Pairing and superconductivity in the flat band: Creutz lattice

We use unbiased numerical methods to study the onset of pair superfluidity in a system that displays flat bands in the noninteracting regime. This is achieved by using a known example of flat band systems, namely, the Creutz lattice, where we investigate the role of local attractive interactions in the U < 0 Hubbard model. Going beyond the standard approach used in these systems where weak interactions are considered, we map the superfluid behavior for a wide range of interaction strengths and exhibit a crossover between BCS and tightly bound bosonic fermion pairs. We further contrast these results with a standard two-leg fermionic ladder, showing that the pair correlations, although displaying algebraic decay in both cases, are longer ranged in the Creutz lattice, signifying the robustness of pairing in this system.