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We investigate the phenomenon of fermionic pairing with mismatched Fermisurfaces in a two-species system in the presence of Feshbach resonance, wherethe resonantly-paired fermions combine to form bosonic molecules. We observethat the Feshbach parameters control the critical temperature of the gapped BCSsuperfluid state, and also determine the range over which a gapless breachedpair state may exist. Demanding the positivity of the superfluid density, it isshown that although a breached pair state with two Fermi surfaces is alwaysunstable, its single Fermi-surface counterpart can be stable if the chemicalpotentials of the two pairing species have opposite signs. This condition issatisfied only over a narrow region in the BEC side, characterized by an upperand a lower limit for the magnetic field. We estimate these limits for amixture of two hyperfine states of $^6$Li using recent experimental data.

Stability of the Breached Pair State for a Two-species Fermionic System in the Presence of Feshbach Resonance