Groundbreaking experiments [1-5] on twisted MoTe2 and pentalayer rhombohedral graphene have observed for the first time the fractional quantum anomalous Hall (FQAH) effect which is the fractional quantum Hall effect at zero magnetic field. I will review the current experimental and theoretical efforts to understand and characterize these phases. In addition to the incompressible abelian FQAH observed, experiments also observed signatures of a compressible state which is likely to be the anomalous analogue of the composite Fermi liquid (CFL). I will argue that the anomalous composite Fermi liquid is fundamentally different from the normal Fermi liquid and characterized by a vanishing Drude weight [7]. I will conclude the talk by discussing a recent intriguing experiment observing the fractional quantum spin Hall effect in twisted MoTe2 [8] and various predictions for possible non-abelian topological order [9].
[1] Cai, J., Anderson, E., Wang, C. et al. Nature 622, 63–68 (2023)
[2] Zeng, Y., Xia, Z., Kang, K. et al Nature 622, 69–73 (2023).
[3] Xu, Fan, et al. Physical Review X 13.3 (2023): 031037
[4] Park, H., Cai, J., Anderson, E. et al. Nature 622, 74–79 (2023).
[5] Lu, Z., Han, T., Yao, Y. et al.. Nature 626, 759–764 (2024)
[6] A. Abouelkomsan, A.P Reddy, L. Fu and Emil J. Bergholtz, Band mixing in the quantum anomalous Hall regime of twisted semiconductor bilayers, Phys. Rev. B 109, L121107 (2024)
[7] A. Abouelkomsan, N. Paul, A. Stern and L. Fu, Compressible quantum matter with vanishing Drude weight, arXiv:2403.14747
[8] Kang, K., Shen, B., Qiu, Y. et al. Nature 628, 522–526 (2024)
[9] A.P Reddy, N. Paul, A. Abouelkomsan and L. Fu, Non-Abelian fractionalization in topological minibands, arXiv:2403.00059