In this chapter, we present the details of the derivation of an effective field theory (EFT) for a Fermi gas of neutral dilute atoms and apply it to study the structure of both vortices and solitons in superfluid Fermi gases throughout the BEC-BCS crossover. One of the merits of the effective field theory is that, for both applications, it can provide some form of analytical results. For one-dimensional solitons, the entire structure can be determined analytically, allowing for an easy analysis of soliton properties and dynamics across the BEC-BCS interaction domain. For vortices on the other hand, a variational model has to be proposed. The variational parameter can be determined analytically using the EFT, allowing to also study the vortex structure (variationally) throughout the BEC-BCS crossover.
Part of the book: Superfluids and Superconductors