Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid

TL;DR

This paper proves that charge transport along the edge states of a 2D topological insulator remains ballistic despite random Rashba spin-orbit coupling and disorder, due to an integrable dynamics that prevents backscattering.

Contribution

It provides an exact proof that random Rashba spin-orbit coupling does not cause backscattering in topological insulator edges, preserving ballistic transport.

Findings

Charge transport remains ballistic at all temperatures.

Random Rashba backscattering does not induce resistance.

The dynamics are integrable, preventing backscattering.

Abstract

The combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrability-breaking terms.