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Exotic p-wave superfluidity of single hyperfine state Fermi gases in optical lattices

We consider p-wave (triplet) pairing of single hyperfine state ultracold atomic gases trapped in quasi-two-dimensional optical lattices. We find that the critical temperatures in the lattice model is considerably higher and experimentally attainable around half-filling in contrast to the predictions of continuum model for p-wave superfluids. In tetragonal lattices, we show that the atomic compressibility and spin susceptibility have a peak at low temperatures exactly at the half-filling, but this peak splits into two in the orthorhombic lattices. These peaks reflect the p-wave structure of the order parameter for superfluidity and they disappear as the critical temperature is approached from below. We also calculate the superfluid density tensor, and show that for the orthorhombic case there is no off-diagonal component, however in the tetragonal case an off-diagonal component develops, and becomes a key signature of the exotic p-wave state.