Robustness of Quantum Spin Hall Effect in an External Magnetic Field

TL;DR

This paper theoretically investigates the robustness of the quantum spin Hall effect under external magnetic fields, showing it can persist despite time reversal symmetry breaking, with implications for experimental observations.

Contribution

It provides a theoretical analysis of topological invariants in a magnetic field, revealing the quantum spin Hall effect's robustness beyond previous expectations.

Findings

Quantum spin Hall effect remains robust up to large magnetic fields.

The critical magnetic field depends mainly on the band gap at the Γ point.

The effect can persist even when time reversal symmetry is broken.

Abstract

The edge states in the quantum spin Hall effect are expected to be protected by time reversal symmetry. The experimental observation of the quantized conductance was reported in the InAs/GaSb quantum well {[}Du et al, arXiv:1306.1925{]}, up to a large magnetic field, which raises a question on the robustness of the edge states in the quantum spin Hall effect under time reversal symmetry breaking. Here we present a theoretical calculation on topological invariants for the Benevig-Hughes-Zhang model in an external magnetic field, and find that the quantum spin Hall effect retains robust up to a large magnetic field. The critical value of the magnetic field breaking the quantum spin Hall effect is dominantly determined by the band gap at the $\Gamma$ point instead of the indirect band gap between the conduction and valence bands. This illustrates that the quantum spin Hall effect could persist even under time reversal symmetry breaking.