Singlet and triplet Bardeen-Cooper-Schrieffer pairs in a gas of two-species fermionic polar molecules

Taking into account the deformation of the Fermi surface, we investigate the spin-singlet and -triplet BCS pairings in a mixture of fermionic polar molecules with two different hyperfine states. In particular, we explore the relation between the critical temperatures and the Fock-exchange interaction. We also show that, by tuning short-range interaction between interspecies molecules, the singlet- and triplet-paired superfluids may coexist.