Unusual effects of lattice-continuum mixing on pairing and superfluidity of atomic Fermi gases in a two-dimensional optical lattice

We study the superfluid behavior of ultracold atomic Fermi gases with a short-range attractive interaction throughout the BCS-BEC crossover in a two-dimensional (2D) optical lattice comprised of a 2D array of 1D lines. We find that the lattice-continuum mixing has an extraordinary effect on pairing phenomena and superfluidity of atomic Fermi gases, besides the wide spread pseudogap phenomena. The topology of the Fermi surface gradually becomes open as the lattice constant $d$ increases or the hopping integral $t$ decreases, leading to an effective number density above half filling in the lattice dimensions. For relatively small $t$ and large $d$, $T_c$ exhibits a remarkable re-entrant behavior in the regime of intermediate pairing strength, and a pair density wave emerges as the ground state where $T_c$ vanishes. In the BCS and unitary regimes, the nature of the in-plane and overall pairing changes from particlelike to holelike, associated with an abnormal increase in the Fermi volume with the pairing strength. These findings are very different from the cases of a pure 3D continuum and a pure 3D lattice.