The effect of nuclear spins on the spin transport at the surface of three-dimensional topological insulator

Topological surface states of a three-dimensional topological insulator offer a promising platform for spintronics applications due to perfect spin-momentum locking feature of its band structure. We investigate the effect of nuclear spins interacting with the electrons at the surface of a three-dimensional topological insulator. The interaction between surface electrons and nuclear spins that are naturally present at the surface has only been considered as a source of backscattering. In this paper, we find that the angular momentum of the electrons can be transferred to the nuclear spin subsystem, leading to dynamical nuclear spin polarization. We also show that the reverse process is also possible, namely a finite nuclear spin polarization can induce a spin current at the surface of a three-dimensional topological insulator. We demonstrate this by deriving the quantum kinetic equation using nonequilibrium Green's function formalism and obtain the diffusion equation for the electrons at the surface of a three-dimensional topological insulator. We show that in the diffusive limit, dynamical polarization of the nuclear spin subsystem is achievable and the degree of polarization depends on the ratio of mean free path and system size.