Kosterlitz-Thouless transition in disordered two-dimensional topological insulators

TL;DR

This paper investigates the disorder-driven metal-insulator transition in quantum spin Hall systems, revealing it as a Kosterlitz-Thouless type transition characterized by vortex-antivortex pair dynamics.

Contribution

It demonstrates that the metal-insulator transition in disordered 2D topological insulators is of KT type, independent of time-reversal symmetry, using scaling analysis of conductance.

Findings

Transition is of Kosterlitz-Thouless type

Conductance becomes size-independent below critical disorder

Vortex-antivortex pairing characterizes the transition

Abstract

The disorder-driven metal-insulator transition in the quantum spin Hall systems is studied by scaling analysis of the Thouless conductance $g$. Below a critical disorder strength, the conductance is independent of the sample size $M$, an indication of critically delocalized electron states. The calculated beta function $\beta=d\ln g/d\ln M$ indicates that the metal-insulator transition is Kosterlitz-Thouless (KT) type, which is characterized by bounding and unbounding of vortex-antivortex pairs of the local currents. The KT like metal-insulator transition is a basic characteristic of the quantum spin Hall state, being independent of the time-reversal symmetry.