Coherent spin ratchets: A spin-orbit based quantum ratchet mechanism for   spin-polarized currents in ballistic conductors
  We demonstrate that the combined effect of a spatially periodic potential, lateral confinement and spin-orbit interaction gives rise to a quantum ratchet mechanism for spin-polarized currents in two-dimensional coherent conductors. Upon adiabatic ac-driving, in the absence of a static bias, the system generates a directed spin current while the total charge current is zero. We analyze the underlying mechanism by employing symmetry properties of the scattering matrix and numerically verify the effect for different setups of ballistic conductors. The spin current direction can be changed upon tuning the Fermi energy or the strength of the Rashba spin-orbit coupling. 
Matthias Scheid, Andreas Pfund, Dario Bercioux, and Klaus Richter