The topological magnetoelectric effect in semiconductor nanostructures: quantum wells, wires, dots and rings

TL;DR

This paper develops a numerical model to study the topological magnetoelectric effect in various semiconductor nanostructures, revealing how geometry influences induced magnetic fields.

Contribution

It introduces a simple, fast numerical implementation of Maxwell equations for topological insulator nanostructures, enabling detailed analysis of shape-dependent magnetoelectric effects.

Findings

Magnetic fields of the order of mT are induced by point charges.

The sign and orientation of magnetic fields depend on nanostructure geometry.

Hall currents on surfaces explain the magnetoelectric effects.

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. Point-like charges give rise to magnetic fields of the order of mT, whose sign and spatial orientation is 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.