Topological and magnetic states in AB-stacked transition metal dichalcogenide moiré bilayers

Narrowband transition metal dichalcogenide heterobilayer moiré materials with hole filling factor u=1 have Mott insulating ground states with three-sublattice magnetic order. Recent experiments have shown that a surprising quantum anomalous Hall appears when the displacement field is close to the value at which the sense of layer polarization changes. We have performed mean-field theory calculations to determine whether or not this behavior can be explained in terms of broken time-reversal states with spontaneous layer polarization that appear when the highest energy valence subbands of the two layers are close to degeneracy. This scenario requires either a first-order phase transition between the quantum anomalous Hall state and the ordinary Mott insulator states on either side when the displacement field is varied, or a displacement field at which the gap vanishes. We will discuss the phase diagram predicted by this scenario over the full range of displacement field needed to reverse the sense of layer polarization, and compare with other proposals for the origin of the quantum anomalous Hall states.