Theory predicts for the two-dimensional electrons gas with only Rashba
spin-orbit interaction a vanishing spin Hall conductivity and at the same time
a finite inverse spin Hall effect. We show how these seemingly contradictory
results are compatible with the Onsager relations: the latter do hold for spin
and particle (charge) currents in the two-dimensional electron gas, although
(i) their form depends on the experimental setup and (ii) a vanishing bulk spin
Hall conductivity does not necessarily imply a vanishing spin Hall effect. We
also discuss the situation in which extrinsic spin orbit from impurities is
present and the bulk spin Hall conductivity can be different from zero.Comment: Accepted versio
