Large valley polarization and the valley-dependent Hall effect in a Janus TiTeBr monolayer

as high as 220 K. It is indicated that an out-of-plane alignment of magnetization demonstrates a valley polarization up to 113 meV in the topmost valence band, as further verified by perturbation theory considering both the spin polarization and spin-orbit coupling. Under an in-plane electric field, the valley-dependent Berry curvature results in the anomalous valley Hall effect (AVHE). Moreover, under a suitable in-plane biaxial strain, the TiTeBr monolayer transforms into a Chern insulator with a nonzero Chern number, yet retains its ferrovalley characters and thus the emergent quantum anomalous valley Hall effect (QAVHE). Our study indicates that the TiTeBr monolayer is a promising ferrovalley material, and it provides a platform for investigating the valley-dependent Hall effect.