Green's function approach to Chern-Simons extended electrodynamics: an effective theory describing topological insulators

TL;DR

This paper develops a Green's function method to analyze boundary effects in Chern-Simons extended electrodynamics, providing a versatile approach to study electromagnetic phenomena in topological insulators with various geometries.

Contribution

It introduces a general Green's function construction for Chern-Simons modified electrodynamics with arbitrary boundary geometries, enabling solutions for complex source configurations in topological insulators.

Findings

Successfully applied to planar $ heta$-boundary for static fields

Calculated force between point charge and boundary using two methods

Analyzed electromagnetic effects of a current-carrying wire near the boundary

Abstract

Boundary effects produced by a Chern-Simons (CS) extension to electrodynamics are analyzed exploiting the Green's function (GF) method. We consider the electromagnetic field coupled to a $\theta$-term in a way that has been proposed to provide the correct low energy effective action for topological insulators (TI). We take the $\theta$-term to be piecewise constant in different regions of space separated by a common interface $\Sigma$, to be called the $\theta$-boundary. Features arising due to the presence of the boundary, such as magnetoelectric effects, are already known in CS extended electrodynamics and solutions for some experimental setups have been found with specific configuration of sources. In this work we illustrate a method to construct the GF that allows to solve the CS modified field equations for a given $\theta$-boundary with otherwise arbitrary configuration of sources. The method is illustrated by solving the case of a planar $\theta$-boundary but can also be applied for cylindrical and spherical geometries for which the $\theta$-boundary can be characterized by a surface where a given coordinate remains constant. The static fields of a point-like charge interacting with a planar TI, as described by a planar discontinuity in $\theta$, are calculated and successfully compared with previously reported results. We also compute the force between the charge and the $\theta$-boundary by two different methods, using the energy momentum tensor approach and the interaction energy calculated via the GF. The infinitely straight current-carrying wire is also analyzed.