Coulomb drag and spin drag in the presence of spin-orbit coupling

Employing diagrammatic perturbation theory, we calculate the (charge) Coulomb drag resistivity rho(D) and spin Coulomb drag resistivity rho(up arrow down arrow) in the presence of Rashba spin-orbit coupling. Analytical expressions for rho(D) and rho(up arrow down arrow) are derived, and it is found that spin-orbit interaction produces a small enhancement to rho(D) and rho(up arrow down arrow) for weakly disordered systems (Boltzmann regime) while rho(D) 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.