We investigate the superfluidity of attractive Fermi gas in a square optical lattice with spin-orbit coupling (SOC). We show that the system displays a variety of new filling-dependent features. At half filling, a quantum phase transition from a semi
metal to a superfluid is found for large SOC. Close to half filling where the emerging Dirac cones governs the behaviors of the system, SOC tends to suppress the BCS superfluidity. Conversely, SOC can significantly enhance both the pairing gap and condensate fraction and lead to a new BCS-BEC crossover for small fillings. Moreover, we demonstrate that the superfluid fraction also exhibits many interesting phenomena compared with the spin-orbit coupled Fermi gas without lattice.
