Anisotropic topological magnetoelectric effect in axion insulators
Zhaochen Liu, Jing Wang
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 ${\ensuremath{\alpha}}_{xx}\ensuremath{\ne}{\ensuremath{\alpha}}_{zz}$. 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 $({\ensuremath{\alpha}}_{xx}\ensuremath{-}{\ensuremath{\alpha}}_{zz})\ensuremath{\propto}1/d$ 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.