BCS-BEC crossover in atomic Fermi gases in quasi-two-dimensional Lieb lattices: Effect of flat band at finite temperature*

The superfluid behavior of ultracold atomic Fermi gases with a short  range attractive interaction in quasi-two-dimensional Lieb lattices  is studied using a pairing fluctuation theory, within the context of  BCS-BEC crossover, with a focus on the interplay of finite  temperature and flat band.  As the Fermi level enters the flat band,  the evolution of $T_c$ as a function of interaction strength $g$  changes from the conventional exponential behavior to power law,  along with strongly enhanced quantum geometric effects. The  temperature dependence of both the superfluid order parameter and  the high superfluid density also undergoes a similar  change due to the influence of flat band. At relatively high  densities and moderate or strong pairing interaction, a pair density   wave emerges. In addition, hole-like pairing occurs when the Fermi   level crosses the van Hove singularity, leading to nonmonotonic dependence  of the chemical potential $mu(g)$ on $g$..