Orbital Hall effect from the Wannier function approach
Phys. Rev. B 114, 214403 – Published 6 October, 2026
DOI: https://doi.org/10.1103/pd3s-q2z7
Abstract
Using the Wannier function approach, we develop a gauge-covariant formalism for the orbital angular momentum (OAM) operator and the orbital Hall conductivity (OHC). The Wannier function formulation resolves the position-operator ambiguity inherent to Bloch states, providing a transparent and rigorous theory of orbital transport. Our formalism is validated through a finite-lattice calculation of the Haldane model, where the OAM operator is evaluated exactly from its real-space definition. Our results are also relevant to other orbital phenomena in solids such as the orbital Edelstein effect, orbital torque generation, and the like, where the OAM plays a crucial role.
