Extension of the Ginzburg - Landau approach for ultracold Fermi gases below a critical temperature

TL;DR

This paper extends the Ginzburg-Landau formalism for superfluid Fermi gases across all temperatures, analyzing corrections below the critical temperature and applying it to vortex structures in the BEC-BCS crossover.

Contribution

It introduces a temperature-dependent correction to the Ginzburg-Landau theory applicable below the critical temperature and models vortices in a two-band Fermi gas system.

Findings

Deviations from standard GL are significant for kinetic energy contributions.

Healing lengths show hidden criticality below T_c.

Formalism successfully describes vortices in strong-coupling regimes.

Abstract

In the context of superfluid Fermi gases, the Ginzburg - Landau (GL) formalism for the macroscopic wave function has been successfully extended to the whole temperature range where the superfluid state exists. After reviewing the formalism, we first investigate the temperature-dependent correction to the standard GL expansion (which is valid close to $T_{c}$). Deviations from the standard GL formalism are particularly important for the kinetic energy contribution to the GL energy functional, which in turn influences the healing length of the macroscopic wave function. We apply the formalism to variationally describe vortices in a strong-coupling Fermi gas in the BEC-BCS crossover regime, in a two-band system. The healing lengths, derived as variational parameters in the vortex wave function, are shown to exhibit hidden criticality well below $T_{c}$.