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Semiconductor moiré materials

Nature Nanotechnology volume 17, pages 686–695 (2022)Cite this article

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Abstract

Moiré materials have emerged as a platform for exploring the physics of strong electronic correlations and non-trivial band topology. Here we review the recent progress in semiconductor moiré materials, with a particular focus on transition metal dichalcogenides. Following a brief overview of the general features in this class of materials, we discuss recent theoretical and experimental studies on Hubbard physics, Kane–Mele–Hubbard physics and equilibrium moiré excitons. We also comment on the future opportunities and challenges in the studies of transition metal dichalcogenide and other semiconductor moiré materials.

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Fig. 1: TMD semiconductor moiré materials.
Fig. 2: Hubbard model physics.
Fig. 3: Experimental moiré Hubbard and Kane–Mele–Hubbard phase diagrams.
Fig. 4: Kane–Mele–Hubbard physics.
Fig. 5: Excitons in a moiré lattice.

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References

  1. Li, G. et al. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2010).

    Article  CAS  Google Scholar 

  2. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    Article  CAS  Google Scholar 

  3. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    Article  CAS  Google Scholar 

  4. Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).

    Article  CAS  Google Scholar 

  5. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233 (2011).

    Article  CAS  Google Scholar 

  6. Li, T. et al. Continuous Mott transition in semiconductor moiré superlattices. Nature 597, 350–354 (2021).

    Article  CAS  Google Scholar 

  7. Ghiotto, A. et al. Quantum criticality in twisted transition metal dichalcogenides. Nature 597, 345–349 (2021).

    Article  CAS  Google Scholar 

  8. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

    Article  CAS  Google Scholar 

  9. Andrei, E. Y. et al. The marvels of moiré materials. Nat. Rev. Mater. 6, 201–206 (2021).

    Article  CAS  Google Scholar 

  10. Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).

    Article  CAS  Google Scholar 

  11. Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).

    Article  CAS  Google Scholar 

  12. Zhang, Y., Yuan, N. F. Q. & Fu, L. Moiré quantum chemistry: charge transfer in transition metal dichalcogenide superlattices. Phys. Rev. B 102, 201115 (2020).

    Article  CAS  Google Scholar 

  13. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    Article  CAS  Google Scholar 

  14. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    Article  CAS  Google Scholar 

  15. Zhang, Y., Tan, Y.-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    Article  CAS  Google Scholar 

  16. Suárez Morell, E., Correa, J. D., Vargas, P., Pacheco, M. & Barticevic, Z. Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407 (2010).

    Article  CAS  Google Scholar 

  17. Mele, E. J. Commensuration and interlayer coherence in twisted bilayer graphene. Phys. Rev. B 81, 161405 (2010).

    Article  CAS  Google Scholar 

  18. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

    Article  CAS  Google Scholar 

  19. Wu, F., Lovorn, T., Tutuc, E. & MacDonald, A. H. Hubbard model physics in transition metal dichalcogenide moiré bands. Phys. Rev. Lett. 121, 026402 (2018).

    Article  CAS  Google Scholar 

  20. Wu, F., Lovorn, T., Tutuc, E., Martin, I. & MacDonald, A. H. Topological insulators in twisted transition metal dichalcogenide homobilayers. Phys. Rev. Lett. 122, 086402 (2019).

    Article  CAS  Google Scholar 

  21. Xian, L., Kennes, D. M., Tancogne-Dejean, N., Altarelli, M. & Rubio, A. Multiflat bands and strong correlations in twisted bilayer boron nitride: doping-induced correlated insulator and superconductor. Nano Lett. 19, 4934–4940 (2019).

    Article  CAS  Google Scholar 

  22. Zou, L., Po, H. C., Vishwanath, A. & Senthil, T. Band structure of twisted bilayer graphene: emergent symmetries, commensurate approximants, and Wannier obstructions. Phys. Rev. B 98, 085435 (2018).

    Article  CAS  Google Scholar 

  23. Mak, K. F., Lee, C., Hone, J., Shan, J. & Heinz, T. F. Atomically thin MoS2: a new direct-gap semiconductor. Phys. Rev. Lett. 105, 136805 (2010).

    Article  CAS  Google Scholar 

  24. Splendiani, A. et al. Emerging photoluminescence in monolayer MoS2. Nano Lett. 10, 1271–1275 (2010).

    Article  CAS  Google Scholar 

  25. Gustafsson, M. V. et al. Ambipolar Landau levels and strong band-selective carrier interactions in monolayer WSe2. Nat. Mater. 17, 411–415 (2018).

    Article  CAS  Google Scholar 

  26. 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).

    Article  CAS  Google Scholar 

  27. Mak, K. F., Xiao, D. & Shan, J. Light–valley interactions in 2D semiconductors. Nat. Photon. 12, 451–460 (2018).

    Article  CAS  Google Scholar 

  28. Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014).

    Article  CAS  Google Scholar 

  29. Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).

    Article  CAS  Google Scholar 

  30. Zhang, Z. et al. Flat bands in twisted bilayer transition metal dichalcogenides. Nat. Phys. 16, 1093–1096 (2020).

    Article  CAS  Google Scholar 

  31. Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).

    Article  CAS  Google Scholar 

  32. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).

    Article  CAS  Google Scholar 

  33. Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).

    Article  CAS  Google Scholar 

  34. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).

    Article  CAS  Google Scholar 

  35. Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures. Nature 567, 81–86 (2019).

    Article  CAS  Google Scholar 

  36. Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).

    Article  CAS  Google Scholar 

  37. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).

    Article  CAS  Google Scholar 

  38. Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016).

    Article  CAS  Google Scholar 

  39. Cao, Y. et al. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117, 116804 (2016).

    Article  CAS  Google Scholar 

  40. Chung, T.-F., Xu, Y. & Chen, Y. P. Transport measurements in twisted bilayer graphene: electron–phonon coupling and Landau level crossing. Phys. Rev. B 98, 035425 (2018).

    Article  CAS  Google Scholar 

  41. Rosenberger, M. R. et al. Twist angle-dependent atomic reconstruction and moiré patterns in transition metal dichalcogenide heterostructures. ACS Nano 14, 4550–4558 (2020).

    Article  CAS  Google Scholar 

  42. Li, H. et al. Imaging moiré flat bands in three-dimensional reconstructed WSe2/WS2 superlattices. Nat. Mater. 20, 945–950 (2021).

    Article  CAS  Google Scholar 

  43. Bai, Y. et al. Excitons in strain-induced one-dimensional moiré potentials at transition metal dichalcogenide heterojunctions. Nat. Mater. 19, 1068–1073 (2020).

    Article  CAS  Google Scholar 

  44. Zhang, Y., Devakul, T. & Fu, L. Spin-textured Chern bands in AB-stacked transition metal dichalcogenide bilayers. Proc. Natl Acad. Sci. USA 118, e2112673118 (2021).

    Article  CAS  Google Scholar 

  45. Pan, H., Wu, F. & Das Sarma, S. Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii–Moriya interaction in twisted bilayer WSe2. Phys. Rev. Res. 2, 033087 (2020).

    Article  CAS  Google Scholar 

  46. Devakul, T., Crépel, V., Zhang, Y. & Fu, L. Magic in twisted transition metal dichalcogenide bilayers. Nat. Commun. 12, 6730 (2021).

    Article  CAS  Google Scholar 

  47. Pan, H., Wu, F. & Das Sarma, S. Quantum phase diagram of a moiré-Hubbard model. Phys. Rev. B 102, 201104 (2020).

    Article  CAS  Google Scholar 

  48. Slagle, K. & Fu, L. Charge transfer excitations, pair density waves, and superconductivity in moiré materials. Phys. Rev. B 102, 235423 (2020).

    Article  CAS  Google Scholar 

  49. Kennes, D. M. et al. Moiré heterostructures as a condensed-matter quantum simulator. Nat. Phys. 17, 155–163 (2021).

    Article  CAS  Google Scholar 

  50. Zhang, Y.-H., Sheng, D. N. & Vishwanath, A. SU(4) chiral spin liquid, exciton supersolid, and electric detection in moiré bilayers. Phys. Rev. Lett. 127, 247701 (2021).

    Article  CAS  Google Scholar 

  51. Xu, Y. et al. Tunable bilayer Hubbard model physics in twisted WSe2. Preprint at https://arxiv.org/abs/2202.02055 (2022).

  52. Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photon. 10, 216–226 (2016).

    Article  CAS  Google Scholar 

  53. Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020).

    Article  CAS  Google Scholar 

  54. Li, T. et al. Charge-order-enhanced capacitance in semiconductor moiré superlattices. Nat. Nanotechnol. 16, 1068–1072 (2021).

    Article  CAS  Google Scholar 

  55. Stepanov, P. et al. Untying the insulating and superconducting orders in magic-angle graphene. Nature 583, 375–378 (2020).

    Article  CAS  Google Scholar 

  56. Saito, Y., Ge, J., Watanabe, K., Taniguchi, T. & Young, A. F. Independent superconductors and correlated insulators in twisted bilayer graphene. Nat. Phys. 16, 926–930 (2020).

    Article  CAS  Google Scholar 

  57. Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).

    Article  CAS  Google Scholar 

  58. Mott, N. F. Metal–insulator transition. Rev. Mod. Phys. 40, 677–683 (1968).

    Article  CAS  Google Scholar 

  59. Imada, M., Fujimori, A. & Tokura, Y. Metal–insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998).

    Article  CAS  Google Scholar 

  60. Senthil, T. Theory of a continuous Mott transition in two dimensions. Phys. Rev. B 78, 045109 (2008).

    Article  CAS  Google Scholar 

  61. Mishmash, R. V., González, I., Melko, R. G., Motrunich, O. I. & Fisher, M. P. A. Continuous Mott transition between a metal and a quantum spin liquid. Phys. Rev. B 91, 235140 (2015).

    Article  CAS  Google Scholar 

  62. Lee, P. A. Moiré bands in transitional metal dichalcogenides: continuous Mott transition, quantum anomalous Hall and more. Journal Club for Condensed Matter Physics https://doi.org/10.36471/JCCM_September_2021_03 (2021).

  63. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010).

    Article  CAS  Google Scholar 

  64. Szasz, A., Motruk, J., Zaletel, M. P. & Moore, J. E. Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study. Phys. Rev. 10, 021042 (2020).

    Article  CAS  Google Scholar 

  65. Yiqing Zhou, D. N., Sheng & Kim, E.-A. Quantum phases of transition metal dichalcogenide moiré systems. Phys. Rev. Lett. 128, 157602 (2021).

    Article  Google Scholar 

  66. Xu, Y. et al. Metal–insulator transition with charge fractionalization. Preprint at https://arxiv.org/abs/2106.14910 (2021).

  67. Morales-Durán, N., MacDonald, A. H. & Potasz, P. Metal–insulator transition in transition metal dichalcogenide heterobilayer moiré superlattices. Phys. Rev. B 103, L241110 (2021).

    Article  Google Scholar 

  68. Pan, H. & Das Sarma, S. Interaction-driven filling-induced metal-insulator transitions in 2D moiré lattices. Phys. Rev. Lett. 127, 096802 (2021).

    Article  CAS  Google Scholar 

  69. Wietek, A. et al. Mott insulating states with competing orders in the triangular lattice Hubbard model. Phys. Rev. 11, 041013 (2021).

    Article  CAS  Google Scholar 

  70. Zang, J., Wang, J., Cano, J., Georges, A. & Millis, A. J. Dynamical mean field theory of moiré bilayer transition metal dichalcogenides: phase diagram, resistivity, and quantum criticality. Phys. Rev. X 12, 021064 (2022).

    CAS  Google Scholar 

  71. Ahn, Seongjin & Sarma, S. D. Disorder induced two-dimensional metal–insulator transition in moiré transition metal dichalcogenide multilayers. Phys. Rev. B 105, 115114 (2021).

    Article  Google Scholar 

  72. Huang, Y., Skinner, B. & Shklovskii, B. I. Conductivity of two-dimensional small gap semiconductors and topological insulators in strong Coulomb disorder. Preprint at https://arxiv.org/abs/2201.11652 (2022).

  73. Zhang, Y., Liu, T. & Fu, L. Electronic structures, charge transfer, and charge order in twisted transition metal dichalcogenide bilayers. Phys. Rev. B 103, 155142 (2021).

    Article  CAS  Google Scholar 

  74. Padhi, B., Chitra, R. & Phillips, P. W. Generalized Wigner crystallization in moiré materials. Phys. Rev. B 103, 125146 (2021).

    Article  CAS  Google Scholar 

  75. Huang, X. et al. Correlated insulating states at fractional fillings of the WS2/WSe2 moiré lattice. Nat. Phys. 17, 715–719 (2021).

    Article  CAS  Google Scholar 

  76. Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).

    Article  CAS  Google Scholar 

  77. Liu, E. et al. Excitonic and valley-polarization signatures of fractional correlated electronic phases in a WSe2/WS2 moiré superlattice. Phys. Rev. Lett. 127, 037402 (2021).

    Article  CAS  Google Scholar 

  78. Emery, V. J., Kivelson, S. A. & Tranquada, J. M. Stripe phases in high-temperature superconductors. Proc. Natl Acad. Sci. USA 96, 8814 (1999).

    Article  CAS  Google Scholar 

  79. Koulakov, A. A., Fogler, M. M. & Shklovskii, B. I. Charge density wave in two-dimensional electron liquid in weak magnetic field. Phys. Rev. Lett. 76, 499–502 (1996).

    Article  CAS  Google Scholar 

  80. Kivelson, S. A., Fradkin, E. & Emery, V. J. Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998).

    Article  CAS  Google Scholar 

  81. Matty, M. & Kim, E.-A. Melting of generalized Wigner crystals in transition metal dichalcogenide heterobilayer Moiré systems. Preprint at https://arxiv.org/abs/2112.08624 (2021).

  82. Jin, C. et al. Stripe phases in WSe2/WS2 moiré superlattices. Nat. Mater. 20, 940–944 (2021).

    Article  CAS  Google Scholar 

  83. Camjayi, A., Haule, K., Dobrosavljević, V. & Kotliar, G. Coulomb correlations and the Wigner–Mott transition. Nat. Phys. 4, 932–935 (2008).

    Article  CAS  Google Scholar 

  84. Musser, S., Senthil, T & Chowdhury, D. Theory of a continuous bandwidth-tuned Wigner–Mott transition. Preprint at https://arxiv.org/abs/2111.09894 (2021).

  85. Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002–1011 (1934).

    Article  CAS  Google Scholar 

  86. Tang, Y. et al. Dielectric catastrophe at the Mott and Wigner transitions in a moiré superlattice. Preprint at https://arxiv.org/abs/2201.12510 (2022).

  87. Kane, C. L. & Mele, E. J. Quantum spin hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

    Article  CAS  Google Scholar 

  88. Hohenadler, M. & Assaad, F. F. Correlation effects in two-dimensional topological insulators. J. Phys. Condens. Matter 25, 143201 (2013).

    Article  CAS  Google Scholar 

  89. Witczak-Krempa, W., Chen, G., Kim, Y. B. & Balents, L. Correlated quantum phenomena in the strong spin-orbit regime. Annu. Rev. Condens. Matter Phys. 5, 57–82 (2014).

    Article  CAS  Google Scholar 

  90. Pan, H., Xie, M., Wu, F. & Sarma, S. D. Topological phases in AB-stacked MoTe2/WSe2: ℤ2 topological insulators, Chern insulators, and topological charge density waves. Preprint at https://arxiv.org/abs/2111.01152 (2021).

  91. Regnault, N. & Bernevig, B. A. Fractional chern insulator. Phys. Rev. 1, 021014 (2011).

    Article  CAS  Google Scholar 

  92. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

    Article  CAS  Google Scholar 

  93. Sharpe Aaron, L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    Article  CAS  Google Scholar 

  94. Hasan, M. Z. & Kane, C. L. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  CAS  Google Scholar 

  95. Ezawa, M., Tanaka, Y. & Nagaosa, N. Topological phase transition without gap closing. Sci. Rep. 3, 2790 (2013).

    Article  Google Scholar 

  96. Xie, Y.-M., Zhang, C.-P., Hu, J.-X., Mak, K. F. & Law, K. Valley polarized quantum anomalous Hall state in moiré MoTe2/WSe2 heterobilayers. Phys. Rev. Lett. 128, 026402 (2021).

    Article  Google Scholar 

  97. Chang, Y.-W. & Chang, Y.-C. Theory of quantum anomalous Hall effect and electric-field-induced phase transition in AB-stacked MoTe2/WSe2 moire heterobilayers. Preprint at https://arxiv.org/abs/2203.10088 (2022).

  98. Rademaker, L. Spin–orbit coupling in transition metal dichalcogenide heterobilayer flat bands. Phys. Rev. B 105, 195428 (2022).

    Article  CAS  Google Scholar 

  99. Wu, F., Lovorn, T. & MacDonald, A. H. Topological exciton bands in moiré heterojunctions. Phys. Rev. Lett. 118, 147401 (2017).

    Article  Google Scholar 

  100. Yu, H., Liu, G.-B., Tang, J., Xu, X. & Yao, W. Moiré excitons: from programmable quantum emitter arrays to spin–orbit-coupled artificial lattices. Sci. Adv. 3, e1701696 (2017).

    Article  CAS  Google Scholar 

  101. Ruiz-Tijerina, D. A. & Fal’ko, V. I. Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides. Phys. Rev. B 99, 125424 (2019).

    Article  CAS  Google Scholar 

  102. Shimazaki, Y. et al. Optical signatures of periodic charge distribution in a Mott-like correlated insulator state. Phys. Rev. 11, 021027 (2021).

    Article  CAS  Google Scholar 

  103. Wilson, N. P., Yao, W., Shan, J. & Xu, X. Excitons and emergent quantum phenomena in stacked 2D semiconductors. Nature 599, 383–392 (2021).

    Article  CAS  Google Scholar 

  104. Huang, D., Choi, J., Shih, C.-K. & Li, X. Excitons in semiconductor moiré superlattices. Nat. Nanotechnol. 17, 227–238 (2022).

    Article  CAS  Google Scholar 

  105. Tang, Y. et al. Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect. Nat. Nanotechnol. 16, 52–57 (2021).

    Article  CAS  Google Scholar 

  106. Zhang, L. et al. Van der Waals heterostructure polaritons with moiré-induced nonlinearity. Nature 591, 61–65 (2021).

    Article  CAS  Google Scholar 

  107. Liu, E. et al. Signatures of moiré trions in WSe2/MoSe2 heterobilayers. Nature 594, 46–50 (2021).

    Article  CAS  Google Scholar 

  108. Wang, X. et al. Moiré trions in MoSe2/WSe2 heterobilayers. Nat. Nanotechnol. 16, 1208–1213 (2021).

    Article  CAS  Google Scholar 

  109. Brotons-Gisbert, M. et al. Moiré-trapped interlayer trions in a charge-tunable WSe2/MoSe2 heterobilayer. Phys. Rev. 11, 031033 (2021).

    Article  CAS  Google Scholar 

  110. Marcellina, E. et al. Evidence for moiré trions in twisted MoSe2 homobilayers. Nano Lett. 21, 4461–4468 (2021).

    Article  CAS  Google Scholar 

  111. Gu, J. et al. Dipolar excitonic insulator in a moiré lattice. Nat. Phys. 18, 395–400 (2022).

    Article  CAS  Google Scholar 

  112. Zuocheng, Z. et al. Correlated interlayer exciton insulator in double layers of monolayer WSe2 and moiré WS2/WSe2. Preprint at https://arxiv.org/abs/2108.07131 (2021).

  113. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).

    Article  CAS  Google Scholar 

  114. Dutta, O. et al. Non-standard Hubbard models in optical lattices: a review. Rep. Prog. Phys. 78, 066001 (2015).

    Article  CAS  Google Scholar 

  115. Xie, M. & MacDonald, A. H. Electrical reservoirs for bilayer excitons. Phys. Rev. Lett. 121, 067702 (2018).

    Article  CAS  Google Scholar 

  116. Ma, L. et al. Strongly correlated excitonic insulator in atomic double layers. Nature 598, 585–589 (2021).

    Article  CAS  Google Scholar 

  117. Zeng, Y. & MacDonald, A. H. Electrically controlled two-dimensional electron-hole fluids. Phys. Rev. B 102, 085154 (2020).

    Article  CAS  Google Scholar 

  118. Eisenstein, J. P. & MacDonald, A. H. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004).

    Article  CAS  Google Scholar 

  119. Zhang, Y.-H. Doping a Mott insulator with excitons in moiré bilayer: fractional superfluid, neutral Fermi surface and Mott transition. Preprint at https://arxiv.org/abs/2204.10937 (2022).

  120. Angeli, M. & MacDonald Allan, H. Γ valley transition metal dichalcogenide moiré bands. Proc. Natl Acad. Sci. USA 118, e2021826118 (2021).

    Article  CAS  Google Scholar 

  121. Kumar, A., Hu, N. C., MacDonald, A. H. & Potter, A. C. Gate-tunable heavy fermion quantum criticality in a moiré Kondo lattice. Preprint at https://arxiv.org/abs/2110.11962 (2021).

  122. Dalal, A. & Ruhman, J. Orbitally selective Mott phase in electron-doped twisted transition metal-dichalcogenides: a possible realization of the Kondo lattice model. Phys. Rev. Res. 3, 043173 (2021).

    Article  CAS  Google Scholar 

  123. Zhang, Y.-H. & Vishwanath, A. Electrical detection of spin liquids in double moiré layers. Preprint at https://arxiv.org/abs/2005.12925 (2020).

  124. Xia, F., Wang, H., Hwang, J. C. M., Neto, A. H. C. & Yang, L. Black phosphorus and its isoelectronic materials. Nat. Rev. Phys. 1, 306–317 (2019).

    Article  CAS  Google Scholar 

  125. Chaves, A. et al. Bandgap engineering of two-dimensional semiconductor materials. npj 2D Mater. Appl. 4, 29 (2020).

    Article  CAS  Google Scholar 

  126. McGuire, M. A. Crystal and magnetic structures in layered, transition metal dihalides and trihalides. Crystals 7, 121 (2017).

    Article  CAS  Google Scholar 

  127. Mak, K. F., Shan, J. & Ralph, D. C. Probing and controlling magnetic states in 2D layered magnetic materials. Nat. Rev. Phys. 1, 646–661 (2019).

    Article  Google Scholar 

  128. Hejazi, K., Luo, Z.-X. & Balents, L. Noncollinear phases in moiré magnets. Proc. Natl Acad. Sci. USA 117, 10721 (2020).

    Article  CAS  Google Scholar 

  129. Tong, Q., Liu, F., Xiao, J. & Yao, W. Skyrmions in the moiré of van der Waals 2D magnets. Nano Lett. 18, 7194–7199 (2018).

    Article  CAS  Google Scholar 

  130. Akram, M. et al. Moiré skyrmions and chiral magnetic phases in twisted CrX3 (X = I, Br, and Cl) bilayers. Nano Lett. 21, 6633–6639 (2021).

    Article  CAS  Google Scholar 

  131. Wang, C., Gao, Y., Lv, H., Xu, X. & Xiao, D. Stacking domain wall magnons in twisted van der Waals magnets. Phys. Rev. Lett. 125, 247201 (2020).

    Article  CAS  Google Scholar 

  132. Xu, Y. et al. Coexisting ferromagnetic–antiferromagnetic state in twisted bilayer CrI3. Nat. Nanotechnol. 17, 143–147 (2022).

    Article  CAS  Google Scholar 

  133. Xie, H. et al. Twist engineering of the two-dimensional magnetism in double bilayer chromium triiodide homostructures. Nat. Phys. 18, 30–36 (2022).

    Article  CAS  Google Scholar 

  134. Song, T. et al. Direct visualization of magnetic domains and moiré magnetism in twisted 2D magnets. Science 374, 1140–1144 (2021).

    Article  CAS  Google Scholar 

  135. Edelberg, D. et al. Approaching the intrinsic limit in transition metal diselenides via point defect control. Nano Lett. 19, 4371–4379 (2019).

    Article  CAS  Google Scholar 

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Acknowledgements

We thank C.-M. Jian for discussions on the electronic structure of twisted bilayer graphene and TMD moiré materials. We acknowledge support from the US Office of Naval Research under award number N00014-21-1-2471 (K.F.M.) and the National Science Foundation (NSF) under DMR- 2114535 (J.S.).

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Authors and Affiliations

  1. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA

    Kin Fai Mak & Jie Shan

  2. School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA

    Kin Fai Mak & Jie Shan

  3. Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA

    Kin Fai Mak & Jie Shan

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  1. Kin Fai Mak
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  2. Jie Shan
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Correspondence to Kin Fai Mak or Jie Shan.

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Mak, K.F., Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022). https://doi.org/10.1038/s41565-022-01165-6

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