Laboratoire de Physique Théorique
Toulouse - UMR 5152

The quantum spin Hall phase is a new phase of matter that is realized experimentally in HgTe/CdTe quantum wells and is one example of a 2D topological insulator. This phase is characterized by two counter-propagating edge states, crossing the bulk band gap. Contrary to the quantum hall phase, in a topological insulator time-reversal symmetry (TRS) is preserved, and the edge states arise without any applied magnetic field. Since in addition, there is a strong spin-orbit coupling in the material, the direction of motion at the edge is correlated with the direction of spin. Such effective 1D systems are called helical liquids. When interactions are included, they resemble a Tomonaga-Luttinger liquid with the additional constraint of topological protection against elastic, single particle, backscattering, imposed by time-reversal symmetry. Experimental measurements of the longitudinal conductance however show clear deviations from the quantized value of G_0 = 2 e^2/h, which call for a detailed investigation of scattering mechanisms in helical liquids. 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 seminar, I will explain, by using a renormalization group approach, how this process can be derived microscopically, in the presence of a time-reversal invariant Rashba impurity potential, that can stem from fluctuations of a transverse electric field. I will show 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/$, with K the Luttinger parameter.