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We study superfluid properties of fermions on a 2D lattice using afinite-range pairing interaction derivable from an extended Hubbard model. Weobtain signatures of unconventional pair-symmetry states, $d_{x^2-y^2}$ andextended-s ($s^*$), in the BCS-BEC crossover region. The fermion momentumdistribution function, $v_k^2$, the ratio of the Bogoliubov coefficients,$v_k/u_k$, and the Fourier transform of $v_k^2$ are among the properties thatare strikingly different for d- and $s^*$ symmetries in the crossover region.Fermionic atoms in 2D optical lattices may provide a way to observe thesesignatures. We discuss possible experimental ramifications of our results.

Pairing with Unconventional Symmetry around BCS-BEC Crossover: Fermionic Atoms in 2D Optical Lattices to Correlated Electron Systems