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Vortex arrays in type-II superconductors admit the translational symmetry ofan infinite system. There are cases, however, like ultra-cold trapped Fermigases and the crust of neutron stars, where finite-size effects make it quitemore complex to account for the geometrical arrangement of vortices. Here, weself-consistently generate these arrays of vortices at zero and finitetemperature through a microscopic description of the non-homogeneous superfluidbased on a differential equation for the local order parameter, obtained bycoarse graining the Bogoliubov-de Gennes (BdG) equations. In this way, thestrength of the inter-particle interaction is varied along the BCS-BECcrossover, from largely overlapping Cooper pairs in the BCS limit to dilutecomposite bosons in the BEC limit. Detailed comparison with two landmarkexperiments on ultra-cold Fermi gases, aimed at revealing the presence of thesuperfluid phase, brings out several features that makes them relevant forother systems in nature as well.

Vortex arrays in neutral trapped Fermi gases throughout the BCS-BEC crossover