Role of Disorder in the Intrinsic Orbital Hall Effect

The orbital Hall effect (OHE) has garnered much attention as a promising approach to realize highly efficient "orbitronic" devices with a wide range of materials. However, the existing theories that attempt to explain the experimental evidence focus on the intrinsic effect, neglecting the omnipresent disorder. Here, we formulate the impact of random defect scattering on the orbital Hall effect by a quantum Boltzmann equation and solve it for a generic two-band model including the in-scattering collision integral (vertex correction). In contrast to the common belief that the intrinsic OHE is robust against the disorder, we find that diffuse scattering by an arbitrarily weak disorder affects and can even fully suppress the intrinsic orbital Hall current, depending on the character of orbital states and the disorder.