Topological valley pumping in Weyl semimetals.

We investigate the topological pumping effect in Weyl semimetals, subject to the modulation of two ac electric fields along y  and z directions, respectively. We show that the pumping effect originates from the anomalous velocity related to the Berry curvature. The direction of the pumping current is dependent on the chirality of the Weyl fermions. While the total particle current is vanishing because the Weyl points of opposite chirality always come in pairs in Weyl semimetals, the pump gives rise to a net chirality current or valley current. The noiseless valley current generated can be useful in valleytronic applications.