Transport in helical Luttinger liquid with Kondo impurities

We study the edge transport in two-dimensional topological insulators which is carried by interacting helical fermions. This transport is ballistic when it is protected by time-reversal symmetry. Recently it was pointed out (Altshuler B. L. et al., Phys. Rev. Lett., 111 (2013) 086401) that coupling of non-interacting helical electrons to an array of randomly anisotropic magnetic (Kondo) impurities can lead to a spontaneous breaking of the symmetry and, thus, can remove this protection. By using a combination of the functional and the Abelian bosonization approaches, we show that the suppression of the ballistic transport turns out to be robust in a broad range of the interaction strength. We have evaluated the renormalization of the localization length and have found that, for strong interaction, it is substantial. We have identified various regimes of the dc transport and discussed its temperature and sample size dependences in each of the regimes.