Absence of induced magnetic monopoles in Maxwellian magnetoelectrics

TL;DR

This paper demonstrates that Maxwellian magnetoelectrics do not support magnetic monopoles, despite vortex-like magnetic fields, and explores related electromagnetic phenomena and topological zero modes.

Contribution

The study explicitly solves electromagnetic fields in magnetoelectric geometries, showing the absence of magnetic monopoles and analyzing the properties of induced topological zero modes.

Findings

Magnetic monopoles are not induced in Maxwellian magnetoelectrics.

Vortex-like magnetic screening fields have zero divergence, indicating no monopoles.

Topologically protected zero modes are induced but are not self-conjugated.

Abstract

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.