Phonon induced backscattering in helical edge states

TL;DR

This paper demonstrates that the quantized conductivity of helical edge states in quantum spin Hall insulators remains protected against inelastic phonon-induced backscattering, even with Coulomb interactions included.

Contribution

It shows that inelastic phonon backscattering does not break the quantized conductance in helical edge states, extending the robustness beyond elastic scattering.

Findings

Quantized conductivity is protected against phonon-induced backscattering.

Protection persists even with Coulomb interactions in a helical Luttinger liquid.

Inelastic mechanisms do not compromise edge state conductance to leading order.

Abstract

A single pair of helical edge states as realized at the boundary of a quantum spin Hall insulator is known to be robust against elastic single particle backscattering as long as time reversal symmetry is preserved. However, there is no symmetry preventing inelastic backscattering as brought about by phonons in the presence of Rashba spin orbit coupling. In this letter, we show that the quantized conductivity of a single channel of helical Dirac electrons is protected even against this inelastic mechanism to leading order. We further demonstrate that this result remains valid even when Coulomb interaction is included in the framework of a helical Tomonaga Luttinger liquid.