Anisotropic Ginzburg-Landau and Lawrence-Doniach models for layered ultracold Fermi gases

We derive and study the anisotropic Ginzburg-Landau and Lawrence-Doniach models describing a layered superfluid ultracold Fermi gas in optical lattices. We compute from the microscopic model the Josephson couplings entering the Lawrence-Doniach model across the crossover BCS-BEC passing from the 3D isotropic case to the quasi-2D one, showing that a model with only nearest-neighbor Josephson couplings is not adequate at the unitary limit (since the pairs have a diameter larger than the interlayer distance). We also show that the effective anisotropy of the system is strongly reduced at the unitary limit. Finally, we obtain a relation between the interlayer Josephson couplings and the Ginzburg-Landau masses: we find that using only couplings between adjacent planes is correct in the BEC side, while at the unitary limit one has to use also next-nearest-neighboring couplings. Copyright (C) EPLA, 2012