Electron Correlation Effects in Non-Centrosymmetric Metals in the Weak Coupling Regime

The two-dimensional Rashba-Hubbard model is investigated in order to clarify the electron correlation effects in non-centrosymmetric metals. The renormalization effect on Rashba spin-orbit coupling (RSOC) is calculated on the basis of second-order and third-order perturbation theories. We show that RSOC is enhanced by the electron correlation. On the other hand, the spin-splitting of the Fermi momentum (SFM) is robust against the electron correlation effect because the enhancement of RSOC is cancelled by the $k$-mass renormalization. The cancellation is almost perfect in often adopted models in which the momentum dependence of RSOC is linear in the quasiparticle velocity. A small correction to the SFM appears otherwise. We show that the same results are obtained for other antisymmetric spin-orbit couplings in non-centrosymmetric systems, such as the synthetic spin-orbit coupling in cold atoms.