title: Orbital ac spin-Hall effect in the hopping regime.
abstract: The Rashba and Dresselhaus spin-orbit interactions are both shown to yield the low temperature spin-Hall effect for strongly localized electrons coupled to phonons. A frequency-dependent electric field E(omega) generates a spin-polarization current, normal to E, due to interference of hopping paths. At zero temperature the corresponding spin-Hall conductivity is real and is proportional to omega2. At nonzero temperatures the coupling to the phonons yields an imaginary term proportional to omega. The interference also yields persistent spin currents at thermal equilibrium, at E=0. The contributions from the Dresselhaus and Rashba interactions to the interference oppose each other.
authors.affiliation: Department of Physics, Ben Gurion University, Beer Sheva 84105, Israel.
authors.forename: O
authors.initials: O
authors.lastname: Entin-Wohlman
authors.forename: A
authors.initials: A
authors.lastname: Aharony
authors.forename: Y M
authors.initials: YM
authors.lastname: Galperin
authors.forename: V I
authors.initials: VI
authors.lastname: Kozub
authors.forename: V
authors.initials: V
authors.lastname: Vinokur