Onsager relations in a two-dimensional electron gas with spin-orbit coupling.
Theory predicts for the two-dimensional electron gas with only a 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.
Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504, CNRS and Université de Strasbourg, 23 rue du Loess, BP 43, F-67034 Strasbourg Cedex 2, France.
C
C
Gorini
R
R
Raimondi
P
P
Schwab