Quantum Correction to the Orbital Hall Effect

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