Renormalization group approach for the scattering off a single Rashba impurity in a helical liquid

The occurrence of two-particle inelastic backscattering has been conjectured in helical edge states of topological insulators and is expected to alter transport. In this Letter, by using a renormalization group approach, we provide a microscopic derivation of this process, in the presence of a time-reversal invariant Rashba impurity potential. Unlike previous approaches to the problem, we are able to prove that such an effect only occurs in the presence of electron-electron interactions. Furthermore, we find that the linear conductance as a function of temperature exhibits a crossover between two scaling behaviors: $T^{4K}$ for $K>1/2$ and $T^{8K-2}$ for $K<1/2$, with $K$ the Luttinger parameter.