Helical edge states coupled to a spin bath: Current-induced magnetization

We study current carrying helical edge states in a two-dimensional topological insulator coupled to an environment of localized spins, i.e., a spin bath. The localized spins mediate elastic spin-flip scattering between the helical edge states, and we show how this induces a spin-bath magnetization for a finite current through the edge states. The magnetization appears near the boundaries of the topological insulator, while the bulk remains unmagnetized, and it reaches its maximal value in the high bias regime. Furthermore, the helical edge states remain ballistic in steady state, if no additional spin-flip mechanisms for the localized spins are present. However, we demonstrate that if such mechanisms are allowed, then these will induce a finite current decrease from the ballistic value.