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  • Letter
  • Open Access

Exciton fractional Chern insulators in moiré heterostructures

Raul Perea-Causin*, Hui Liu†, and Emil J. Bergholtz‡

  • *Contact author: raul.perea.causin@fysik.su.se
  • †Contact author: hui.liu@fysik.su.se
  • ‡Contact author: emil.bergholtz@fysik.su.se
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Phys. Rev. Research 7, L042033 – Published 10 November, 2025

DOI: https://doi.org/10.1103/55zv-s9xv

Abstract

Moiré materials have emerged as a powerful platform for exploring exotic quantum phases. While recent experiments have unveiled fractional Chern insulators exhibiting the fractional quantum anomalous Hall effect based on electrons or holes, the exploration of analogous many-body states with bosonic constituents remains largely uncharted. In this work, we predict the emergence of bosonic fractional Chern insulators arising from long-lived excitons in a moiré superlattice formed by twisted bilayer WSe2 stacked on monolayer MoSe2. Performing exact diagonalization on the exciton flat Chern band present in this structure, we provide compelling evidence for the existence of Abelian and non-Abelian phases at band filling 12 and 1, respectively, through multiple robust signatures, including ground-state degeneracy, spectral flow, many-body Chern number, and particle-cut entanglement spectrum. The obtained energy gap of ∼10meV for the Abelian states suggests a remarkably high stability of this phase, which persists for a relatively wide range of twist angles and vertical electric fields. Our findings establish the presence of robust bosonic fractional Chern insulators in highly tunable and experimentally accessible moiré heterostructures and unveil a promising pathway for realizing non-Abelian anyons.

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References (84)

  1. L. Ju, A. H. MacDonald, K. F. Mak, J. Sha, and X. Xu, The fractional quantum anomalous Hall effect, Nat. Rev. Mater. 9, 455 (2024).
  2. S. A. Parameswaran, R. Roy, and S. L. Sondhi, Fractional quantum Hall physics in topological flat bands, C. R. Phys. 14, 816 (2013), Topological insulators/Isolants topologiques.
  3. Z. Liu and E. J. Bergholtz, Recent developments in fractional Chern insulators, in Encyclopedia of Condensed Matter Physics, edited by T. Chakraborty (Academic Press, Oxford, 2024), 2nd ed., pp. 515–538.
  4. E. M. Spanton, A. A. Zibrov, H. Zhou, T. Taniguchi, K. Watanabe, M. P. Zaletel, and A. F. Young, Observation of fractional Chern insulators in a van der Waals heterostructure, Science 360, 62 (2018).
  5. Y. Xie, A. T. Pierce, J. M. Park, D. E. Parker, E. Khalaf, P. Ledwith, Y. Cao, S. H. Lee, S. Chen, P. R. Forrester, K. Watanabe, T. Taniguchi, A. Vishwanath, P. Jarillo-Herrero, and A. Yacoby, Fractional Chern insulators in magic-angle twisted bilayer graphene, Nature (London) 600, 439 (2021).
  6. A. Abouelkomsan, Z. Liu, and E. J. Bergholtz, Particle-hole duality, emergent Fermi liquids, and fractional Chern insulators in moiré flatbands, Phys. Rev. Lett. 124, 106803 (2020).
  7. C. Repellin and T. Senthil, Chern bands of twisted bilayer graphene: Fractional Chern insulators and spin phase transition, Phys. Rev. Res. 2, 023238 (2020).
  8. P. J. Ledwith, G. Tarnopolsky, E. Khalaf, and A. Vishwanath, Fractional Chern insulator states in twisted bilayer graphene: An analytical approach, Phys. Rev. Res. 2, 023237 (2020).
  9. H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu, T. Taniguchi, K. Watanabe, J.-H. Chu, T. Cao, L. Fu, W. Yao, C.-Z. Chang, D. Cobden, D. Xiao, and X. Xu, Observation of fractionally quantized anomalous Hall effect, Nature (London) 622, 74 (2023).
  10. Y. Zeng, Z. Xia, K. Kang, J. Zhu, P. Knüppel, C. Vaswani, K. Watanabe, T. Taniguchi, K. F. Mak, and J. Shan, Thermodynamic evidence of fractional Chern insulator in moiré MoTe2, Nature (London) 622, 69 (2023).
  11. F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong, J. Jia, Z. Shi, S. Jiang, Y. Zhang, X. Liu, and T. Li, Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2, Phys. Rev. X 13, 031037 (2023).
  12. Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous Hall effect in multilayer graphene, Nature (London) 626, 759 (2024).
  13. A. P. Reddy, N. Paul, A. Abouelkomsan, and L. Fu, Non-Abelian fractionalization in topological minibands, Phys. Rev. Lett. 133, 166503 (2024).
  14. C.-E. Ahn, W. Lee, K. Yananose, Y. Kim, and G. Y. Cho, Non-Abelian fractional quantum anomalous Hall states and first Landau level physics of the second moiré band of twisted bilayer MoTe2, Phys. Rev. B 110, L161109 (2024).
  15. F. Chen, W.-W. Luo, W. Zhu, and D. N. Sheng, Robust non-Abelian even-denominator fractional Chern insulator in twisted bilayer MoTe2, Nat. Commun. 16, 2115 (2025).
  16. H. Liu, Z. Liu, and E. J. Bergholtz, Non-Abelian fractional Chern insulators and competing states in flat moiré Bands, Phys. Rev. Lett. 135, 106604 (2025).
  17. C. Xu, N. Mao, T. Zeng, and Y. Zhang, Multiple Chern bands in twisted MoTe2 and possible non-Abelian states, Phys. Rev. Lett. 134, 066601 (2025).
  18. C. Wang, X.-W. Zhang, X. Liu, J. Wang, T. Cao, and D. Xiao, Higher Landau-level analogs and signatures of non-Abelian states in twisted bilayer MoTe2, Phys. Rev. Lett. 134, 076503 (2025).
  19. H. Liu, R. Perea-Causin, and E. J. Bergholtz, Parafermions in moiré minibands, Nat. Commun. 16, 1770 (2025).
  20. C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80, 1083 (2008).
  21. G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Colloquium: Excitons in atomically thin transition metal dichalcogenides, Rev. Mod. Phys. 90, 021001 (2018).
  22. K. F. Mak and J. Sha, Semiconductor moiré materials, Nat. Nanotechnol. 17, 686 (2022).
  23. E. C. Regan, D. Wang, E. Y. Paik, Y. Zeng, L. Zhang, J. Zhu, A. H. MacDonald, H. Deng, and F. Wang, Emerging exciton physics in transition metal dichalcogenide heterobilayers, Nat. Rev. Mater. 7, 778 (2022).
  24. L. A. Jauregui, A. Y. Joe, K. Pistunova, D. S. Wild, A. A. High, Y. Zhou, G. Scuri, K. D. Greve, A. Sushko, C.-H. Yu, T. Taniguchi, K. Watanabe, D. J. Needleman, M. D. Lukin, H. Park, and P. Kim, Electrical control of interlayer exciton dynamics in atomically thin heterostructures, Science 366, 870 (2019).
  25. J. Choi, M. Florian, A. Steinhoff, D. Erben, K. Tran, D. S. Kim, L. Sun, J. Quan, R. Claassen, S. Majumder, J. A. Hollingsworth, T. Taniguchi, K. Watanabe, K. Ueno, A. Singh, G. Moody, F. Jahnke, and X. Li, Twist angle-dependent interlayer exciton lifetimes in van der Waals heterostructures, Phys. Rev. Lett. 126, 047401 (2021).
  26. C. Jiang, W. Xu, A. Rasmita, Z. Huang, K. L. Qihua Xiong, and W.-B. Gao, Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures, Nat. Commun. 9, 753 (2018).
  27. D. Schmitt, J. P. Bange, W. Bennecke, A. AlMutairi, G. Meneghini, K. Watanabe, T. Taniguchi, D. Steil, D. R. Luke, R. T. Weitz, S. Steil, G. S. M. Jansen, S. Brem, E. Malic, S. Hofmann, M. Reutzel, and S. Mathias, Formation of moiré interlayer excitons in space and time, Nature (London) 608, 499 (2022).
  28. Z. Wang, Y.-H. Chiu, K. Honz, K. F. Mak, and J. Shan, Electrical tuning of interlayer exciton gases in WSe2 bilayers, Nano Lett. 18, 137 (2018).
  29. F. Tagarelli, E. Lopriore, D. Erkensten, R. Perea-Causín, S. Brem, J. Hagel, Z. Sun, G. Pasquale, K. Watanabe, T. Taniguchi, E. Malic, and A. Kis, Electrical control of hybrid exciton transport in a van der Waals heterostructure, Nat. Photon. 17, 615 (2023).
  30. Z. Zhang, E. C. Regan, D. Wang, W. Zhao, S. Wang, M. Sayyad, K. Yumigeta, K. Watanabe, T. Taniguchi, S. Tongay, M. Crommie, A. Zettl, M. P. Zaletel, and F. Wang, Correlated interlayer exciton insulator in heterostructures of monolayer WSe2 and moiré WS2/WSe2, Nat. Phys. 18, 1214 (2022).
  31. J. Gu, L. Ma, S. Liu, K. Watanabe, T. Taniguchi, J. C. Hone, J. Shan, and K. F. Mak, Dipolar excitonic insulator in a moiré lattice, Nat. Phys. 18, 395 (2022).
  32. D. Chen, Z. Lian, X. Huang, Y. Su, M. Rashetnia, L. Ma, L. Yan, M. Blei, L. Xiang, T. Taniguchi, K. Watanabe, S. Tongay, D. Smirnov, Z. Wang, C. Zhang, Y.-T. Cui, and S.-F. Shi, Excitonic insulator in a heterojunction moiré superlattice, Nat. Phys. 18, 1171 (2022).
  33. R. Xiong, J. H. Nie, S. L. Brantly, P. Hays, R. Sailus, K. Watanabe, T. Taniguchi, S. Tongay, and C. Jin, Correlated insulator of excitons in WSe2/WS2 moiré superlattices, Science 380, 860 (2023).
  34. F. Wu, T. Lovorn, and A. H. MacDonald, Topological exciton bands in moiré heterojunctions, Phys. Rev. Lett. 118, 147401 (2017).
  35. M. Xie, M. Hafezi, and S. Das Sarma, Long-lived topological flatband excitons in semiconductor moiré heterostructures: A bosonic Kane-Mele model platform, Phys. Rev. Lett. 133, 136403 (2024).
  36. R. Roy, Band geometry of fractional topological insulators, Phys. Rev. B 90, 165139 (2014).
  37. J. Wang, J. Cano, A. J. Millis, Z. Liu, and B. Yang, Exact Landau level description of geometry and interaction in a flatband, Phys. Rev. Lett. 127, 246403 (2021).
  38. P. J. Ledwith, A. Vishwanath, and D. E. Parker, Vortexability: A unifying criterion for ideal fractional Chern insulators, Phys. Rev. B 108, 205144 (2023).
  39. H. Liu, K. Yang, A. Abouelkomsan, Z. Liu, and E. J. Bergholtz, Broken symmetry in ideal Chern bands, Phys. Rev. B 111, L201105 (2025).
  40. R. Perea-Causin, H. Liu, and E. J. Bergholtz, Quantum anomalous Hall crystals in moiré bands with higher Chern number, Nat. Commun. 16, 6875 (2025).
  41. G. Ji and B. Yang, Quantum metric induced hole dispersion and emergent particle-hole symmetry in topological flat bands, arXiv:2409.08324.
  42. S. H. Simon, F. Harper, and N. Read, Fractional Chern insulators in bands with zero Berry curvature, Phys. Rev. B 92, 195104 (2015).
  43. L. Ma, P. X. Nguyen, Z. Wang, Y. Zeng, K. Watanabe, T. Taniguchi, A. H. MacDonald, K. F. Mak, and J. Shan, Strongly correlated excitonic insulator in atomic double layers, Nature (London) 598, 585 (2021).
  44. See Supplemental Material at http://link.aps.org/supplemental/10.1103/55zv-s9xv for additional details.
  45. T. Fukui, Y. Hatsugai, and H. Suzuki, Chern numbers in discretized Brillouin zone: Efficient method of computing (spin) Hall conductances, J. Phys. Soc. Jpn. 74, 1674 (2005).
  46. C. Repellin, B. A. Bernevig, and N. Regnault, Z2 fractional topological insulators in two dimensions, Phys. Rev. B 90, 245401 (2014).
  47. S. Brem, C. Linderälv, P. Erhart, and E. Malic, Tunable phases of moiré excitons in van der Waals heterostructures, Nano Lett. 20, 8534 (2020).
  48. W. J. Jankowski, J. J. P. Thompson, B. Monserrat, and R.-J. Slager, Excitonic topology and quantum geometry in organic semiconductors, Nat. Commun. 16, 4661 (2025).
  49. G. Tarnopolsky, A. J. Kruchkov, and A. Vishwanath, Origin of magic angles in twisted bilayer graphene, Phys. Rev. Lett. 122, 106405 (2019).
  50. A. Abouelkomsan, K. Yang, and E. J. Bergholtz, Quantum metric induced phases in moiré materials, Phys. Rev. Res. 5, L012015 (2023).
  51. H. Haug and S. Schmitt-Rink, Electron theory of the optical properties of laser-excited semiconductors, Prog. Quantum Electron. 9, 3 (1984).
  52. R. B. Laughlin, Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations, Phys. Rev. Lett. 50, 1395 (1983).
  53. F. D. M. Haldane, Fractional quantization of the Hall effect: A hierarchy of incompressible quantum fluid states, Phys. Rev. Lett. 51, 605 (1983).
  54. Y. H. Kwan, Y. Hu, S. H. Simon, and S. A. Parameswaran, Excitonic fractional quantum Hall hierarchy in moiré heterostructures, Phys. Rev. B 105, 235121 (2022).
  55. N. Stefanidis and I. Sodemann, Excitonic Laughlin states in ideal topological insulator flat bands and their possible presence in moiré superlattice materials, Phys. Rev. B 102, 035158 (2020).
  56. Y. Hu, J. W. F. Venderbos, and C. L. Kane, Fractional excitonic insulator, Phys. Rev. Lett. 121, 126601 (2018).
  57. E. J. Bergholtz and A. Karlhede, Half-filled lowest Landau level on a thin torus, Phys. Rev. Lett. 94, 026802 (2005).
  58. E. Ardonne, E. J. Bergholtz, J. Kailasvuori, and E. Wikberg, Degeneracy of non-Abelian quantum Hall states on the torus: Domain walls and conformal field theory, J. Stat. Mech. (2008) P04016.
  59. A. Sterdyniak, N. Regnault, and B. A. Bernevig, Extracting excitations from model state entanglement, Phys. Rev. Lett. 106, 100405 (2011).
  60. D. Erkensten, S. Brem, R. Perea-Causín, and E. Malic, Microscopic origin of anomalous interlayer exciton transport in van der Waals heterostructures, Phys. Rev. Mater. 6, 094006 (2022).
  61. A. Steinhoff, E. Wietek, M. Florian, T. Schulz, T. Taniguchi, K. Watanabe, S. Zhao, A. Högele, F. Jahnke, and A. Chernikov, Exciton-exciton interactions in van der Waals heterobilayers, Phys. Rev. X 14, 031025 (2024).
  62. O. Kyriienko, E. B. Magnusson, and I. A. Shelykh, Spin dynamics of cold exciton condensates, Phys. Rev. B 86, 115324 (2012).
  63. S. Brem and E. Malic, Bosonic delocalization of dipolar moiré excitons, Nano Lett. 23, 4627 (2023).
  64. A. P. Reddy, F. Alsallom, Y. Zhang, T. Devakul, and L. Fu, Fractional quantum anomalous Hall states in twisted bilayer MoTe2 and WSe2, Phys. Rev. B 108, 085117 (2023).
  65. H. Park, W. Li, C. Hu, C. Beach, M. Gonçalves, J. F. Mendez-Valderrama, J. Herzog-Arbeitman, T. Taniguchi, K. Watanabe, D. Cobden, L. Fu, B. A. Bernevig, N. Regnault, J.-H. Chu, D. Xiao, and X. Xu, Observation of high-temperature dissipationless fractional Chern insulator, arXiv:2503.10989.
  66. G. Moore and N. Read, Nonabelions in the fractional quantum Hall effect, Nucl. Phys. B 360, 362 (1991).
  67. M. Greiter, X.-G. Wen, and F. Wilczek, Paired Hall states, Nucl. Phys. B 374, 567 (1992).
  68. N. R. Cooper, N. K. Wilkin, and J. M. F. Gunn, Quantum phases of vortices in rotating Bose-Einstein condensates, Phys. Rev. Lett. 87, 120405 (2001).
  69. N. Regnault and T. Jolicoeur, Quantum Hall fractions in rotating Bose-Einstein condensates, Phys. Rev. Lett. 91, 030402 (2003).
  70. Z. Liu, E. J. Bergholtz, and E. Kapit, Non-Abelian fractional Chern insulators from long-range interactions, Phys. Rev. B 88, 205101 (2013).
  71. E. J. Bergholtz, J. Kailasvuori, E. Wikberg, T. H. Hansson, and A. Karlhede, Pfaffian quantum Hall state made simple: Multiple vacua and domain walls on a thin torus, Phys. Rev. B 74, 081308 (2006).
  72. A. Seidel and D.-H. Lee, Abelian and non-Abelian Hall liquids and charge-density wave: Quantum number fractionalization in one and two dimensions, Phys. Rev. Lett. 97, 056804 (2006).
  73. J.-J. Su and A. H. MacDonald, How to make a bilayer exciton condensate flow, Nat. Phys. 4, 799 (2008).
  74. N. J. Zhang, R. Q. Nguyen, N. Batra, X. Liu, K. Watanabe, T. Taniguchi, D. E. Feldman, and J. I. A. Li, Excitons in the fractional quantum Hall effect, Nature (London) 637, 327 (2025).
  75. D. Unuchek, A. Ciarrocchi, A. Avsar, K. Watanabe, T. Taniguchi, and A. Kis, Room-temperature electrical control of exciton flux in a van der Waals heterostructure, Nature (London) 560, 340 (2018).
  76. R. Rosati, R. Schmidt, S. Brem, R. Perea-Causín, I. Niehues, J. Kern, J. A. Preuß, R. Schneider, S. M. de Vasconcellos, and R. Bratschitsch, Dark exciton anti-funneling in atomically thin semiconductors, Nat. Commun. 12, 7221 (2021).
  77. A. Tüğen, A. M. Seiler, K. Watanabe, T. Taniguchi, M. Kroner, and A. İmamoğlu, Optical injection and detection of long-lived interlayer excitons in van der Waals heterostructures, arXiv:2506.06098.
  78. N. Read and E. Rezayi, Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level, Phys. Rev. B 59, 8084 (1999).
  79. M. P. A. Fisher, P. B. Weichman, G. Grinstein, and D. S. Fisher, Boson localization and the superfluid-insulator transition, Phys. Rev. B 40, 546 (1989).
  80. H. Lu, H.-Q. Wu, B.-B. Chen, and Z. Y. Meng, Continuous transition between bosonic fractional Chern insulator and superfluid, Phys. Rev. Lett. 134, 076601 (2025).
  81. T.-S. Huang, P. Lunts, and M. Hafezi, Nonbosonic moiré excitons, Phys. Rev. Lett. 132, 186202 (2024).
  82. I. Schwartz, Y. Shimazaki, C. Kuhlenkamp, K. Watanabe, T. Taniguchi, M. Kroner, and A. Imamoğlu, Electrically tunable Feshbach resonances in twisted bilayer semiconductors, Science 374, 336 (2021).
  83. T. Venanzi, M. Cuccu, R. Perea-Causin, X. Sun, S. Brem, D. Erkensten, T. Taniguchi, K. Watanabe, E. Malic, M. Helm, S. Winnerl, and A. Chernikov, Ultrafast switching of trions in 2D materials by terahertz photons, Nat. Photon. 18, 1344 (2024).
  84. M. Xie, H. Pan, F. Wu, and S. Das Sarma, Nematic excitonic insulator in transition metal dichalcogenide moiré heterobilayers, Phys. Rev. Lett. 131, 046402 (2023).

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Phys. Rev. Research 7, L042033– Published 10 November, 2025
  • Received 15 April 2025
  • Accepted 19 October 2025
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