Abstract
Recent experiments on the twisted semiconductor bilayer system tMoTe₂ have observed integer and fractional quantum anomalous Hall effects, which occur in topological moir\'e bands at zero magnetic field. Here, we present a global phase diagram of tMoTe₂ 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 work sets the stage for future exploration of LLL-like and beyond-LLL phases in fractional quantum anomalous Hall systems.