Stability of a topological insulator: interactions, disorder and parity of Kramers doublets

TL;DR

This paper investigates the stability of multiple edge states in topological insulators, showing that interactions and disorder can localize or gap out these states depending on their number and system parameters.

Contribution

It provides a comprehensive analysis of how interactions, disorder, and parity affect the stability of multiple Kramers doublets at the edges of topological insulators.

Findings

For N=1 or 2, the system can be a trivial or topological insulator depending on interactions.

For N>2, all edge states become localized due to disorder, regardless of parity.

Relevant perturbations can open gaps or localize edge states, affecting topological protection.

Abstract

We study stability of multiple conducting edge states in a topological insulator against all multi-particle perturbations allowed by the time-reversal symmetry. We model a system as a multi-channel Luttinger liquid, where the number of channels equals the number of Kramers doublets at the edge. We show that in the clean system with N Kramers doublets there always exist relevant perturbations (either of superconducting or charge density wave character) which always open (N-1) gaps. In the charge density wave regime, (N-1) edge states get localised. The single remaining gapless mode describes sliding of 'Wigner crystal' like structure. Disorder introduces multi-particle backscattering processes. While the single-particle backscattering turns out to be irrelevant, the two-particle process may localise this gapless, in translation invariant system, mode. Our main result is that an interacting system with N Kramers doublets at the edge may be either a trivial insulator or a topological insulator for N=1 or 2, depending on density-density repulsion parameters whereas any higher number N>2 of doublets gets fully localised by the disorder pinning irrespective of the parity issue.