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

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 $T_{c}$.