A topological look at the quantum spin Hall state

TL;DR

This paper offers a topological perspective on the quantum spin Hall state, emphasizing that edge states are protected by band topology alone, independent of symmetries, and demonstrates their robustness through a Kane-Mele model analysis.

Contribution

It introduces a symmetry-independent topological framework for understanding quantum spin Hall states and confirms the existence of robust edge states via a modified Kane-Mele model.

Findings

Edge states exist without symmetry considerations.

Gapless edge states are protected by topology.

Edge states remain robust with impurities.

Abstract

We propose a topological understanding of the quantum spin Hall state without considering any symmetries, and it follows from the gauge invariance that either the energy gap or the spin spectrum gap needs to close on the system edges, the former scenario generally resulting in counterpropagating gapless edge states. Based upon the Kane-Mele model with a uniform exchange field and a sublattice staggered confining potential near the sample boundaries, we demonstrate the existence of such gapless edge states and their robust properties in the presence of impurities. These gapless edge states are protected by the band topology alone, rather than any symmetries.