Bulk versus surface: Nonuniversal partitioning of the topological magnetoelectric effect

TL;DR

This paper investigates how the topological magnetoelectric effect in 3D insulators is distributed between surface and interior in different symmetry cases, revealing nonuniversal partitioning in antiferromagnetic topological insulators.

Contribution

It provides explicit calculations showing nonuniversal surface and interior partitioning of the magnetoelectric response in $ ext{Z}_2$ topological insulator thin films with antiferromagnetic symmetry, extending understanding of topological responses.

Findings

Magnetoelectric response is localized at the surface in nonmagnetic cases.

In antiferromagnetic cases, the response is partitioned nonuniversally between surface and interior.

The magnetic field induced polarization relates to an anomalous Landau level subspace modeled by a generalized Su-Schrieffer-Heeger model.

Abstract

The electronic ground state of a three-dimensional (3D) band insulator with time-reversal ($\Theta$) symmetry or time-reversal times a discrete translation ($\Theta T_{1/2}$) symmetry is classified by a $\mathbb{Z}_{2}$-valued topological invariant and characterized by quantized magnetoelectric response. Here we demonstrate by explicit calculation in model $\mathbb{Z}_{2}$ topological insulator thin-films that whereas the magnetoelectric response is localized at the surface in the $\Theta$ symmetry (nonmagnetic) case, it is nonuniversally partitioned between surface and interior contributions in the $\Theta T_{1/2}$ (antiferromagnetic) case, while remaining quantized. Within our model the magnetic field induced polarization arises entirely from an anomalous $\mathscr{N}=0$ Landau level subspace within which the projected Hamiltonian is a generalized Su-Schrieffer-Heeger model whose topological properties are consistent with those of the starting 3D model. We identify a new connection between the ground-state geometry of that 3D model and surface-interior partitioning in thin films.