Stability of Time-Reversal Symmetry Protected Topological Phases

TL;DR

This paper investigates how coupling to an environment affects the stability of time-reversal symmetry protected topological phases, revealing that dissipation can break degeneracy and disrupt quantized conductance.

Contribution

It introduces a non-Hermitian Hamiltonian approach to analyze the stability of topological phases under environmental coupling respecting time-reversal symmetry.

Findings

Dissipation can split Kramers degeneracy in spectral functions.

Backscattering between edge states can be induced by dissipation.

Quantized conductance in quantum spin Hall effect can be compromised.

Abstract

In a closed system, it is well known that the time-reversal symmetry can lead to Kramers degeneracy and protect nontrivial topological states such as quantum spin Hall insulator. In this letter we address the issue whether these effects are stable against coupling to environment, provided that both environment and the coupling to environment also respect the time-reversal symmetry. By employing a non-Hermitian Hamiltonian with the Langevin noise term and ultilizing the non-Hermitian linear response theory, we show that the spectral functions for Kramers degenerate states can be split by dissipation, and the backscattering between counter-propagating edge states can be induced by dissipation. The latter leads to the absence of accurate quantization of conductance in the case of quantum spin Hall effect. As an example, we demonstrate this concretely with the Kane-Mele model. Our study could also be extended to interacting topological phases protected by the time-reversal symmetry.