Magnetoelectric effect of a conducting sphere near a planar topological insulator

TL;DR

This paper investigates the magnetic field generated by a conducting sphere near a topological insulator surface, demonstrating measurable magnetoelectric effects that could be detected with current magnetometry technology.

Contribution

It extends the theoretical understanding of magnetoelectric effects from point charges to finite-sized conducting spheres near topological insulators, using bispherical coordinates.

Findings

Magnetic field strength estimated between 10-100 mG.

Fields can be interpreted as point electric and image magnetic charges.

Potential for experimental detection with existing magnetometers.

Abstract

When time-reversal symmetry is broken on its surface, topological insulators exhibit a magnetoelectric response which is described by axion electrodynamics. A direct consequence of this theory is the appearance of a magnetic field that resembles the one produced by a magnetic image monopole when a point-like electric charge is located near the surface of the material. In this paper we investigate the more realistic problem when the point-like charge is replaced by a finite size sphere at constant potential. We calculate the electromagnetic fields using the potential formulation in a particular bispherical coordinate system. We find that the electromagnetic fields can be interpreted in terms of point electric and image magnetic charges as if the medium were the vacuum. As a manifestation of the magnetoelectric effect, we highlight the resulting magnetic field, which we analyze in detail along the symmetry axis, since such estimates could be useful in evaluating the experimental possibility of its measurement via sensible magnetometers. Our numerical estimates show that the proposed setup provides a magnetic field strength in the range of 10-100 mG, which is attainable with present day sensitivities in NV center-diamond magnetometers, for example.