Nonadiabatic quantum spin pump: Interplay between spatial interference and photon-assisted tunneling in two-dimensional Rashba systems

We investigate the nonadiabatic transport property of parametric quantum spin pumps in the presence of Rashba spin-orbit (SO) interaction. It is well known that in the adiabatic regime, the pumped charge and spin currents are zero when all the pumping parameters are in phase. But the pumped charge and spin currents can be nonzero with nonadiabatic contribution and spatial interference. In such a case, we have analytically proved the following: (i) If the potential including the pumping potential has the symmetry V(x,y,t)=V(-x,y,t) or V(x,y,t)=V(-x,-y,t), where x is along the direction of pumped current, then the pumped charge current is zero but the pumped spin current may not be zero; (ii) if the potential including the pumping potential has the symmetry V(x,y,t)=V(x,-y,t), then the pumped spin currents with spin along the x and z directions are zero. Since the phases of pumping potential are very easy to control, this provides a robust way of generating pure spin current. Numerically, we have verified the analytic results and calculated the pumped charge and spin current in the nonadiabatic regime at finite pumping frequency and finite pumping amplitude as well as external bias. In general, both charge current and spin current are pumped out of the system in the presence of SO interaction. Since both pumped charge current and spin current depend sensitively on the system parameters, the pure spin current without accompanying charge current can be produced by controlling system parameters such as external bias, phase difference between two pumping amplitudes, and the pumping frequency. An interesting interplay between spatial interference and photon-assisted tunneling processes is observed.