Current response of a topological insulator to a static Zeeman field

TL;DR

This paper investigates the surface current response of a topological insulator to a static Zeeman field, demonstrating that the response is a bulk property unaffected by surface states or boundary conditions.

Contribution

It provides evidence through exact diagonalization that the surface current response remains unchanged despite surface state modifications, supporting the bulk nature of orbital magnetization.

Findings

Surface current is unaffected by surface state gapping.

Surface current response is independent of chemical potential within the bulk gap.

Orbital magnetization is confirmed as a bulk property.

Abstract

We study the magnetoelectric coupling at the surface of a topological insulator. We are in particular interested in the surface current induced by a static Zeeman/exchange field. This surface current can be related to the orbital magnetization of the system. For an insulator with zero Chern number, the orbital magnetization is independent of the details at the boundary. With the appearance of surface states in the topological insulator, it is not immediately obvious if the response is not affected by the conditions at the surface. We investigate this question using exact diagonalization to a lattice model. By applying a time-reversal symmetry-breaking term near the boundary, no matter if the surface states are gapped out, we still find no change in the surface current. This arises from cancelations between Pauli and Van-Vleck contributions between surface and bulk scattering states. We also show that the surface current response is independent of the chemical potential when it is within the bulk gap. Our results are consistent with the claim that orbital magnetization is a bulk property.