The electromagnetic response of topological insulators is governed by axion
electrodynamics, which features a topological magnetoelectric term in the
Maxwell equations. As a consequence magnetic fields become the source of
electric fields and vice-versa, a phenomenon that is general for any material
exhibiting a linear magnetoelectric effect. Axion electrodynamics has been
associated with the possibility to create magnetic monopoles, in particular by
a electrical charge that is screened above the surface of a magnetoelectric
material. Here we present the exact solution for the electromagnetic fields in
this geometry and show that while vortex-like magnetic screening fields are
generated by the electrical charge their divergence is identically zero at
every point in space which implies a strict absence of magnetic monopoles.
Although magnetic image charges can be made explicit in the problem, no bound
state with electric charges yielding a dyon arises. A dyon-like angular
momentum follows from our analysis, but is quantized in a universal way,
because of its dependence on the dielectric constant. This is consistent with a
general argument that precludes magnetic monopoles to be generated in Maxwell
magnetoelectrics.Comment: v2: 9 pages, 3 figures; improved presentation and more detailed
appendices; added calculation of angular momentum; appendix is made more
pedagogical and now includes the detailed solution for a point charge in the
presence of a topological dielectric sphere; several references are adde
