Fundamental limits to helical edge conductivity due to spin-phonon scattering

TL;DR

This paper investigates how spin-phonon interactions caused by bulk acoustic phonons affect the electrical conductance of helical edge states in two-dimensional topological insulators, revealing fundamental temperature-dependent limits.

Contribution

It demonstrates that spin-phonon coupling induces inelastic backscattering, leading to diffusive transport and a temperature-dependent conductivity limit in helical edge channels.

Findings

Conductivity follows a metallic Bloch-Grüneisen law.

At the Debye temperature, conductivity drops significantly.

Low-temperature conductance correction scales as T^5.

Abstract

We study the effect of electron-phonon interactions on the electrical conductance of a helical edge state of a two-dimensional topological insulator. We show that the edge deformation caused by bulk acoustic phonons modifies the spin texture of the edge state, and that the resulting spin-phonon coupling leads to inelastic backscattering which makes the transport diffusive. Using a semiclassical Boltzmann equation we compute the electrical conductivity and show that it exhibits a metallic Bloch-Gr\"uneisen law. At temperatures on the order of the Debye temperature of the host material, spin-phonon scattering thus lowers the conductivity of the edge state drastically. Transport remains ballistic only for short enough edges, and in this case the correction to the quantized conductance vanishes as $\delta G \propto T^5$ at low temperatures. Relying only on parallel transport of the helical spin texture along the deformed edge, the coupling strength is determined by the host material's density and sound velocity. Our results impose fundamental limits for the finite-temperature conductivity of a helical edge channel.