  The spin-resolved non-equilibrium real-time electron transport through a double-quantum-dot (DQD) Aharonov-Bohm (AB) interferometer with spin-orbit interaction (SOI) is explored. The SOI and AB interference in the real-time dynamics of spin transport is expressed by effective magnetic fluxes. Analytical formulae for the time-dependent currents, for initially unpolarized spins, are presented. In many cases, there appear spin currents in the electrodes, for which the spins in each electrode are polarized along characteristic directions, pre-determined by the SOI parameters and by the geometry of the system. Special choices of the system parameters yield steady-state currents in which the spins are fully polarized along these characteristic directions. The time required to reach this steady state depends on the couplings of the DQD to the leads. The magnitudes of the currents depend strongly on the SOI-induced effective fluxes. Without the magnetic flux, the spin-polarized current cannot be sustained to the steady states, due to the phase rigidity for this system. For a non-degenerate DQD, transient spin transport can be produced by the sole effects of SOI. We also show that one can extract the spin-resolved currents from measurements of the total charge current. 
Real-time dynamics of spin-dependent transport through a   double-quantum-dot Aharonov-Bohm interferometer with spin-orbit interaction