Signatures of Fermion Pairing with Unconventional Symmetry around BCS-BEC Crossover in a Quasi-2D Lattice

We consider fermions on a 2D square lattice with a finite-range pairing interaction, and obtain signatures for unconventional pair-symmetry states, $d_{x^2-y^2}$ and extended-s ($s^{\ast }$), in the BCS-BEC crossover region. We find that the fermion momentum distribution function, $v_k^2$, the ratio of the Bogoliubov coefficients, $v_k\mathrm{/}{u}_k$, and the Fourier transform of $v_k^2$ are strikingly different for $d$- and $s^{\ast }$ symmetries in the crossover region. The chemical potential and the gaps functions for both pairing symmetries show several interesting features as a function of interaction. Fermionic atoms in 2D optical lattices may provide a way to test these signatures. We discuss current generation cold atom experiments that may be utilized.