van Hove Singularity-Induced Non-Equilibrium Anomalous Valley Hall Effect in a Two-Dimensional Lattice

van Hove singularity and valley represent two fundamental phenomena in materials science and condensed matter physics, which have recently attracted considerable interest. Here, we propose that the interplay between van Hove singularity and valley can generate a previously unreported anomalous valley Hall effect (AVHE) in a two-dimensional (2D) lattice, termed the non-equilibrium AVHE, which is characterized by the non-equilibrium transverse accumulation of valley carriers from different valleys. The physics relates to van Hove singularity-induced breaking of time-reversal symmetry and the resulting valley polarization under carrier doping, which guarantees the unique properties of non-equilibrium valley carriers. Remarkably, in contrast to typical AVHE relying on intrinsic magnetic materials, the non-equilibrium AVHE is rooted in 2D nonmagnetic systems. Using first-principles calculations, we validate the proposed mechanism and the predicted phenomena in monolayer In₂Se₃, known to exhibit nonmagnetic and ferroelectric natures. These findings open an avenue for exploring unconventional AVHE in 2D nonmagnetic systems.