The magnetoelectric coupling in Electrodynamics

TL;DR

This paper investigates a model of electrodynamics with a piecewise constant axion-like parameter, revealing novel magnetoelectric effects and boundary phenomena in topological materials, especially topological insulators, through Green's function methods.

Contribution

It introduces a Green's function approach to analyze boundary-value problems in $ heta$-media, highlighting the topological $ heta$-vacuum and its effects on electromagnetic responses and the Casimir effect.

Findings

Identification of boundary conditions for $ heta$-media

Demonstration of magnetoelectric effects in topological insulators

Application of Green's functions to Casimir effect modifications

Abstract

We explore a model akin to axion electrodynamics in which the axion field $\theta (t,\mathbf{x})$ rather than being dynamical is a piecewise constant effective parameter $\theta$ encoding the microscopic properties of the medium inasmuch as its permittivity or permeability, defining what we call a $\theta$-medium. This model describes a large class of phenomena, among which we highlight the electromagnetic response of materials with topological order, like topological insulators for example. We pursue a Green's function formulation of what amounts to typical boundary-value problems of $\theta$-media, when external sources or boundary conditions are given. As an illustration of our methods, which we have also extended to ponderable media, we interpret the constant $\theta$ as a novel topological property of vacuum, a so called $\theta$-vacuum, and restrict our discussion to the cases where the permittivity and the permeability of the media is one. In this way we concentrate upon the effects of the additional $\theta$ coupling which induce remarkable magnetoelectric effects. The issue of boundary conditions for electromagnetic radiation is crucial for the occurrence of the Casimir effect, therefore we apply the methods described above as an alternative way to approach the modifications to the Casimir effect by the inclusion of topological insulators.