Reliability of the Ginzburg-Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

TL;DR

This paper assesses the reliability of the Ginzburg-Landau theory, including Gaussian fluctuations, in describing the BCS-BEC crossover in 3D attractive fermions, highlighting its limitations near the BEC regime.

Contribution

It provides a detailed comparison of Ginzburg-Landau parameters with and without Gaussian fluctuations across the BCS-BEC crossover, revealing the theory's limitations near the BEC regime.

Findings

Gaussian fluctuations significantly alter Ginzburg-Landau parameters near BEC

Qualitative trends are captured by the theory across the crossover

Ginzburg-Landau theory becomes unreliable approaching the BEC regime

Abstract

We calculate the parameters of the Ginzburg-Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg-Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg-Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg-Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.