Flat band effects on the ground-state BCS-BEC crossover in atomic Fermi gases in a quasi-two-dimensional Lieb lattice

The ground-state superfluid behavior of ultracold atomic Fermi gases with an on-site attractive interaction in a quasi-two-dimensional Lieb lattice is studied using BCS mean-field theory, within the context of BCS-BEC crossover. We find that the flat band leads to nontrivial exotic effects. As the Fermi level enters the flat band, both the gap and the in-plane superfluid density exhibit an unusual power law as a function of interaction strength, in addition to a dramatic increase of compressibility as the interaction approaches the BCS limit as well as strongly enhanced quantum geometric effect. As the Fermi level crosses the van Hove singularities, the character of pairing changes from particle-like to hole-like or vice versa. We present the computed phase diagram, in which a pair density wave state emerges at high densities away from half filling and relatively strong interaction strength.