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Employing diagrammatic perturbation theory, we calculate the (charge) Coulomb drag resistivity ρD and spin Coulomb drag resistivity ρ_↑↓ in the presence of Rashba spin-orbit coupling. Analytical expressions for ρD and ρ_↑↓ are derived, and it is found that spin-orbit interaction produces a small enhancement to ρD and ρ_↑↓ for weakly disordered systems (Boltzmann regime) while ρD is unchanged for dirty systems (diffusive regime). This enhancement in the Boltzmann regime is attributed to the enhancement of the nonlinear susceptibility (i.e., current produced through the rectification of the thermal electric potential fluctuations in the passive layer) while the lack of enhancement in the diffusive regime is due to the suppression by disorder.
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Tse et al. (2007) studied this question.
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