Critical temperature in the BCS-BEC crossover with spin-orbit coupling

TL;DR

This paper reviews the superfluid transition in fermionic systems across the BCS-BEC crossover with spin-orbit coupling, emphasizing the importance of quantum fluctuations beyond mean-field theory to accurately determine the critical temperature.

Contribution

It provides a detailed derivation of equations for critical temperature considering spin-orbit couplings, highlighting the role of quantum fluctuations beyond mean-field approximations.

Findings

Two-body bound states exist for all interaction strengths with Rashba coupling.

Effective masses of bosonic excitations are finite across the entire crossover.

Quantum fluctuations are crucial for accurate $T_c$ predictions.

Abstract

We review the study of the superfluid phase transition in a system of fermions whose interaction can be tuned continuously along the crossover from Bardeen-Cooper-Schrieffer (BCS) superconducting phase to a Bose-Einstein condensate (BEC), also in the presence of a spin-orbit coupling. Below a critical temperature the system is characterized by an order parameter. Generally a mean field approximation cannot reproduce the correct behavior of the critical temperature $T_c$ over the whole crossover. We analyze the crucial role of quantum fluctuations beyond the mean-field approach useful to find $T_c$ along the crossover in the presence of a spin-orbit coupling, within a path integral approach. A formal and detailed derivation for the set of equations useful to derive $T_c$ is performed in the presence of Rashba, Dresselhaus and Zeeman couplings. In particular in the case of only Rashba coupling, for which the spin-orbit effects are more relevant, the two-body bound state exists for any value of the interaction, namely in the full crossover. As a result the effective masses of the emerging bosonic excitations are finite also in the BCS regime.