Superfluidity of a dipolar Fermi gas in 2D optical lattices bilayer

Ultracold Fermi molecules lying in 2D square optical lattices bilayers with its dipole moment perpendicularly aligned to the layers, having interlayer finite range s-wave interactions, are shown to form superfluid phases, both, in the Bardeen, Cooper and Schrieffer (BCS) regime of Cooper pairs, and in the condensate regime of bound dimeric molecules. We demonstrate this result using a functional integral scheme within the Ginzburg-Landau theory. For the deep Berezinskii-Kosterlitz-Thouless (BKT) phase transition, we predict critical temperatures around 5nK and 20nK for (NaK)-Na-23-K-40 and OH molecules, which are within reach of current experiments [J. W. Park, S. Will and M. Zwierlein, Phys. Rev. Lett. 114, 205302 (2015)].