Classical electromagnetic model of surface states in topological insulators

Abstract

A topological insulator is classically modeled as an isotropic dielectric-magnetic with a magnetoelectric pseudoscalar $\Psi$ existing in its bulk while its surface is charge-free and current-free. An alternative model is obtained by setting $\Psi\equiv0$ and incorporating surface charge and current densities characterized by an admittance $\gamma$. Analysis of plane-wave reflection and refraction due to a topological-insulator half space reveals that the parameters $\Psi$ and $\gamma$ arise identically in the reflection and transmission coefficients, implying that the two classical models cannot be distinguished on the basis of any scattering scenario. However, as $\Psi$ disappears from the Maxwell equations applicable to any region occupied by the topological insulator, and because surface states exist on topological insulators as protected conducting states, the alternative model must be chosen.