Twist-Angle-Dependent Quantum Phase Diagrams of Moiré Bilayer MoTe₂

The source is a bibliography of 75 publications and preprints tracing research into moiré semiconductor materials, especially twisted bilayers of MoTe₂ and WSe₂. The cited work covers fractional Chern insulators, quantum anomalous and quantum spin Hall effects, topology, magnetism, correlated insulating phases, composite Fermi liquids and superconductivity, alongside theoretical studies of moiré band structure and quantum geometry published between 1961 and 2026.

Foundational work and moiré materials

1. Puotinen, D. & Newnham, R. E. The crystal structure of MoTe₂. Acta Crystallogr. 14, 691–692 (1961). Article

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

3. Fallahazad, B. et al. Shubnikov–de 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). Article

4. 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

5. Yu, H., Chen, M. & Yao, W. Giant magnetic field from moiré induced Berry phase in homobilayer semiconductors. Natl Sci. Rev. 7, 12–20 (2020). Article

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

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

8. Li, H., Kumar, U., Sun, K. & Lin, S.-Z. Spontaneous fractional Chern insulators in transition metal dichalcogenide moiré superlattices. Phys. Rev. Res. 3, L032070 (2021). Article

9. Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022). Article

10. Mao, N. et al. Transfer learning relaxation, electronic structure and continuum model for twisted bilayer MoTe₂. Commun. Phys. 7, 262 (2024). Article

11. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013). Article

Fractional Chern and quantum anomalous Hall states

12. Crépel, V. & Fu, L. Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides. Phys. Rev. B 107, L201109 (2023). Article

13. Dong, J., Wang, J., Ledwith, P. J., Vishwanath, A. & Parker, D. E. Composite Fermi liquid at zero magnetic field in twisted MoTe₂. Phys. Rev. Lett. 131, 136502 (2023). Article

14. Goldman, H., Reddy, A. P., Paul, N. & Fu, L. Zero-field composite Fermi liquid in twisted semiconductor bilayers. Phys. Rev. Lett. 131, 136501 (2023). Article

15. Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe₂. Nature 622, 63–68 (2023). Article

16. Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe₂. Nature 622, 69–73 (2023). Article

17. Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023). Article

18. Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe₂. Phys. Rev. X 13, 031037 (2023).

19. Reddy, A. P., Alsallom, F., Zhang, Y., Devakul, T. & Fu, L. Fractional quantum anomalous Hall states in twisted bilayer MoTe₂ and WSe₂. Phys. Rev. B 108, 085117 (2023). Article

20. Wang, C. et al. Fractional Chern insulator in twisted bilayer MoTe₂. Phys. Rev. Lett. 132, 036501 (2024). Article

21. Ji, Z. et al. Local probe of bulk and edge states in a fractional Chern insulator. Nature 635, 578–583 (2024). Article

22. Redekop, E. et al. Direct magnetic imaging of fractional Chern insulators in twisted MoTe₂. Nature 635, 584–589 (2024). Article

23. Sheng, D. N., Reddy, A. P., Abouelkomsan, A., Bergholtz, E. J. & Fu, L. Quantum anomalous Hall crystal at fractional filling of Moiré superlattices. Phys. Rev. Lett. 133, 066601 (2024). Article

24. Yu, J. et al. Fractional Chern insulators versus nonmagnetic states in twisted bilayer MoTe₂. Phys. Rev. B 109, 045147 (2024). Article

25. Abouelkomsan, A., Reddy, A. P., Fu, L. & Bergholtz, E. J. Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers. Phys. Rev. B 109, L121107 (2024). Article

26. Li, B. H., Qiu, W.-X. & Wu, F. Electrically tuned topology and magnetism in twisted bilayer MoTe₂ at ν_h = 1. Phys. Rev. B 109, L041106 (2024). Article

27. Morales-Durán, N., Wei, N., Shi, J. & MacDonald, A. H. Magic angles and fractional Chern insulators in twisted homobilayer transition metal dichalcogenides. Phys. Rev. Lett. 132, 096602 (2024). Article

28. Lu, T. & Santos, L. H. Fractional Chern insulators in twisted bilayer MoTe₂: a composite fermion perspective. Phys. Rev. Lett. 133, 186602 (2024). Article

29. Stern, A. & Fu, L. Transport properties of a half-filled Chern band at the electron and composite fermion phases. Phys. Rev. Lett. 133, 246602 (2024). Article

30. Xu, F. et al. Interplay between topology and correlations in the second moiré band of twisted bilayer MoTe₂. Nat. Phys. 21, 542–548 (2025). Article

31. Park, H. et al. Ferromagnetism and topology of the higher flat band in a fractional Chern insulator. Nat. Phys. 21, 549–555 (2025). Article

32. Wang, Y. et al. Hidden states and dynamics of fractional fillings in twisted MoTe₂ bilayers. Nature 641, 1149–1155 (2025). Article

33. Li, T., Liu, J., Xie, J. & Lu, X. Fractional quantum anomalous Hall effect in moiré fractional Chern insulators. Nat. Mater. (2026). Article

34. Park, H. et al. Observation of dissipationless fractional Chern insulator. Nat. Phys. 22, 389–395 (2026). Article

35. Pan, H. et al. Optical signatures of \(-\frac{1}{3}\) fractional quantum anomalous Hall state in twisted MoTe₂. Phys. Rev. Lett. 136, 056601 (2026). Article

36. Gao, B. et al. Probing quantum anomalous Hall states in twisted bilayer WSe₂ via attractive polaron spectroscopy. Phys. Rev. X 16, 021037 (2026).

Quantum spin Hall, magnetic and correlated phases

37. Kang, K. et al. Evidence of the fractional quantum spin Hall effect in moiré MoTe₂. Nature 628, 522–526 (2024). Article

38. Li, W. et al. Universal magnetic phases in twisted bilayer MoTe₂. Nano Lett. 25, 18044–18050 (2025). Article

39. Qiu, W.-X., Li, B., Luo, X.-J. & Wu, F. Interaction-driven topological phase diagram of twisted bilayer MoTe₂. Phys. Rev. X 13, 041026 (2023).

40. Wang, T., Devakul, T., Zaletel, M. P. & Fu, L. Diverse magnetic orders and quantum anomalous Hall effect in twisted bilayer MoTe₂ and WSe₂. Preprint at arxiv.org/abs/2306.02501 (2024).

41. Muñoz-Segovia, D., Crépel, V., Queiroz, R. & Millis, A. J. Twist-angle evolution of the intervalley-coherent antiferromagnet in twisted WSe₂. Phys. Rev. B 112, 085111 (2025). Article

42. Foutty, B. A. et al. Mapping twist-tuned multiband topology in bilayer WSe₂. Science 384, 343–347 (2024). Article

43. Knüppel, P. et al. Correlated states controlled by a tunable van Hove singularity in moiré WSe₂ bilayers. Nat. Commun. 16, 1959 (2025). Article

44. Anderson, E. et al. Trion sensing of a zero-field composite Fermi liquid. Nature 635, 590–595 (2024). Article

45. Li, B. H., Qiu, W.-X., Wu, F. & MacDonald, A. H. Quantum phases in twisted homobilayer transition metal dichalcogenides. Natl Sci. Rev. 13, nwaf570 (2025). Article

46. Qiu, W.-X., Li, B., Luo, X.-J. & Wu, F. Interaction-driven topological phase diagram of twisted bilayer MoTe₂. Phys. Rev. X 13, 041026 (2023).

47. Wang, T. et al. Diverse magnetic orders and quantum anomalous Hall effect in twisted bilayer MoTe₂ and WSe₂. Preprint at arxiv.org/abs/2306.02501 (2024).

48. Zhang, M. et al. Transport evidence for Wigner crystals in monolayer MoTe₂. Preprint at arxiv.org/abs/2506.20392 (2025).

Superconductivity in twisted WSe₂ and related systems

48. Xia, Y. et al. Superconductivity in twisted bilayer WSe₂. Nature 637, 833–838 (2025). Article

49. Guo, Y. et al. Superconductivity in 5.0° twisted bilayer WSe₂. Nature 637, 839–845 (2025). Article

50. Xia, Y. et al. Bandwidth-tuned Mott transition and superconductivity in moiré WSe₂. Nature 650, 585–591 (2026). Article

51. Guo, Y. et al. Angle evolution of the superconducting phase diagram in twisted bilayer WSe₂. Nature 652, 622–627 (2026). Article

52. Xu, F. et al. Signatures of unconventional superconductivity near reentrant and fractional quantum anomalous Hall insulators. Preprint at arxiv.org/abs/2504.06972 (2025).

53. Schrade, C. & Fu, L. Nematic, chiral, and topological superconductivity in twisted transition metal dichalcogenides. Phys. Rev. B 110, 035143 (2024). Article

54. Fischer, A. et al. Theory of intervalley-coherent AFM order and topological superconductivity in tWSe₂. Phys. Rev. X 15, 041055 (2025).

55. Qin, W., Qiu, W.-X. & Wu, F. Topological chiral superconductivity mediated by intervalley antiferromagnetic fluctuations in twisted bilayer WSe₂. Phys. Rev. Lett. 135, 246002 (2025). Article

56. Chubukov, A. V. & Varma, C. M. Quantum criticality and superconductivity in twisted transition metal dichalcogenides. Phys. Rev. B 111, 014507 (2025). Article

57. Christos, M., Bonetti, P. M. & Scheurer, M. S. Approximate symmetries, insulators, and superconductivity in the continuum-model description of twisted WSe₂. Phys. Rev. Lett. 135, 046503 (2025). Article

58. Tuo, C., Li, M.-R., Wu, Z., Sun, W. & Yao, H. Theory of topological superconductivity and antiferromagnetic correlated insulators in twisted bilayer WSe₂. Nat. Commun. 16, 9525 (2025). Article

59. Xie, F. et al. Superconductivity in twisted WSe₂ from topology-induced quantum fluctuations. Phys. Rev. Lett. 134, 136503 (2025). Article

60. Zhu, J., Chou, Y.-Z., Xie, M. & Sarma, S. D. Superconductivity in twisted transition metal dichalcogenide homobilayers. Phys. Rev. B 111, L060501 (2025). Article

61. Kim, S., Mendez-Valderrama, J. F., Wang, X. & Chowdhury, D. Theory of correlated insulators and superconductor at ν = 1 in twisted WSe₂. Nat. Commun. 16, 1701 (2025). Article

62. 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). Article

63. Zegrodnik, M. & Biborski, A. Mixed singlet-triplet superconducting state within the moiré t−J−U model applied to twisted bilayer WSe₂. Phys. Rev. B 108, 064506 (2023). Article

64. Zang, J., Wang, J., Cano, J. & Millis, A. J. Hartree-Fock study of the moiré Hubbard model for twisted bilayer transition metal dichalcogenides. Phys. Rev. B 104, 075150 (2021). Article

65. Zegrodnik, M., Akbar, W., Biborski, A. & Rademaker, L. Optimal superconductivity in twisted bilayer WSe₂ where the Van Hove singularity crosses half-filling. Phys. Rev. Res. 8, L012070 (2026). Article

66. Xu, C. et al. Chiral superconductivity from spin polarized Chern band in twisted MoTe₂. Phys. Rev. Lett. 135, 266005 (2025). Article

67. Guerci, D., Abouelkomsan, A. & Fu, L. From fractionalization to Chiral topological superconductivity in a flat Chern band. Phys. Rev. Lett. 135, 186601 (2025). Article

Anyon superconductivity and wider theoretical directions

67. Reddy, A. P. & Fu, L. Toward a global phase diagram of the fractional quantum anomalous Hall effect. Phys. Rev. B 108, 245159 (2023). Article

68. Shi, Z. D. & Senthil, T. Anyon delocalization transitions out of a disordered fractional quantum anomalous Hall insulator. Proc. Natl Acad. Sci. USA 122, e2520608122 (2025). Article

69. Nosov, P. A., Han, Z. & Khalaf, E. Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators. Phys. Rev. Lett. 136, 106501 (2026). Article

70. Wang, T. & Zaletel, M. P. Chiral superconductivity near a fractional Chern insulator. Preprint at arxiv.org/abs/2507.07921 (2025).

71. Pichler, F., Kuhlenkamp, C., Knap, M. & Vishwanath, A. Microscopic mechanism of anyon superconductivity emerging from fractional Chern insulators. Newton 2, 100340 (2026). Article

72. Liu, F. et al. From fractional Chern insulators to topological electronic crystals in moiré MoTe₂: quantum geometry tuning via remote layer. Preprint at arxiv.org/abs/2512.03622 (2025).

73. Bernevig, B. A. et al. Fractional quantization in insulators from Hall to Chern. Nat. Phys. 21, 1702–1713 (2025). Article

74. Li, T., Liu, J., Xie, J. & Lu, X. Fractional quantum anomalous Hall effect in moiré fractional Chern insulators. Nat. Mater. (2026). Article

75. Anderson, E. et al. Trion sensing of a zero-field composite Fermi liquid. Nature 635, 590–595 (2024). Article

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