# On the matter of topological insulators as magnetoelectrics

### Submission summary

 Authors (as Contributors): N. Peter Armitage
Submission information
Date accepted: 2019-02-05
Date submitted: 2019-01-25 01:00
Submitted by: Armitage, N. Peter
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Experiment
• Condensed Matter Physics - Theory
Approaches: Experimental, Theoretical

### 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.

Published as SciPost Phys. 6, 046 (2019)

Dear Editor,

We have replied to all the comments and critiques of the referees and hope that you and they will now find the manuscript suitable for SciPost.

-Peter Armitage

### List of changes

- In this revised version we have added some additional discussion on the significance of the effect we found. Moreover near the end of the manuscript we have added some text on how the isolated 1⁄2 quantized response can be measured directly.

- We have added text explaining what experiments we believe still need to be done.

- We now say so explicitly that no experiment has measured an isolated single surface.

- We have changed Im to Re for Eq. 11

- We cite additional papers that the referee has pointed out on the fact that one cannot create Wannier functions that are localized and strictly respect the symmetry?

- We have added discussion on the important paper of Pesin and MacDonald.

- We have also now added a table at the end of the manuscript that makes a comparison between 1D polarization and the 3D ME effect.