Backscattering between helical edge states via dynamic nuclear polarization

We show that the nonequilibrium spin polarization of one-dimensional helical edge states at the boundary of a two-dimensional topological insulator can dynamically induce a polarization of nuclei via the hyperfine interaction. When combined with a spatially inhomogeneous Rashba coupling, the steady-state polarization of the nuclei produces backscattering between the topologically protected edge states leading to a reduction in the conductance which persists to zero temperature. We study these effects in both short and long edges, uncovering deviations from Ohmic transport at finite temperature and a current noise spectrum which may hold the fingerprints for experimental verification of the backscattering mechanism.