Non-conservation of the valley density and its implications for the observation of the valley Hall effect

Alexander Kazantsev, Amelia Mills, Eoin O'Neill, Giovanni Vignale, Alessandro Principi

Published 2022-11-22Version 1

We show that the conservation of the valley density in a multi-valley insulator is broken in an unexpected way by an electric field, such as the one that is used to drive the valley Hall effect. This observation explains how a fully gapped insulator (i.e., one without edge states that cross the Fermi level) can support a valley Hall current in the bulk and yet show no valley density accumulation at the edges. If the insulator is not fully gapped, either because there are edge states crossing the Fermi level or because carriers are introduced in the conduction or valence band, then valley density accumulation at the edges is possible, paving the way to a direct observation of the valley Hall effect. However, the magnitude of the accumulation depends crucially on the inclusion of the anomalous electric field term in the continuity equation that relates valley current and density.