• Neupert, T., Santos, L., Chamon, C. & Mudry, C. Fractional quantum Hall states at zero magnetic field. Phys. Rev. Lett. 106, 236804 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Sheng, D., Gu, Z.-C., Sun, K. & Sheng, L. Fractional quantum Hall effect in the absence of Landau levels. Nat. Commun. 2, 389 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Regnault, N. & Bernevig, B. A. Fractional Chern insulator. Phys. Rev. X 1, 021014 (2011).


    Google Scholar
     

  • Tang, E., Mei, J.-W. & Wen, X.-G. High-temperature fractional quantum Hall states. Phys. Rev. Lett. 106, 236802 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Sun, K., Gu, Z., Katsura, H. & Das Sarma, S. Nearly flatbands with nontrivial topology. Phys. Rev. Lett. 106, 236803 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Xiao, D., Zhu, W., Ran, Y., Nagaosa, N. & Okamoto, S. Interface engineering of quantum Hall effects in digital transition metal oxide heterostructures. Nat. Commun. 2, 596 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559 (1982).

    Article 
    ADS 

    Google Scholar
     

  • Laughlin, R. B. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395 (1983).

    Article 
    ADS 

    Google Scholar
     

  • Chernikov, A. et al. Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2. Phys. Rev. Lett. 113, 076802 (2014).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

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


    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

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

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

  • Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Lu, Z. et al. Extended quantum anomalous Hall states in graphene/hBN moiré superlattices. Nature 637, 1090–1095 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Choi, Y. et al. Superconductivity and quantized anomalous Hall effect in rhombohedral graphene. Nature 639, 342–347 (2025).

  • Xie, J. et al. Tunable fractional Chern insulators in rhombohedral graphene superlattices. Nat. Mater. 24, 1042–1048 (2025).

  • Aronson, S. H. et al. Displacement field-controlled fractional Chern insulators and charge density waves in a graphene/hBN moiré superlattice. Phys. Rev. X 15, 031026 (2025).


    Google Scholar
     

  • Jain, J. K. Composite Fermions (Cambridge Univ. Press, 2007).

  • Halperin, B. I. & Jain, J. K. Fractional Quantum Hall Effects: New Developments (World Scientific, 2020).

  • Chung, Y. J. et al. Ultra-high-quality two-dimensional electron systems. Nat. Mater. 20, 632–637 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Anderson, E. et al. Programming correlated magnetic states with gate-controlled moiré geometry. Science 381, 325–330 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Xia, Y. et al. Superconductivity in twisted bilayer WSe2. Nature 637, 833–838 (2024).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

  • 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 
    ADS 

    Google Scholar
     

  • 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 
    ADS 

    Google Scholar
     

  • Anderson, E. et al. Magnetoelectric control of helical light emission in a moiré Chern magnet. Phys. Rev. X 15, 031057 (2025).


    Google Scholar
     

  • Schulze-Wischeler, F., Mariani, E., Hohls, F. & Haug, R. J. Direct measurement of the g factor of composite fermions. Phys. Rev. Lett. 92, 156401 (2004).

    Article 
    ADS 

    Google Scholar
     

  • Gonçalves, M. et al. Spinless and spinful charge excitations in moiré fractional Chern insulators. Preprint at http://arxiv.org/abs/2506.05330 (2025).

  • Girvin, S., MacDonald, A. & Platzman, P. Magneto-roton theory of collective excitations in the fractional quantum Hall effect. Phys. Rev. B 33, 2481 (1986).

    Article 
    ADS 

    Google Scholar
     

  • Pinczuk, A., Dennis, B., Pfeiffer, L. & West, K. Observation of collective excitations in the fractional quantum Hall effect. Phys. Rev. Lett. 70, 3983 (1993).

    Article 
    ADS 

    Google Scholar
     

  • Nakajima, T. & Aoki, H. Composite-fermion picture for the spin-wave excitation in the fractional quantum Hall system. Phys. Rev. Lett. 73, 3568 (1994).

    Article 
    ADS 

    Google Scholar
     

  • Halperin, B. I., Lee, P. A. & Read, N. Theory of the half-filled Landau level. Phys. Rev. B 47, 7312 (1993).

    Article 
    ADS 

    Google Scholar
     

  • Stern, A. & Halperin, B. I. Singularities in the Fermi-liquid description of a partially filled Landau level and the energy gaps of fractional quantum Hall states. Phys. Rev. B 52, 5890 (1995).

    Article 
    ADS 

    Google Scholar
     

  • Nayak, C. & Wilczek, F. Non-Fermi liquid fixed point in 2 + 1 dimensions. Nucl. Phys. B 417, 359–373 (1994).

    Article 
    ADS 

    Google Scholar
     

  • Morf, R., d’Ambrumenil, N. & Sarma, S. D. Excitation gaps in fractional quantum Hall states: an exact diagonalization study. Phys. Rev. B 66, 075408 (2002).

    Article 
    ADS 

    Google Scholar
     

  • Boebinger, G. et al. Activation energies and localization in the fractional quantum Hall effect. Phys. Rev. B 36, 7919 (1987).

    Article 
    ADS 

    Google Scholar
     

  • Willett, R., Stormer, H., Tsui, D., Gossard, A. & English, J. Quantitative experimental test for the theoretical gap energies in the fractional quantum Hall effect. Phys. Rev. B 37, 8476 (1988).

    Article 
    ADS 

    Google Scholar
     

  • Du, R., Stormer, H., Tsui, D., Pfeiffer, L. & West, K. Experimental evidence for new particles in the fractional quantum Hall effect. Phys. Rev. Lett. 70, 2944 (1993).

    Article 
    ADS 

    Google Scholar
     

  • Manoharan, H., Shayegan, M. & Klepper, S. Signatures of a novel Fermi liquid in a two-dimensional composite particle metal. Phys. Rev. Lett. 73, 3270 (1994).

    Article 
    ADS 

    Google Scholar
     

  • Villegas Rosales, K. et al. Fractional quantum Hall effect energy gaps: role of electron layer thickness. Phys. Rev. Lett. 127, 056801 (2021).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

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

    Article 

    Google Scholar
     

  • Zhang, X.-W. et al. Polarization-driven band topology evolution in twisted MoTe2 and WSe2. Nat. Commun. 15, 4223 (2024).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

  • Xu, C., Li, J., Xu, Y., Bi, Z. & Zhang, Y. Maximally localized Wannier functions, interaction models, and fractional quantum anomalous Hall effect in twisted bilayer MoTe2. Proc. Natl Acad. Sci. USA 121, e2316749121 (2024).

    Article 

    Google Scholar
     

  • 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 
    ADS 

    Google Scholar
     

  • Éfros, A. L. & Shklovskii, B. I. Coulomb gap and low temperature conductivity of disordered systems. J. Phys. C 8, L49 (1975).

    Article 
    ADS 

    Google Scholar
     

  • Shklovskii, B. I. & Efros, A. L. in Electronic Properties of Doped Semiconductors 202–227 (Springer Nature, 1984).

  • Wang, M., Wang, X. & Vafek, O. Phase diagram of twisted bilayer MoTe2 in a magnetic field with an account for the electron–electron interaction. Phys. Rev. B 110, L201107 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Zhang, S. et al. VASP2KP: k⋅p models and Landé g-factors from ab initio calculations. Chin. Phys. Lett. 40, 127101 (2023).

    Article 
    ADS 

    Google Scholar