Quantum correction to the orbital Hall effect

Abstract

Evaluations of the orbital Hall effect (OHE) have only retained inter-band matrix elements of the position operator. Here we evaluate the OHE including all matrix elements of the position operator, including the technically challenging intra-band elements. We recover previous results and find quantum corrections due to the non-commutativity of the position and velocity operators and inter-band matrix elements of the orbital angular momentum. The quantum corrections dominate the OHE responses of the topological antiferromagnet CuMnAs and of massive Dirac fermions.