Absence of induced magnetic monopoles in Maxwellian magnetoelectrics

Flavio S. Nogueira, Jeroen van den Brink

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
an electrical charge that is screened above the surface of a magnetoelectric
material. Here we explicitly solve 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 an absence of induced magnetic monopoles.
Nevertheless magnetic image charges can be made explicit in the problem and
even if no bound state with electric charges yielding a dyon arises, a
dyon-like angular momentum follows from our analysis. Because of its dependence
on the dielectric constant this angular momentum is not quantized, which is
consistent with a general argument that precludes magnetic monopoles to be
generated in Maxwell magnetoelectrics. We also solve for topologically
protected zero modes in the Dirac equation induced by the point charge. Since
the induced topological defect on the TI surface carries an electric charge as
a result of the axion term, these zero modes are not self-conjugated.