# Induced interactions in the BCS-BEC crossover of two-dimensional Fermi gases with Rashba spin-orbit coupling

## TL;DR

This paper studies how induced interactions affect the superfluid transition temperature in two-dimensional Fermi gases with Rashba spin-orbit coupling across the BCS-BEC crossover, revealing complex interplay between screening effects.

## Contribution

It introduces a detailed analysis of the Gorkov--Melik-Barkhudarov correction considering SOC-induced mixing, highlighting its impact on transition temperature estimates across different SOC regimes.

## Key findings

- GM correction lowers transition temperature estimates
- Crossover behavior in correction effect with increasing SOC
- Agreement with quantum Monte Carlo results for condensate fraction

## Abstract

We investigate the Gorkov--Melik-Barkhudarov (GM) correction to superfluid transition temperature in two-dimensional Fermi gases with Rashba spin-orbit coupling (SOC) across the SOC-driven BCS-BEC crossover. In the calculation of the induced interaction, we find that the spin-component mixing due to SOC can induce both of the conventional screening and additional antiscreening contributions that interplay significantly in the strong SOC regime. While the GM correction generally lowers the estimate of transition temperature, it turns out that at a fixed weak interaction, the correction effect exhibits a crossover behavior where the ratio between the estimates without and with the correction first decreases with SOC and then becomes insensitive to SOC when it goes into the strong SOC regime. We demonstrate the applicability of the GM correction by comparing the zero-temperature condensate fraction with the recent quantum Monte Carlo results.