Equilibrium spin current induced by spin-orbital interaction in a quantum dot system

We report a theoretical study of the equilibrium spin current flowing in a quantum dot system. Two electrodes are the two-dimensional electron gas with Rashba or Dresselhaus spin-orbital interaction. By using the Keldysh Green's function technique, we demonstrated that a nonzero spin current can flow in the system without bias. At the weak coupling between electrodes and the quantum dot, the spin current is approximately proportional to the cross product of two average pseudo-magnetizations in two electrodes, which agrees with the result of the linear response theory; whereas at the opposite case, the strong coupling between the quantum dot and electrodes can lead to a non-sinusoidal behavior of the equilibrium spin current. These behaviors of the equilibrium spin current are similar to the Josephson current.