Gorkov-Melik-Barkhudarov correction to superfluid transition temperature of Rashba spin-orbit coupled Fermi gases in two dimensions

Abstract

We investigate the influence of the medium-induced interaction to the superfluid transition temperature of attractively interacting two-dimensional Fermi gases with Rashba spin-orbit coupling. The effective interaction is calculated to incorporate screening and anti-screening contributions induced from the medium, up to the second order of interaction strength within the Gorkov--Melik-Barkhudarov diagrammatic approach. We find that the SOC-dependence of the induced interaction effects shows distinctive behavior across the weak and strong SOC regimes in accordance with the undergoing Lifshitz-type transition of the Fermi surface topology. In computation of the induced interaction correction to the mean-field transition temperature and the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, we find that the correction factor generally decreases as the SOC strength increases, and in particular for the BKT transitions temperature, the correction effect diminishes in the limit of strong SOC strength.