Anisotropic topological magnetoelectric effect in axion insulators

TL;DR

This paper investigates the finite-size effects on the topological magnetoelectric effect in axion insulators, revealing anisotropic coefficients that converge to quantized values as film thickness increases, with measurable optical signatures.

Contribution

It demonstrates the anisotropic nature of the magnetoelectric coefficients in finite-sized axion insulators and links their thickness dependence to observable optical phenomena.

Findings

Magnetoelectric coefficients become anisotropic in finite films.

Coefficients approach quantized values as thickness increases.

Thickness-dependent optical rotation serves as a signature of axion insulators.

Abstract

Three-dimensional topological insulators or axion insulators exhibit the topological magnetoelectric effect, which is isotropic with a universal coefficient of proportionality quantized in units of $e^2/2h$. Here we study the finite-size effect of topological magnetoelectric effect, and find the magnetoelectric coefficients are anisotropic, namely $\alpha_{xx}\neq\alpha_{zz}$. Both of them are shown to converge to a quantized value when the thickness of topological insulator film $d$ increases reaching the three-dimensional bulk limit. The nonzero value of $(\alpha_{xx}-\alpha_{zz})\propto1/d$ could be measured by using the gyrotropic or nonreciprocal birefringence of terahertz light. The unique $1/d$ dependence on film thickness of the rotation angle of optical principle axes is the manifestation of topological magnetoelectric effect, which may also serve as a smoking gun signature for axion insulators.