Orbital Hall effect as an alternative to valley Hall effect in gapped graphene

TL;DR

This paper proposes that the orbital Hall effect offers a clearer and more consistent framework than the valley Hall effect for understanding electron transport in gapped graphene, linking orbital magnetic moments to observable phenomena.

Contribution

It redefines the valley Hall effect as an orbital Hall effect, removing arbitrariness and providing a unified description using orbital Berry curvature.

Findings

Orbital Hall effect explains edge orbital moments observed experimentally.

Reformulation removes the need for arbitrary cut-offs in valley Hall conductivity.

Provides a physical basis for valley-related phenomena in gapped graphene.

Abstract

Gapped graphene has been proposed to be a good platform to observe the valley Hall effect, a transport phenomenon involving the flow of electrons that are characterized by different valley indices. In the present work, we show that this phenomenon is better described as an instance of the orbital Hall effect, where the ambiguous "valley" indices are replaced by a physical quantity, the orbital magnetic moment, which can be defined uniformly over the entire Brillouin zone. This description removes the arbitrariness in the choice of arbitrary cut-off for the valley-restricted integrals in the valley Hall conductivity, as the conductivity in the orbital Hall effect is now defined as the Brillouin zone integral of a new quantity, called the orbital Berry curvature. This reformulation in terms of OHE provides the direct explanation to the accumulated opposite orbital moments at the edges of the sample, observed in previous Kerr rotation measurements.