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The functional renormalization group (RG) in combination with Fermi surfacepatching is a well-established method for studying Fermi liquid instabilitiesof correlated electron systems. In this article, we further develop this methodand combine it with mean-field theory to approach multiband systems withspin-orbit coupling, and we apply this to a tight-binding Rashba model with anattractive, local interaction. The spin dependence of the interaction vertex isfully implemented in a RG flow without SU(2) symmetry, and its momentumdependence is approximated in a refined projection scheme. In particular, wediscuss the necessity of including in the RG flow contributions from both bandsof the model, even if they are not intersected by the Fermi level. As theleading instability of the Rashba model, we find a superconducting phase with asinglet-type interaction between electrons with opposite momenta. While the gapfunction has a singlet spin structure, the order parameter indicates anunconventional superconducting phase, with the ratio between singlet andtriplet amplitudes being plus or minus one on the Fermi lines of the upper orlower band, respectively. We expect our combined functional RG and mean-fieldapproach to be useful for an unbiased theoretical description of thelow-temperature properties of spin-based materials.

physical review. b./physical review. b

Functional renormalization and mean-field approach to multiband systems  with spin-orbit coupling: Application to the Rashba model with attractive  interaction