Persistence of spin edge currents in disordered quantum spin Hall systems

TL;DR

This paper proves that spin edge currents in disordered quantum spin Hall systems persist under certain conditions, even without time-reversal symmetry, highlighting their topological protection.

Contribution

It demonstrates the persistence of spin edge currents in disordered systems with broken spin invariance, extending topological protection concepts beyond time-reversal symmetry.

Findings

Spin edge currents persist with spectral gap and non-trivial spin Chern numbers.

Protection of edge currents does not require time-reversal symmetry.

Results apply to models like Kane-Mele with disorder and Rashba coupling.

Abstract

For a disordered two-dimensional model of a topological insulator (such as a Kane-Mele model with disordered potential) with small coupling of spin invariance breaking term (such as the Rashba coupling), it is proved that the spin edge currents persist provided there is a spectral gap and the spin Chern numbers are well-defined and non-trivial. These conditions on being in the quantum spin Hall phase do not require time-reversal symmetry. The result materializes the general philosophy that topological insulators are non-trivial bulk systems with edge currents that are topologically protected against Anderson localization.