Protection of Edge transport in Quantum Spin Hall samples: Spin-Symmetry Based General Approach and Examples

TL;DR

This paper analyzes mechanisms affecting helical edge transport in Quantum Spin Hall systems, proposing a spin conservation-based framework to identify conditions under which ballistic conductance remains protected despite various perturbations.

Contribution

It introduces a systematic spin conservation approach to evaluate the robustness of edge transport in QSH systems and applies it to specific models with magnetic impurities and spin-orbit interactions.

Findings

Ballistic conductance can be protected even with local time-reversal symmetry breaking if total spin is conserved.

Spin-orbit interactions can weaken edge protection under certain symmetry conditions.

Magnetic impurities with U(1) symmetry do not necessarily disrupt ballistic edge transport.

Abstract

Understanding possible mechanisms, which can lead to suppression of helical edge transport in Quantum Spin Hall (QSH) systems, attracted huge attention right after the first experiments revealing the fragility of the ballistic conductance. Despite the very intensive research and the abundance of theoretical models, the fully consistent explanation of the experimental results is still lacking. We systematize various theories of helical transport with the help of the spin conservation analysis which allows one to single out setups with the ballistic conductance being robustly protected regardless of the electron backscattering. First, we briefly review different theories of edge transport in the QSH samples with and without the spin axial symmetry of the electrons including those theoretical predictions which are not consistent with the spin conservation analysis and, thus, call for a deeper study. Next, we illustrate the general approach by a detailed study of representative examples. One of them addresses the helical edge coupled to an array of Heisenberg-interacting magnetic impurities (MIs) and demonstrates that the conductance remains ballistic even if the time-reversal symmetry on the edge is (locally) broken but the total spin is conserved. Another example focuses on the effects of the space-fluctuating spin-orbit interaction on the QSH edge. It reveals weakness of the protection in several cases, including, e.g., the presence of either the U(1)-symmetric, though not fully isotropic, MIs or generic electron-electron interactions.