Moiré-driven band renormalization and quantum transport in twisted 2D materials
Source abstract
Abstract
Abstract Moiré superlattices formed in twisted two-dimensional (2D) materials provide a highly tunable platform to investigate strongly correlated quantum phenomena. Recent advances have revealed a rich landscape of interaction-driven phases, including correlated insulators, superconductivity, magnetism, and fractional topological states, many of which are inaccessible in conventional materials. This review provides an overview of moiré-induced quantum phases, focusing on their underlying mechanisms and recent progress toward zero-magnetic-field fractional states. We aim to provide an integrated perspective bridging fundamental physics and potential applications in quantum electronics.
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Research context
OpenAlex topics: Topological Materials and Phenomena · 2D Materials and Applications · Quantum and electron transport phenomena
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References (100+)
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1. Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).10.1038/s41563-020-00840-0 ↗
2. Mak, K. F. & Shan, J. Semiconductor moire materials. Nat. Nanotechnol. 17, 686–695 (2022).10.1038/s41565-022-01165-6 ↗
3. Behura, S. K. et al. Moiré physics in twisted van der Waals heterostructures of 2D materials. Emergent Mater. 4, 813–826 (2021).10.1007/s42247-021-00270-x ↗
4. Sun, X. et al. Twisted van der Waals quantum materials: fundamentals, tunability, and applications. Chem. Rev. 124, 1992–2079 (2024).10.1021/acs.chemrev.3c00627 ↗
5. Nuckolls, K. P. & Yazdani, A. A microscopic perspective on moiré materials. Nat. Rev. Mater. 9, 460–480 (2024).10.1038/s41578-024-00682-1 ↗
6. Tran, K., Choi, J. & Singh, A. Moiré and beyond in transition metal dichalcogenide twisted bilayers. 2D Mater. 8, 022002 (2020).10.1088/2053-1583/abd3e7 ↗
7. Xiao, Y., Liu, J. & Fu, L. Moiré is more: access to new properties of two-dimensional layered materials. Matter 3, 1142–1161 (2020).10.1016/j.matt.2020.07.001 ↗
8. Vijayakrishnan, S. et al. Anomalous electronic transport in high-mobility Corbino rings. Nat. Commun. 14, 3906 (2023).10.1038/s41467-023-39526-x ↗
9. Wan, Z. et al. Induced superconductivity in high-mobility two-dimensional electron gas in gallium arsenide heterostructures. Nat. Commun. 6, 7426 (2015).10.1038/ncomms8426 ↗
10. Fu, H. et al. 3/2 fractional quantum Hall plateau in confined two-dimensional electron gas. Nat. Commun. 10, 4351 (2019).10.1038/s41467-019-12245-y ↗
11. Sun, W., Wan, Z., Qian, Q. & Qiu, G. Recent progress on quantum Hall effect in unconventional material systems. Appl. Phys. Lett. 126, 020501 (2025).10.1063/5.0245526 ↗
12. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).10.1038/nature04233 ↗
13. Soni, A. & Pal, S. K. Valley degree of freedom in two-dimensional van der Waals materials. J. Phys. D. Appl. Phys. 55, 303003 (2022).10.1088/1361-6463/ac5bc9 ↗
14. Schaibley, J. R. et al. Valleytronics in 2D materials. Nat. Rev. Mater. 1, 16055 (2016).10.1038/natrevmats.2016.55 ↗
15. Mak, K. F., McGill, K. L., Park, J. & McEuen, P. L. The valley Hall effect in MoS2. Science 344, 1489–1492 (2014).10.1126/science.1250140 ↗
16. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).10.1038/nature26160 ↗
17. Codecido, E. et al. Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle. Sci. Adv. 5, eaaw9770 (2019).10.1126/sciadv.aaw9770 ↗
18. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).10.1038/nature26154 ↗
19. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moire superlattices. Nature 579, 353–358 (2020).10.1038/s41586-020-2085-3 ↗
20. Kang, K. et al. Evidence of the fractional quantum spin Hall effect in moire MoTe2. Nature 628, 522–526 (2024).10.1038/s41586-024-07214-5 ↗
21. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).10.1126/science.aay5533 ↗
22. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).10.1126/science.aaw3780 ↗
23. Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moire superlattices. Nature 579, 359–363 (2020).10.1038/s41586-020-2092-4 ↗
24. Kang, K. et al. Double quantum spin Hall phase in moire WSe2. Nano Lett. 24, 14901–14907 (2024).10.1021/acs.nanolett.4c05308 ↗
25. Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).10.1038/s41586-023-06536-0 ↗
26. Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).10.1038/s41586-023-06289-w ↗
27. Xia, Y. et al. Superconductivity in twisted bilayer WSe2. Nature 637, 833–838 (2025).10.1038/s41586-024-08116-2 ↗
28. Carr, S., Fang, S., Jarillo-Herrero, P. & Kaxiras, E. Pressure dependence of the magic twist angle in graphene superlattices. Phys. Rev. B 98, 085144 (2018).10.1103/PhysRevB.98.085144 ↗
29. Shi, H. et al. Large-area, periodic, and tunable intrinsic pseudo-magnetic fields in low-angle twisted bilayer graphene. Nat. Commun. 11, 371 (2020).10.1038/s41467-019-14207-w ↗
30. Yan, W. et al. Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer. Nat. Commun. 4, 2159 (2013).10.1038/ncomms3159 ↗
31. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).10.1126/science.aav1910 ↗
32. de Vries, F. K. et al. Gate-defined Josephson junctions in magic-angle twisted bilayer graphene. Nat. Nanotechnol. 16, 760–763 (2021).10.1038/s41565-021-00896-2 ↗
33. Klein, D. R. et al. Electrical switching of a bistable moire superconductor. Nat. Nanotechnol. 18, 331–335 (2023).10.1038/s41565-022-01314-x ↗
34. Portoles, E. et al. A tunable monolithic SQUID in twisted bilayer graphene. Nat. Nanotechnol. 17, 1159–1164 (2022).10.1038/s41565-022-01222-0 ↗
35. Yan, X. et al. Moire synaptic transistor with room-temperature neuromorphic functionality. Nature 624, 551–556 (2023).10.1038/s41586-023-06791-1 ↗
36. Lopes Dos Santos, J. M., Peres, N. M. & Castro Neto, A. H. Graphene bilayer with a twist: electronic structure. Phys. Rev. Lett. 99, 256802 (2007).10.1103/PhysRevLett.99.256802 ↗
37. Li, G. et al. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2009).10.1038/nphys1463 ↗
38. Bistritzer, R. & MacDonald, A. H. Moire bands in twisted double-layer graphene. Proc. Natl. Acad. Sci. USA 108, 12233–12237 (2011).10.1073/pnas.1108174108 ↗
39. Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).10.1038/nphys2272 ↗
40. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moire superlattices. Nature 497, 598–602 (2013).10.1038/nature12186 ↗
41. Wang, L. et al. Evidence for a fractional fractal quantum Hall effect in graphene superlattices. Science 350, 1231–1234 (2015).10.1126/science.aad2102 ↗
42. Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249–255 (2021).10.1038/s41586-021-03192-0 ↗
43. Park, J. M. et al. Robust superconductivity in magic-angle multilayer graphene family. Nat. Mater. 21, 877–883 (2022).10.1038/s41563-022-01287-1 ↗
44. Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).10.1038/s41563-020-0708-6 ↗
45. Li, Y., Wan, Q. & Xu, N. Recent advances in moire superlattice systems by angle-resolved photoemission spectroscopy. Adv. Mater. 37, e2305175 (2023).10.1002/adma.202305175 ↗
46. Tarruell, L. & Sanchez-Palencia, L. Quantum simulation of the Hubbard model with ultracold fermions in optical lattices. C. R. Phys. 19, 365–393 (2018).10.1016/j.crhy.2018.10.013 ↗
47. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).10.1103/PhysRev.108.1175 ↗
48. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).10.1103/RevModPhys.78.17 ↗
49. Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987).10.1126/science.235.4793.1196 ↗
50. Chen, Q., Wang, Z., Boyack, R., Yang, S. & Levin, K. When superconductivity crosses over: from BCS to BEC. Rev. Mod. Phys. 96, 025002 (2024).10.1103/RevModPhys.96.025002 ↗
51. Damascelli, A., Hussain, Z. & Shen, Z.-X. Angle-resolved photoemission studies of the cuprate superconductors. Rev. Mod. Phys. 75, 473–541 (2003).10.1103/RevModPhys.75.473 ↗
52. Drozdov, I. K. et al. Phase diagram of Bi2Sr2CaCu2O8+δ revisited. Nat. Commun. 9, 5210 (2018).10.1038/s41467-018-07686-w ↗
53. Peotta, S. & Torma, P. Superfluidity in topologically nontrivial flat bands. Nat. Commun. 6, 8944 (2015).10.1038/ncomms9944 ↗
54. Utama, M. I. B. et al. Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist. Nat. Phys. 17, 184–188 (2020).10.1038/s41567-020-0974-x ↗
55. 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).10.1103/PhysRevB.82.121407 ↗
56. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).10.1038/s41586-019-1695-0 ↗
57. 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).10.1038/s41567-020-0928-3 ↗
58. Stepanov, P. et al. Untying the insulating and superconducting orders in magic-angle graphene. Nature 583, 375–378 (2020).10.1038/s41586-020-2459-6 ↗
59. Goodwin, Z. A. H., Corsetti, F., Mostofi, A. A. & Lischner, J. Twist-angle sensitivity of electron correlations in moiré graphene bilayers. Phys. Rev. B 100, 121106 (2019).10.1103/PhysRevB.100.121106 ↗
60. Pizarro, J. M., Rösner, M., Thomale, R., Valentí, R. & Wehling, T. O. Internal screening and dielectric engineering in magic-angle twisted bilayer graphene. Phys. Rev. B 100, 161102 (2019).10.1103/PhysRevB.100.161102 ↗
61. Saito, Y. et al. Superconductivity protected by spin–valley locking in ion-gated MoS2. Nat. Phys. 12, 144–149 (2015).10.1038/nphys3580 ↗
62. Rademaker, L. Spin-orbit coupling in transition metal dichalcogenide heterobilayer flat bands. Phys. Rev. B 105, 195428 (2022).10.1103/PhysRevB.105.195428 ↗
63. Guo, Y. et al. Superconductivity in 5.0 degrees twisted bilayer WSe2. Nature 637, 839–845 (2025).10.1038/s41586-024-08381-1 ↗
64. Yankowitz, M. et al. Dynamic band-structure tuning of graphene moire superlattices with pressure. Nature 557, 404–408 (2018).10.1038/s41586-018-0107-1 ↗
65. Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).10.1038/s41567-020-0825-9 ↗
66. Hao, Z. et al. Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene. Science 371, 1133–1138 (2021).10.1126/science.abg0399 ↗
67. Craig, I. M. et al. Local atomic stacking and symmetry in twisted graphene trilayers. Nat. Mater. 23, 323–330 (2024).10.1038/s41563-023-01783-y ↗
68. Chebrolu, N. R., Chittari, B. L. & Jung, J. Flat bands in twisted double bilayer graphene. Phys. Rev. B 99, 235417 (2019).10.1103/PhysRevB.99.235417 ↗
69. Qin, W. & MacDonald, A. H. In-plane critical magnetic fields in magic-angle twisted trilayer graphene. Phys. Rev. Lett. 127, 097001 (2021).10.1103/PhysRevLett.127.097001 ↗
70. Cao, Y., Park, J. M., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Pauli-limit violation and re-entrant superconductivity in moire graphene. Nature 595, 526–531 (2021).10.1038/s41586-021-03685-y ↗
71. Han, T. et al. Signatures of chiral superconductivity in rhombohedral graphene. Nature 643, 654–661 (2025).10.1038/s41586-025-09169-7 ↗
72. Yang, J. et al. Impact of spin–orbit coupling on superconductivity in rhombohedral graphene. Nat. Mater. 24, 1058–1065 (2025).10.1038/s41563-025-02156-3 ↗
73. Li, C. et al. Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene. Nature 631, 300–306 (2024).10.1038/s41586-024-07584-w ↗
74. Pantaleón, P. A. et al. Superconductivity and correlated phases in non-twisted bilayer and trilayer graphene. Nat. Rev. Phys. 5, 304–315 (2023).10.1038/s42254-023-00575-2 ↗
75. Zhou, H., Xie, T., Taniguchi, T., Watanabe, K. & Young, A. F. Superconductivity in rhombohedral trilayer graphene. Nature 598, 434–438 (2021).10.1038/s41586-021-03926-0 ↗
76. Orton, J. W. & Powell, M. J. The Hall effect in polycrystalline and powdered semiconductors. Rep. Prog. Phys. 43, 1263 (1980).10.1088/0034-4885/43/11/001 ↗
77. Mitta, S. B. et al. Electrical characterization of 2D materials-based field-effect transistors. 2D Mater. 8, 012002 (2020).10.1088/2053-1583/abc187 ↗
78. Mahmood, N. B., Hamodi, A., Jaffar, Z. M. & Saeed, F. R. Simulation of Hall effect in semiconductor for current sensors applications. J. Phys. Conf. Ser. 1804, 012139 (2021).10.1088/1742-6596/1804/1/012139 ↗
79. Khan, M. A., Sun, J., Li, B., Przybysz, A. & Kosel, J. Magnetic sensors-A review and recent technologies. Eng. Res. Exp. 3, 022005 (2021).10.1088/2631-8695/ac0838 ↗
80. Crescentini, M., Syeda, S. F. & Gibiino, G. P. Hall-effect current sensors: principles of operation and implementation techniques. IEEE Sens. J. 22, 10137–10151 (2022).10.1109/JSEN.2021.3119766 ↗
81. Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1539–1592 (2010).10.1103/RevModPhys.82.1539 ↗
82. Liu, X.-J., Liu, X. & Sinova, J. Scaling of the anomalous Hall effect in the insulating regime. Phys. Rev. B 84, 165304 (2011).10.1103/PhysRevB.84.165304 ↗
83. Ming-Che Chang, Q. N. Berry phase, hyperorbits, and the Hofstadter spectrum Semiclassical dynamics in magnetic Bloch bands. Phys. Rev. B 53, 7010–7023 (1996).10.1103/PhysRevB.53.7010 ↗
84. Sinitsyn, N. A., MacDonald, A. H., Jungwirth, T., Dugaev, V. K. & Sinova, J. Anomalous Hall effect in a two-dimensional Dirac band: the link between the Kubo-Streda formula and the semiclassical Boltzmann equation approach. Phys. Rev. B 75, 045315 (2007).10.1103/PhysRevB.75.045315 ↗
85. Hirsch, J. E. Spin Hall effect. Phys. Rev. Lett. 83, 1834–1837 (1999).10.1103/PhysRevLett.83.1834 ↗
86. Kato, Y. K., Myers, R. C., Gossard, A. C. & Awschalom, D. D. Observation of the spin Hall effect in semiconductors. Science 306, 1910–1913 (2004).10.1126/science.1105514 ↗
87. Wunderlich, J., Kaestner, B., Sinova, J. & Jungwirth, T. Experimental observation of the spin-Hall effect in a two-dimensional spin-orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005).10.1103/PhysRevLett.94.047204 ↗
88. Sinova, J., Valenzuela, S. O., Wunderlich, J., Back, C. H. & Jungwirth, T. Spin Hall effects. Rev. Mod. Phys. 87, 1213–1260 (2015).10.1103/RevModPhys.87.1213 ↗
89. von Klitzing, K. The quantized Hall effect. Rev. Mod. Phys. 58, 519–531 (1986).10.1103/RevModPhys.58.519 ↗
90. 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).10.1038/s41578-024-00671-4 ↗
91. 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).10.1038/nature04235 ↗
92. Novoselov, K. S. et al. Room-temperature quantum Hall effect in graphene. Science 315, 1379 (2007).10.1126/science.1137201 ↗
93. von Klitzing, K. et al. 40 years of the quantum Hall effect. Nat. Rev. Phys. 2, 397–401 (2020).10.1038/s42254-020-0209-1 ↗
94. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405–408 (1982).10.1103/PhysRevLett.49.405 ↗
95. Haldane, F. D. Model for a quantum Hall effect without Landau levels: condensed-matter realization of the “parity anomaly. Phys. Rev. Lett. 61, 2015–2018 (1988).10.1103/PhysRevLett.61.2015 ↗
96. Klitzing, K. V., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).10.1103/PhysRevLett.45.494 ↗
97. Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).10.1103/PhysRevLett.48.1559 ↗
98. Chang, C.-Z., Liu, C.-X. & MacDonald, A. H. Colloquium: quantum anomalous Hall effect. Rev. Mod. Phys. 95, 011002 (2023).10.1103/RevModPhys.95.011002 ↗
99. Sheng, D. N., Reddy, A. P., Abouelkomsan, A., Bergholtz, E. J. & Fu, L. Quantum anomalous hall crystal at fractional filling of moire superlattices. Phys. Rev. Lett. 133, 066601 (2024).10.1103/PhysRevLett.133.066601 ↗
100. Li, T. et al. Quantum anomalous Hall effect from intertwined moire bands. Nature 600, 641–646 (2021).10.1038/s41586-021-04171-1 ↗