Finite temperature effective field theory and two-band superfluidity in Fermi gases

TL;DR

This paper develops an effective field theory for fermionic superfluids that extends beyond the critical temperature, accurately describing two-band superfluidity, vortex structures, and collective excitations with less computational effort than traditional methods.

Contribution

It introduces a non-perturbative effective field theory for superfluid Fermi gases, including two-band systems, capturing finite-temperature effects and collective modes.

Findings

Effective field theory matches Bogoliubov-de Gennes results.

Identifies two healing lengths in two-band superfluids.

Provides insight into the Leggett mode in superconductors.

Abstract

We develop a description of fermionic superfluids in terms of an effective field theory for the pairing order parameter. Our effective field theory improves on the existing Ginzburg - Landau theory for superfluid Fermi gases in that it is not restricted to temperatures close to the critical temperature. This is achieved by taking into account long-range fluctuations to all orders. The results of the present effective field theory compare well with the results obtained in the framework of the Bogoliubov - de Gennes method. The advantage of an effective field theory over Bogoliubov - de Gennes calculations is that much less computation time is required. In the second part of the paper, we extend the effective field theory to the case of a two-band superfluid. The present theory allows us to reveal the presence of two healing lengths in the two-band superfluids, to analyze the finite-temperature vortex structure in the BEC-BCS crossover, and to obtain the ground state parameters and spectra of collective excitations. For the Leggett mode our treatment provides an interpretation of the observation of this mode in two-band superconductors.