Spin transistor action from Onsager reciprocity and SU(2) gauge theory
  We construct a local gauge transformation to show how, in confined systems, a generic, weak nonhomogeneous SU(2) spin-orbit Hamiltonian reduces to two U(1) Hamiltonians for spinless fermions at opposite magnetic fields, to leading order in the spin-orbit strength. Using an Onsager relation, we further show how the resulting spin conductance vanishes in a two-terminal setup, and how it is turned on by either weakly breaking time-reversal symmetry or opening additional transport terminals. We numerically check our theory for mesoscopic cavities as well as Aharonov-Bohm rings. 
I. Adagideli, V. Lutsker, M. Scheid, Ph. Jacquod and K. Richter
cond-mat.mes-hall