On the matter of topological insulators as magnetoelectrics

TL;DR

This paper clarifies the conditions under which topological insulators can be considered bulk magnetoelectrics with a quantized response, addressing real-world factors like disorder and symmetry that affect their observable properties.

Contribution

It provides a detailed analysis of the practical scenarios and limitations for observing the magnetoelectric effects in topological insulators, bridging theory and experiment.

Findings

Conditions for quantized magnetoelectric response in real materials

Impact of inversion symmetry and dissipation on topological insulators

Role of finite frequency measurements in detecting effects

Abstract

It has been proposed that topological insulators can be best characterized not as surface conductors, but as bulk magnetoelectrics that -- under the right conditions-- have a universal quantized magnetoelectric response coefficient $e^2/2h$. However, it is not clear to what extent these conditions are achievable in real materials that can have disorder, finite chemical potential, residual dissipation, and even inversion symmetry. This has led to some confusion and misconceptions. The primary goal of this work is to illustrate exactly under what real life scenarios and in what context topological insulators can be described as magnetoelectrics. We explore analogies of the 3D magnetoelectric response to electric polarization in 1D in detail, the formal vs. effective polarization and magnetoelectric susceptibility, the 1/2 quantized surface quantum Hall effect, the multivalued nature of the magnetoelectric susceptibility, the role of inversion symmetry, the effects of dissipation, and the necessity for finite frequency measurements. We present these issues from the perspective of experimentalists who have struggled to take the beautiful theoretical ideas and to try to measure their (sometimes subtle) physical consequences in messy real material systems.