Quantum spin Hall effect induced by non-magnetic and magnetic staggered potentials

TL;DR

This paper compares how non-magnetic and magnetic staggered potentials induce quantum spin Hall effects, revealing that both can drive topological phase transitions and that the resulting edge states are robust under certain conditions.

Contribution

It demonstrates that both time-reversal preserving and breaking systems can host QSH effects through staggered potentials, highlighting their similar roles in topological phase transitions.

Findings

Both non-magnetic and magnetic potentials induce QSH effects.

Edge states are robust in ${ m T}$ invariant systems.

Edge states remain robust with additional symmetry in ${ m T}$ breaking systems.

Abstract

We have a comparative study of the quantum spin Hall (QSH) effects induced by non-magnetic and magnetic staggered potentials respectively and show that they have the same effect in driving the topological phase transition. The result implies that both time-reversal (${\cal T}$) preserving and breaking systems can host QSH effect. We also investigate the stability of the resulting QSH effect to disorder and find that for ${\cal T}$ invariant system the edge states are always robust while those of ${\cal T}$ breaking system are also robust if there is additional symmetry in the system.