Persistent Hall voltages across thin planar charged quantum rings on the surface of a three-dimensional topological insulator

Abstract

We study theoretically, the electromagnetic response due to localized charge current distributions above a topological insulator (coated with a thin ferromagnetic layer) using the electromagnetic duality symmetry. We show that the localized current induces an electric field which depends on the current —this is a manifestation of the topological magnetoelectric (TME) effect. We also show that if the charge carriers have spin, then they acquire Aharanov-Casher phases which depend on the current. As an application, we consider thin planar charged quantum rings with persistent currents on the surface of a TI and show that the TME manifests itself as persistent Hall voltages across the charged ring. If the spin is also taken into account, then persistent spin Hall voltages develop across the ring.