Toward a global phase diagram of the fractional quantum anomalous Hall effect

Recent experiments on the twisted semiconductor bilayer system tMoTe(2) have observed integer and fractional quantum anomalous Hall effects, which occur in topological moir & eacute; bands at zero magnetic field. Here, we present a global phase diagram of tMoTe(2) throughout the filling range 0 < n <= 1 substantiated by exact diagonalization calculations. At a magic angle, we find that the system resembles the lowest Landau level (LLL) to a remarkable degree, exhibiting an abundance of incompressible fractional quantum anomalous Hall states and compressible anomalous composite Fermi liquid states. Away from the magic angle, particle-hole symmetry is strongly broken. Some LLL-like features remain robust near half-filling, while others are replaced, predominantly by charge density waves near n = 0 and anomalous Hall Fermi liquids near n = 1. Among LLL-like phases, we find the anomalous composite Fermi liquid at n = 1/2 to be most robust against deviations from the magic angle. Within the band-projected model, we show that strong particle-hole asymmetry above the magic angle results from interaction-enhanced quasiparticle dispersion near n = 1. Our paper sets the stage for future exploration of LLL-like and beyond-LLL phases in fractional quantum anomalous Hall systems.