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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 ¼ 2 (two holes per moiré unit cell) and a valley-polarized quantum anomalous Hall state at filling ν ¼ 1 were observed in AB stacked moiré MoTe 2 =WSe 2 heterobilayers. However, how the topologically nontrivial states emerge is not known. In this Letter, we propose that the pseudomagnetic 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 timereversal invariant quantum valley Hall insulator is formed at full filling ν ¼ 2, when two moiré bands with opposite Chern numbers are filled. At half filling ν ¼ 1, the 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 nontrivial states in heterobilayer TMD materials.

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Recently, signatures of nonlinear Hall effects induced by Berry curvature dipoles have been found in atomically thin 1T'/T d -WTe2. In this work, we show that in strained polar transition-metal dichalcogenides(TMDs) with 2H-structures, Berry curvature dipoles created by spin degrees of freedom lead to strong nonlinear Hall effects. Under easily accessible uniaxial strain of order ∼ 0.2%, strong nonlinear Hall signals, characterized by Berry curvature dipole in the order of ∼ 1Å, arise in electron-doped polar TMDs such as MoSSe, which is easily detectable experimentally. Moreover, the magnitude and sign of the nonlinear Hall current can be easily tuned by electric gating and strain. These properties can be used to distinguish nonlinear Hall effects from classical mechanisms such as ratchet effects. Importantly, our system provides a potential scheme for building electrically switchable energy harvesting rectifiers.