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Valley-Polarized Quantum Anomalous Hall State in Moiré MoTe$_2$/WSe$_2$ Heterobilayers

Moiré heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moiré bands in heterobilayer TMDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling $ν=2$ (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling $ν=1$ were observed in AB stacked moiré MoTe$_2$/WSe$_2$ heterobilayers. However, how the topologically nontrivial states emerge is not known. In this work, we propose that the pseudo-magnetic fields induced by lattice relaxation in moiré MoTe$_2$/WSe$_2$ heterobilayers could naturally give rise to moiré bands with finite Chern numbers. We show that a time-reversal invariant quantum valley Hall insulator is formed at full-filing $ν=2$, when two moiré bands with opposite Chern numbers are filled. At half-filling $ν=1$, Coulomb interaction lifts the valley degeneracy and results in a valley-polarized quantum anomalous Hall state, as observed in the experiment. Our theory identifies a new way to achieve topologically non-trivial states in heterobilayer TMD materials.