (1993).
Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864 (1964).
Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
Fröhlich, H. On the theory of superconductivity: the one-dimensional case. Proc. R. Soc. Lond. Ser. A 223, 296–305 (1954).
McMillan, W. Landau theory of charge-density waves in transition-metal dichalcogenides. Phys. Rev. B 12, 1187 (1975).
Lai, J., Zhan, J., Liu, P., Chen, X.-Q. & Sun, Y. Electric field tunable nonlinear Hall terahertz detector in the dual quantum spin Hall insulator TaIrTe4. Phys. Rev. B 110, 155122 (2024).
Li, J. et al. Interaction-driven topological transitions in monolayer TaIrTe4. Preprint at http://arxiv.org/abs/2506.18412 (2025).
Tang, J. Replication data for: Bistable superlattice switching in a quantum spin Hall insulator. Harvard Dataverse https://doi.org/10.7910/DVN/ULKFAE (2026).