In-plane noncollinear exchange coupling mediated by helical edge states in quantum spin Hall systems

We study the Ruderman-Kittel-Kasuya-Yoshida interaction mediated by helical edge states in quantum spin Hall system. The helical edge states induce an in-plane noncollinear exchange coupling between two local spins, in contrast to the isotropic coupling induced in normal metal. The angle between the two local spins in the ground state depends on the Fermi level. This property may be used to control the angle of spins by tuning the electric gate.