Topological magnetoelectric effect in semiconductor nanostructures: Quantum wells, wires, dots, and rings

Abstract

Electrostatic charges placed near the interface between ordinary and topological insulators induce magnetic fields through the so-called topological magnetoelectric effect. Here we present a numerical implementation of the associated Maxwell equations. The resulting model is simple, fast, and quantitatively as accurate as the image charge method but with the advantage of providing easy access to elaborate geometries when pursuing specific effects. The model is used to study how magnetoelectric fields are influenced by the dimensions and the shape of the most common semiconductor nanostructures: quantum wells, quantum wires, quantum dots, and quantum rings. Pointlike charges give rise to magnetic fields of the order of mT, whose sign and spatial orientation are governed by the geometry of the nanostructure and the location of the charge. The results are rationalized in terms of the Hall currents induced on the surface, which constitute a simple yet valid framework for the deterministic design of magnetoelectric fields.