Stabilization of Quantum Spin Hall Effect by Designed Removal of Time-Reversal Symmetry of Edge States

TL;DR

This paper proposes a method to stabilize the quantum spin Hall effect by spatially separating edge states using a narrow ferromagnetic region, making the effect robust against time-reversal symmetry-breaking perturbations.

Contribution

Introducing a designed ferromagnetic region near the edge to spatially separate edge states, enhancing the robustness of the quantum spin Hall effect against symmetry-breaking perturbations.

Findings

Edge states are spatially separated into different regions.

Quantum spin Hall effect becomes more robust.

Edge states retain their spin and propagation characteristics.

Abstract

The quantum spin Hall (QSH) effect is known to be unstable to perturbations violating time-reversal symmetry. We show that creating a narrow ferromagnetic (FM) region near the edge of a QSH sample can push one of the counterpropagating edge states to the inner boundary of the FM region, and leave the other at the outer boundary, without changing their spin polarizations and propagation directions. Since the two edge states are spatially separated into different "lanes", the QSH effect becomes robust against symmetry-breaking perturbations.