Geometric valley Hall effect and valley filtering through a singular Berry flux

Conventionally, a basic requirement to generate valley Hall effect (VHE) is that the Berry curvature for conducting carriers in the momentum space be finite so as to generate anomalous deflections of the carriers originated from distinct valleys into different directions. We uncover a geometric valley Hall effect (gVHE) in which the valley-contrasting Berry curvature for carriers vanishes completely except for the singular points. The underlying physics is a singular non-π fractional Berry flux located at each conical intersection point in the momentum space, analogous to the classic Aharonov-Bohm effect of a confined magnetic flux in real space. We demonstrate that, associated with gVHE, exceptional skew scattering of valley-contrasting quasiparticles from a valley-independent, scalar type of impurities can generate charge-neutral, transverse valley currents. As a result, the massless nature of the quasiparticles and their high mobility are retained. We further demonstrate that, for the particular Berry flux of π/2, gVHE is considerably enhanced about the skew scattering resonance, which is electrically controllable. A remarkable phenomenon of significant practical interest is that, associated with gVHE, highly efficient valley filtering can arise. These phenomena are robust against thermal fluctuations and disorders, making them promising for valleytronics applications.