Competition of superfluid phases in low-dimensional spin-$\frac{1}{2}$ fermions with $s$- and $p$-wave interactions

The ground state of spin-$\frac{1}{2}$ fermions with contact $s$-wave inter- and $p$-wave intra-species interactions is discussed. Particularly, we formulate the mean field scheme for calculating thermodynamic properties of the system in arbitrary dimension $D<2$ and discuss in detail the phase diagram in 1D case. Except clean phases with either singlet or triplet Cooper pairings, we have identified two mixed phases (one stable and another metastable) of the one-dimensional two-component fermions where both pairing mechanisms coexist.