Topological spin pumps:  The effect of spin rotation on quantum pumps

We have established semiclassical kinetic equations for various spin-correlated pumping phenomena incorporating adiabatic spin rotation in wave functions. We employ this technique to study topological pumps and illustrate spin pumping in a few models where various spin configurations or topological motors drive adiabatic pumps. In the Rashba model we find that a topological spin pump is driven by a meron with positive one-half Skyrmion charge, the size of which can be controlled by external applied gates or Zeeman fields. In the Dresselhaus model on the other hand, electron spins are pumped out by a negative meron. We examine the effects of Zeeman fields on topological spin pumping and responses of Fermi seas in various topological pumps. The phenomena of topological pumping are attributed to the beam splitting of electrons in the presence of spin rotation, or topological Stern-Gerlach splitting, and occur in a transverse direction along which charge-pumping currents might either vanish or are negligible. The transport equations established here might also be applied to the studies of anomalous Hall effect and spin-Hall effect as demonstrated in one of the appendixes. All results are obtained in an adiabatic expansion.