Skew Scattering and Side Jump Drive Exciton Valley Hall Effect in Two-Dimensional Crystals

Exciton valley Hall effect is the spatial separation of the valley-tagged excitons by a drag force. Usually, the effect is associated with the anomalous velocity acquired by the particles due to the Berry curvature of the Bloch bands. Here we show that the anomalous velocity plays no role in the exciton valley Hall effect, which is governed by the side-jump and skew scattering. We develop a microscopic theory of the exciton valley Hall effect in the presence of a synthetic electric field and phonon drag and calculate all relevant contributions to the valley Hall current also demonstrating the cancellation of the anomalous velocity. The sensitivity of the effect to the origin of the drag force and to the scattering processes is shown. We extend the drift-diffusion model to account for the valley Hall effect and calculate the exciton density and valley polarization profiles.