Persistence of spin edge currents in disordered quantum spin Hall systems

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.

Final version to appear in Commun. Math. Phys

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• The $K$-theoretic bulk-edge correspondence for topological insulators
• A noncommutative framework for topological insulators
• ${\mathbb{Z}}_2$ invariants of topological insulators as geometric obstructions
• Spectral flows associated to flux tubes
• Wannier functions and Z_2 invariants in time-reversal symmetric topological insulators
• A new approach to transport coefficients in the quantum spin Hall effect
• Spin Conductance and Spin Conductivity in Topological Insulators: Analysis of Kubo-like terms
• Quantization of interface currents
• Approximate symmetries and conservation laws in topological insulators and associated $\mathbb{Z}$-invariants
• From charge to spin: analogies and differences in quantum transport coefficients
• Středa formula for charge and spin currents
• Topological insulators from the perspective of non-commutative geometry and index theory
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure