Bound states and controllable currents on topological insulator surfaces with extended magnetic defects

We show that a magnetic line defect on the surface of a topological insulator generically supports two distinct branches of spin-polarized and current carrying one-dimensional bound states. We identify the components of magnetic scattering that lead to the bound states. The velocity, and hence spin texture, of each of those branches can be independently tuned by a magnetic field rotated in the plane of the surface. We compute the local net and spin-resolved density of states as well as spin accumulation and charge currents. The net spin polarization and current due to both bound and scattering states vary stepwise as a function of the electrostatic and magnetic components of the scattering potential, and can be tuned by an applied field. We discuss stability of the bound states with respect to impurity scattering.