Pair Susceptibilities and Gap Equations in Non-Fermi Liquids

The pair susceptibility and superconducting gap equation are obtained when a branch-cut spectrum, with either spin-charge separation or an anomalous Fermi surface exponent α>0 is introduced for the normal state. For k-nondiagonal pairing interactions, spin-charge separation leads to an enhancement of Tc and Δₖ(0) compared to a Fermi liquid. For α>0, a critical coupling is required for a solution. For spin-charge separation or 0<α<1/2, an arbitrarily small k-diagonal contribution to the pairing interaction still leads to a solution, as in a Fermi liquid.