  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.
