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A model with both Rashba and Dresselhaus spin orbit (SO) couplings andHubbard electron-electron interaction is studied on planar strips at quarterfilling at zero temperature in the clean limit. In the absence of Hubbardrepulsion and at equilibrium, within linear response theory, a nonmonotonicbehavior of the spin Hall conductivity as a function of the ratio of the Rashba(alpha) and Dresselhaus (beta) strengths was found for large enough SOstrengths. This behavior is signalled by a peak or a cusp, depending on thestrip width, at intermediate values of beta/alpha in the interval [0,1]. Thisbehavior of the spin Hall conductivity was correlated with the one for thelongitudinal spin conductivity. This study was then extended to theout-of-equilibrium regime that arises by imposing a finite voltage bias betweenthe two ends of an open strip. This system, in the presence of a Hubbard termwith coupling U, was treated with the density matrix renormalization grouptechnique and with the Landauer-Buttiker formalism. It was found that relevantproperties to the spin Hall effect, such as the transversal spin current andthe spin accumulation, present a similar nonmonotonic behavior as the one foundfor the spin conductivities. More importantly, it was also found that theseproperties are enhanced by the repulsive Hubbard interaction up to a moderatevalue of U.

Spin Hall effect in Rashba-Dresselhaus planar strips in the presence of electron correlations