Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265â1275 (2020).
Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725â733 (2020).
Kennes, D. M. et al. Moiré heterostructures as a condensed-matter quantum simulator. Nat. Phys. 17, 155â163 (2021).
Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686â695 (2022).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43â50 (2018).
Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653â657 (2019).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059â1064 (2019).
Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249â255 (2021).
Hao, Z. et al. Electric field-tunable superconductivity in alternating-twist magic-angle trilayer graphene. Science 371, 1133â1138 (2021).
Wu, F., Lovorn, T., Tutuc, E., Martin, I. & MacDonald, A. Topological insulators in twisted transition metal dichalcogenide homobilayers. Phys. Rev. Lett. 122, 086402 (2019).
Devakul, T., Crépel, V., Zhang, Y. & Fu, L. Magic in twisted transition metal dichalcogenide bilayers. Nat. Commun. 12, 6730 (2021).
Uemura, Y. Condensation, excitation, pairing, and superfluid density in high-Tc superconductors: the magnetic resonance mode as a roton analogue and a possible spin-mediated pairing. J. Phys. Condens. Matter 16, S4515 (2004).
Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17â85 (2006).
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).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359â363 (2020).
Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353â358 (2020).
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861â866 (2020).
Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214â218 (2020).
Zhao, W. et al. Gate-tunable heavy fermions in a moiré Kondo lattice. Nature 616, 61â65 (2023).
Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641â646 (2021).
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63â68 (2023).
Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69â73 (2023).
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74â79 (2023).
Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. 13, 031037 (2023).
Foutty, B. A. et al. Mapping twist-tuned multiband topology in bilayer WSe2. Science 384, 343â347 (2024).
Kang, K. et al. Evidence of the fractional quantum spin Hall effect in moiré MoTe2. Nature 628, 522â526 (2024).
Oh, M. et al. Evidence for unconventional superconductivity in twisted bilayer graphene. Nature 600, 240â245 (2021).
Zhou, H., Xie, T., Taniguchi, T., Watanabe, K. & Young, A. F. Superconductivity in rhombohedral trilayer graphene. Nature 598, 434â438 (2021).
Kim, H. et al. Evidence for unconventional superconductivity in twisted trilayer graphene. Nature 606, 494â500 (2022).
Zhou, H. et al. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 375, 774â778 (2022).
Zhang, Y. et al. Enhanced superconductivity in spinâorbit proximitized bilayer graphene. Nature 613, 268â273 (2023).
Hsu, Y.-T., Vaezi, A., Fischer, M. H. & Kim, E.-A. Topological superconductivity in monolayer transition metal dichalcogenides. Nat. Commun. 8, 14985 (2017).
Slagle, K. & Fu, L. Charge transfer excitations, pair density waves, and superconductivity in moiré materials. Phys. Rev. B 102, 235423 (2020).
Schrade, C. & Fu, L. Nematic, chiral and topological superconductivity in transition metal dichalcogenides. Phys. Rev. B 110, 035143 (2024).
Hsu, Y.-T., Wu, F. & Das Sarma, S. Spinâvalley locked instabilities in moiré transition metal dichalcogenides with conventional and higher-order Van Hove singularities. Phys. Rev. B 104, 195134 (2021).
Bélanger, M., Fournier, J. & Sénéchal, D. Superconductivity in the twisted bilayer transition metal dichalcogenide WSe2: a quantum cluster study. Phys. Rev. B 106, 235135 (2022).
Scherer, M. M., Kennes, D. M. & Classen, L. Chiral superconductivity with enhanced quantized Hall responses in moiré transition metal dichalcogenides. npj Quantum Mater. 7, 100 (2022).
Crépel, V., Guerci, D., Cano, J., Pixley, J. & Millis, A. Topological superconductivity in doped magnetic moiré semiconductors. Phys. Rev. Lett. 131, 056001 (2023).
Klebl, L., Fischer, A., Classen, L., Scherer, M. M. & Kennes, D. M. Competition of density waves and superconductivity in twisted tungsten diselenide. Phys. Rev. Res. 5, L012034 (2023).
Wu, Y.-M., Wu, Z. & Yao, H. Pair-density-wave and chiral superconductivity in twisted bilayer transition metal dichalcogenides. Phys. Rev. Lett. 130, 126001 (2023).
Zegrodnik, M. & Biborski, A. Mixed singlet-triplet superconducting state within the moiré tâJâU model applied to twisted bilayer WSe2. Phys. Rev. B 108, 064506 (2023).
Zhou, B. & Zhang, Y.-H. Chiral and nodal superconductors in the tâJ model with valley contrasting flux on a triangular moiré lattice. Phys. Rev. B 108, 155111 (2023).
Xie, Y.-M. & Law, K. Orbital FuldeâFerrell pairing state in moiré Ising superconductors. Phys. Rev. Lett. 131, 016001 (2023).
Akbar, W., Biborski, A., Rademaker, L. & Zegrodnik, M. Topological superconductivity with mixed singlet-triplet pairing in moiré transition metal dichalcogenide bilayers. Phys. Rev. B 110, 064516 (2024).
Tinkham, M. Introduction to Superconductivity (Courier Corporation, 2004).
Saito, Y., Nojima, T. & Iwasa, Y. Highly crystalline 2D superconductors. Nat. Rev. Mater. 2, 16094 (2017).
Smidman, M. et al. Unconventional fully gapped superconductivity in the heavy-fermion metal CeCu2Si2. Rev. Mod. Phys. 95, 031002 (2023).
Törmä, P., Peotta, S. & Bernevig, B. A. Superconductivity, superfluidity and quantum geometry in twisted multilayer systems. Nat. Rev. Phys. 4, 528â542 (2022).
Pan, H., Wu, F. & Das Sarma, S. Band topology, Hubbard model, Heisenberg model, and DzyaloshinskiiâMoriya interaction in twisted bilayer WSe2. Phy. Rev. Res. 2, 033087 (2020).
Bi, Z. & Fu, L. Excitonic density wave and spin-valley superfluid in bilayer transition metal dichalcogenide. Nat. Commun. 12, 642 (2021).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614â617 (2013).
Ghiotto, A. et al. Quantum criticality in twisted transition metal dichalcogenides. Nature 597, 345â349 (2021).
Gustafsson, M. V. et al. Ambipolar Landau levels and strong band-selective carrier interactions in monolayer WSe2. Nat. Mater. 17, 411â415 (2018).
Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat. Nanotechnol. 13, 246â252 (2018).
Fallahazad, B. et al. Shubnikovâde Haas oscillations of high-mobility holes in monolayer and bilayer WSe2: Landau level degeneracy, effective mass, and negative compressibility. Phys. Rev. Lett. 116, 086601 (2016).
Li, T. et al. Continuous Mott transition in semiconductor moiré superlattices. Nature 597, 350â354 (2021).
Tang, Y. et al. Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect. Nat. Nanotechnol. 16, 52â57 (2021).
Mourachkine, A. High-Temperature Superconductivity in Cuprates: The Nonlinear Mechanism and Tunneling Measurements (Kluwer Academic Publishers, 2002).
