[Paper Review] Absence of magnetic monopoles in Maxwellian magnetoelectrics

Flavio S. Nogueira, Jeroen van den Brink|arXiv (Cornell University)|Jul 13, 2018

Topological Materials and Phenomena6 citations

TL;DR

This paper investigates the electromagnetic response of topological insulators governed by axion electrodynamics, showing that despite the coupling between electric and magnetic fields, exact solutions reveal no magnetic monopoles—vortex-like screening fields have zero divergence everywhere, precluding monopole formation. Although dyon-like angular momentum arises, it is universally quantized via the dielectric constant, confirming the absence of magnetic monopoles in Maxwellian magnetoelectrics.

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 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.

Motivation & Objective

• To investigate whether magnetic monopoles can emerge in topological insulators governed by axion electrodynamics.
• To analyze the electromagnetic response of a charged particle near a magnetoelectric interface, particularly the nature of screening fields.
• To determine whether bound states (dyons) between electric charges and magnetic images can form in such systems.
• To assess whether angular momentum associated with the system exhibits monopole-like behavior and its quantization.
• To establish a general argument against the generation of magnetic monopoles in Maxwellian magnetoelectrics.

Proposed method

• Exact analytical solution of the electromagnetic fields in the presence of a point charge near a magnetoelectric interface.
• Application of axion electrodynamics with a topological magnetoelectric term in the Maxwell equations.
• Computation of the divergence of the magnetic field to verify monopole presence or absence.
• Explicit construction of magnetic image charges in the system to analyze their role in field configurations.
• Analysis of angular momentum arising from the electromagnetic field configuration, particularly its quantization.
• Use of the dielectric constant as a key parameter in determining the quantization of the dyon-like angular momentum.

Experimental results

Research questions

• RQ1 Can magnetic monopoles be generated in Maxwellian magnetoelectrics via a screened electric charge at a surface?
• RQ2 Do the magnetic fields induced by the electric charge exhibit non-zero divergence, indicating monopole sources?
• RQ3 Can a bound state between an electric charge and a magnetic image charge form, resembling a dyon?
• RQ4 Does the angular momentum in the system exhibit monopole-like characteristics, and is it quantized?
• RQ5 Is the absence of magnetic monopoles consistent with a general theoretical argument in axion electrodynamics?

Key findings

• The divergence of the magnetic field is identically zero at every point in space, proving the absence of magnetic monopoles despite the presence of vortex-like screening fields.
• Magnetic image charges can be explicitly defined, but they do not lead to a bound state with the electric charge, precluding dyon formation.
• A dyon-like angular momentum arises from the field configuration, but it is universally quantized due to its dependence on the dielectric constant.
• The quantization of angular momentum is independent of material-specific parameters and is instead determined solely by the dielectric constant.
• The results support a general theoretical argument that magnetic monopoles cannot be generated in Maxwellian magnetoelectrics.
• The exact solution confirms that the topological magnetoelectric effect does not lead to monopole-like phenomena in the classical electromagnetic sense.