Moire 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 moire bands in heterobilayer T
MDs were believed to be topologically trivial. Recently, it was reported that both a quantum valley Hall insulating state at filling $ u=2$ (two holes per moire unit cell) and a valley polarized quantum anomalous Hall state at filling $ u=1$ were observed in AB stacked moire 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 moire MoTe$_2$/WSe$_2$ heterobilayers could naturally give rise to moire bands with finite Chern numbers. We show that a time-reversal invariant quantum valley Hall insulator is formed at full-filing $ u=2$, when two moire bands with opposite Chern numbers are filled. At half-filling $ u=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.
In recent years, it has been shown that Berry curvature monopoles and dipoles play essential roles in the anomalous Hall effect and the nonlinear Hall effect respectively. In this work, we demonstrate that Berry curvature multipoles (the higher momen
ts of Berry curvatures at the Fermi energy) can induce higher-order nonlinear anomalous Hall (NLAH) effect. Specifically, an AC Hall voltage perpendicular to the current direction emerges, where the frequency is an integer multiple of the frequency of the applied current. Importantly, by analyzing the symmetry properties of all the 3D and 2D magnetic point groups, we note that the quadrupole, hexapole and even higher Berry curvature moments can cause the leading-order frequency multiplication in certain materials. To provide concrete examples, we point out that the third-order NLAH voltage can be the leading-order Hall response in certain antiferromagnets due to Berry curvature quadrupoles, and the fourth-order NLAH voltage can be the leading response in the surface states of topological insulators induced by Berry curvature hexapoles. Our results are established by symmetry analysis, effective Hamiltonian and first-principles calculations. Other materials which support the higher-order NLAH effect are further proposed, including 2D antiferromagnets and ferromagnets, Weyl semimetals and twisted bilayer graphene near the quantum anomalous Hall phase.
Recent studies have shown that moir{e} flat bands in a twisted bilayer graphene(TBG) can acquire nontrivial Berry curvatures when aligned with hexagonal boron nitride substrate [1, 2], which can be manifested as a correlated Chern insulator near the
3/4 filling [3, 4]. In this work, we show that the large Berry curvatures in the moir{e} bands lead to strong nonlinear Hall(NLH) effect in a strained TBG with general filling factors. Under a weak uniaxial strain $sim 0.1%$, the Berry curvature dipole which characterizes the nonlinear Hall response can be as large as $sim$ 200{AA}, exceeding the values of all previously known nonlinear Hall materials [5-14] by two orders of magnitude. The dependence of the giant NLH effect as a function of electric gating, strain and twist angle is further investigated systematically. Importantly, we point out that the giant NLH effect appears generically for twist angle near the magic angle due to the strong susceptibility of nearly flat moir{e} bands to symmetry breaking induced by strains. Our results establish TBG as a practical platform for tunable NLH effect and novel transport phenomena driven by nontrivial Berry phases.
Recently, it has been pointed out that the twisting of bilayer WSe$_2$ would generate topologically non-trivial flat bands near the Fermi energy. In this work, we show that twisted bilayer WSe$_2$ (tWSe$_2$) with uniaxial strain exhibits a large nonl
inear Hall (NLH) response due to the non-trivial Berry curvatures of the flat bands. Moreover, the NLH effect is greatly enhanced near the topological phase transition point which can be tuned by a vertical displacement field. Importantly, the nonlinear Hall signal changes sign across the topological phase transition point and provides a way to identify the topological phase transition and probe the topological properties of the flat bands. The strong enhancement and high tunability of the NLH effect near the topological phase transition point renders tWSe$_2$ and related moire materials new platforms for rectification and second harmonic generations.
Recently, signatures of nonlinear Hall effects induced by Berry-curvature dipoles have been found in atomically thin 1T/Td-WTe$_2$. In this work, we show that in strained polar transition-metal dichalcogenides(TMDs) with 2H-structures, Berry-curvatur
e dipoles created by spin degrees of freedom lead to strong nonlinear Hall effects. Under an easily accessible uniaxial strain of order 0.2%, strong nonlinear Hall signals, characterized by a Berry-curvature dipole on the order of 1{AA}, arise in electron-doped polar TMDs such as MoSSe, and this 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.
