Stability of Time-Reversal Symmetry Protected Topological Phases

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.

5+7 pages, 1+2 figures

References in corpus (5)

• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Nonlocal edge state transport in the quantum spin Hall state
• Observation of the Quantum Spin Hall Effect up to 100 Kelvin in a Monolayer Crystal
• Fragility of Time-Reversal Symmetry Protected Topological Phases
• Symmetry protected topological edge modes and emergent partial time reversal symmetry breaking in open quantum many-body systems

Cited by in corpus (9)

• Dissipative Topological Phase Transition with Strong System-Environment Coupling
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Non-Hermitian Absorption Spectroscopy
• Kramers' degeneracy for open systems in thermal equilibrium
• Symmetry protected topological edge modes and emergent partial time reversal symmetry breaking in open quantum many-body systems
• Elastic backscattering of quantum spin Hall edge modes from Coulomb interactions with non-magnetic impurities
• Violation and Revival of Kramers' Degeneracy in Open Quantum Systems
• Dissipative Symmetry-Protected Topological Order
• Fate of symmetry protected coherence in open quantum system