Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology

TL;DR

This paper analyzes the stability of the quantum spin Hall effect in 2D systems, showing how interactions, disorder, and topological properties influence the robustness of edge states and phase transitions.

Contribution

It provides a detailed many-body analysis of the stability conditions for QSHE, highlighting the role of Kramers pairs, interactions, and disorder in topological insulators.

Findings

Single Kramers pair QSHE is stable to weak interactions and disorder.

Two Kramers pairs can be destabilized but stabilized by interactions.

Changing screening length can induce a phase transition between QSHE and insulator.

Abstract

The stability to interactions and disorder of the quantum spin Hall effect (QSHE) proposed for time-reversal-invariant 2D systems is discussed. The QSHE requires an energy gap in the bulk and gapless edge modes that conduct spin-up and spin-down excitations in opposite directions. When the number of Kramers pairs of edge modes is odd, certain one-particle scattering processes are forbidden due to a topological $\mathbb{Z}_2$ index. We show that in a many-body description, there are other scattering processes that can localize the edge modes and destroy the QSHE: the region of stability for both classes of models (even or odd number of Kramers pairs) is obtained explicitly in the chiral boson theory. For a single Kramers pair the QSHE is stable to weak interactions and disorder, while for two Kramers pairs it is not; however, the two-pair case can be stabilized by {\it either} finite attractive or repulsive interactions. For the simplest case of a single pair of edge modes, it is shown that changing the screening length in an edge with screened Coulomb interactions can be used to drive a phase transition between the QSHE state and the ordinary insulator.