Topologically Protected Extended States in Disordered Quantum Spin-Hall Systems without Time-Reversal Symmetry

TL;DR

This paper demonstrates the existence of robust bulk extended states in disordered quantum spin-Hall systems with broken time-reversal symmetry, linked to protected spin-Chern numbers, through numerical analysis of the Kane-Mele model.

Contribution

It reveals the persistence of topologically protected extended states in disordered systems without time-reversal symmetry, expanding understanding of topological phases.

Findings

Robust bulk extended states exist in disordered Kane-Mele models with Zeeman fields.

Spin-Chern numbers are protected by finite energy and spin mobility gaps.

Transitions in topological invariants are associated with the closing of mobility gaps.

Abstract

We demonstrate the existence of robust bulk extended states in the disordered Kane-Mele model with vertical and horizontal Zeeman fields, in the presence of a large Rashba coupling. The phase diagrams are mapped out by using level statistics analysis and computations of the localization length and spin-Chern numbers $C_\pm$. $C_\pm$ are protected by the finite energy and spin mobility gaps. The latter is shown to stay open for arbitrarily large vertical Zeeman fields, or for horizontal Zeeman fields below a critical strength or at moderate disorder. In such cases, a change of $C_\pm$ is necessarily accompanied by the closing of the mobility gap at the Fermi level. The numerical simulations reveal sharp changes in the quantized values of $C_\pm$ when crossing the regions of bulk extended states, indicating that the topological nature of the extended states is indeed linked to the spin-Chern numbers. For large horizontal Zeeman fields, the spin-gap closes at strong disorder prompting a change in the quantized spin-Chern numbers without a closing of the energy mobility gap.