Orbital Hall effect from the Wannier function approach

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.