Classical electromagnetic model of surface states in topological insulators

Akhlesh Lakhtakia,Tom G Mackay

doi:10.1117/1.jnp.10.033004

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.

Highlights

The discovery of topological insulators[1] has prompted researchers in classical optics[2,3,4] to examine electromagnetic scattering due to bound objects made of these materials, exemplified by chalcogenides such as Bi2Se3, Bi2Te3, and Sb2Te3
The surface of the topological insulator is assumed to be charge free and current free, and the scattering problem can be solved by following textbook techniques.[5]
According to condensed-matter theory, surface states exist on topological insulators as protected conducting states,[2] and the characteristic electromagnetic responses of these materials are due to those surface states

Summary

Introduction

The discovery of topological insulators[1] has prompted researchers in classical optics[2,3,4] to examine electromagnetic scattering due to bound objects made of these materials, exemplified by chalcogenides such as Bi2Se3, Bi2Te3, and Sb2Te3. As a topological insulator is considered to be an isotropic material, its frequency-domain constitutive relations are formulated to contain a magnetoelectric pseudoscalar (denoted by Ψ here) in addition to the permittivity scalar ε and the permeability scalar μ. I. the bulk constitutive parameter Ψ with the surface of the topological insulator being charge free and current free, or II. Lakhtakia and Mackay: Classical electromagnetic model of surface states in topological insulators. This communication is devoted to a comparison of models I and II, through the fundamental boundary-value problem of reflection and refraction of a plane wave.

Fundamental Boundary-Value Problem

Discussion and Conclusion