Spin-transfer torque and electric current in helical edge states in quantum spin Hall devices

We study the dynamics of a quantum spin Hall edge coupled to a magnet with its own dynamics. Using spin-transfer-torque principles, we analyze the interplay between spin currents in the edge state and dynamics of the axis of the magnet, and draw parallels with circuit analogies. As a highlighting feature, we show that while coupling to a magnet typically renders the edge state insulating by opening a gap, in the presence of a small potential bias, spin-transfer torque can restore perfect conductance by transferring angular momentum to the magnet. In the presence of interactions within the edge state, we employ a Luttinger liquid treatment to show that the edge, when subject to a small voltage bias, tends to form a unique dynamic rotating spin wave state that naturally couples into the dynamics of the magnet. We briefly discuss realistic physical parameters and constraints for observing this interplay between quantum spin Hall and spin-transfer torque physics.