Halperin, B. I. & Jain, J. K. (eds) Fractional Quantum Hall Effects: New Developments (World Scientific, 2020).
Laughlin, R. B. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395 (1983).
Halperin, B. I. Statistics of quasiparticles and the hierarchy of fractional quantized Hall states. Phys. Rev. Lett. 52, 1583 (1984).
Arovas, D., Schrieffer, J. R. & Wilczek, F. Fractional statistics and the quantum Hall effect. Phys. Rev. Lett. 53, 722 (1984).
de-Picciotto, R. et al. Direct observation of a fractional charge. Nature 389, 162–164 (1997).
Reznikov, M. et al. Observation of quasiparticles with one-fifth of an electron’s charge. Nature 399, 238–241 (1999).
Dolev, M. et al. Observation of a quarter of an electron charge at the ν = 5/2 quantum Hall state. Nature 452, 829–834 (2008).
Goldman, V. J. & Su, B. Resonant tunneling in the quantum Hall regime: measurement of fractional charge. Science 267, 1010–1012 (1995).
Martin, J. et al. Localization of fractionally charged quasi-particles. Science 305, 980–983 (2004).
Banerjee, M. et al. Observation of half-integer thermal Hall conductance. Nature 559, 205–210 (2018).
Bartolomei, H. et al. Fractional statistics in anyon collisions. Science 368, 173–177 (2020).
Lee, J. Y. M. et al. Partitioning of diluted anyons reveals their braiding statistics. Nature 617, 277–281 (2023).
Nakamura, J. et al. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).
Tang, E., Mei, J.-W. & Wen, X.-G. High-temperature fractional quantum Hall states. Phys. Rev. Lett. 106, 236802 (2011).
Sun, K., Gu, Z., Katsura, H. & Das Sarma, S. Nearly flatbands with nontrivial topology. Phys. Rev. Lett. 106, 236803 (2011).
Neupert, T., Santos, L., Chamon, C. & Mudry, C. Fractional quantum Hall states at zero magnetic field. Phys. Rev. Lett. 106, 236804 (2011).
Sheng, D. N., Gu, Z.-C., Sun, K. & Sheng, L. Fractional quantum Hall effect in the absence of Landau levels. Nat. Commun. 2, 389 (2011).
Regnault, N. & Bernevig, B. A. Fractional Chern insulator. Phys. Rev. X 1, 021014 (2011).
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).
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).
Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).
Berkelbach, T. C., Hybertsen, M. S. & Reichman, D. R. Theory of neutral and charged excitons in monolayer transition metal dichalcogenides. Phys. Rev. B 88, 045318 (2013).
Wójs, A. & Quinn, J. J. Energy spectra of fractional quantum Hall systems in the presence of a valence hole. Phys. Rev. B 63, 045303 (2000).
Byszewski, M. et al. Optical probing of composite fermions in a two-dimensional electron gas. Nat. Phys. 2, 239–243 (2006).
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).
Anderson, E. et al. Trion sensing of a zero-field composite Fermi liquid. Nature 635, 590–595 (2024).
Mostaan, N., Goldman, N., İmamoğlu, A. & Grusdt, F. Anyon-trions in atomically thin semiconductor heterostructures. Preprint at https://arxiv.org/abs/2507.08933v2 (2025).
Wagner, G. & Neupert, T. Sensing the binding and unbinding of anyons at impurities. Preprint at https://arxiv.org/abs/2507.08928v1 (2025).
Anderson, E. et al. Programming correlated magnetic states with gate-controlled moiré geometry. Science 381, 325–330 (2023).
He, Y. M. et al. Single quantum emitters in monolayer semiconductors. Nat. Nanotechnol. 10, 497–502 (2015).
Srivastava, A. et al. Optically active quantum dots in monolayer WSe2. Nat. Nanotechnol. 10, 491–496 (2015).
Chakraborty, C. et al. Voltage-controlled quantum light from an atomically thin semiconductor. Nat. Nanotechnol. 10, 507–511 (2015).
Koperski, M. et al. Single photon emitters in exfoliated WSe2 structures. Nat. Nanotechnol. 10, 503–506 (2015).
Kumar, S., Kaczmarczyk, A. & Gerardot, B. D. Strain-induced spatial and spectral isolation of quantum emitters in mono-and bilayer WSe2. Nano Lett. 15, 7567–7573 (2015).
Thureja, D. et al. Electrically tunable quantum confinement of neutral excitons. Nature 606, 298–304 (2022).
Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. X 13, 031037 (2023).
Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023).
Ji, Z. et al. Local probe of bulk and edge states in a fractional Chern insulator. Nature 635, 578583 (2024).
Redekop, E. et al. Direct magnetic imaging of fractional Chern insulators in twisted MoTe2. Nature 635, 584–589 (2024).
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).
Jain, J. K. Composite Fermions (Cambridge Univ. Press, 2007).
Crépel, V. & Fu, L. Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides. Phys. Rev. B 107, L201109 (2023).
Anderson, E. et al. Magnetoelectric control of helical light emission in a moiré Chern magnet. Phys. Rev. X 15, 031057 (2025).
Liu, Z., Li, B. & Wu, F. Characterization of fractional Chern insulator quasiparticles in moiré transition metal dichalcogenides. Phys. Rev. B 112, 245104 (2025).
Park, H. et al. Observation of high-temperature dissipationless fractional Chern insulator. Preprint at https://arxiv.org/abs/2503.10989v1 (2025).
