Pairing of spinless fermions in two dimensions

We study the real-space pairing instability of spinless fermions on a two-dimensional square lattice with short-range attractive interactions. Various symmetries of the pairing order parameter are considered. It is found that in both nonflux and flux phases the most stable pairing state is chiral and anisotropic. It breaks both the parity and the time-reversal symmetries. The quasiparticle excitation has a minimum gap which could be much smaller than its average over the Fermi surface. The temperature dependence of the order parameter and the critical magnetic field are found to be similar to those of the classical BCS solutions. A possible connection with the high-temperature superconductivity is discussed