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Electrostatic charges placed near the interface between ordinary andtopological insulators induce magnetic fields, through the so-calledtopological magnetoelectric effect. Here, we present a numerical implementationof the associated Maxwell equations. The resulting model is simple, fast andquantitatively as accurate as the image charge method, but with the advantageof providing easy access to elaborate geometries when pursuing specificeffects. The model is used to study how magnetoelectric fields are influencedby the dimensions and the shape of the most common semiconductornanostructures: quantum wells, quantum wires, quantum dots and quantum rings.Point-like charges give rise to magnetic fields of the order of mT, whose signand spatial orientation is governed by the geometry of the nanostructure andthe location of the charge. The results are rationalized in terms of the Hallcurrents induced on the surface, which constitute a simple yet valid frameworkfor the deterministic design of magnetoelectric fields.

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