Interactions for odd-ω gap singlet superconductors

A class of singlet superconductors with a gap function ∆(k, ωn) which is odd in both momentum and Matsubara frequency was proposed recently [1]. To show an instability in the odd gap channel, a model phonon propagator was used with the p-wave interaction strength larger than the s-wave. We argue that the positive scattering matrix element entering the Eliashberg equations leads to a constraint on the relative strength of pand s-wave interactions which inhibits odd pairing. However, a general spin dependent electron-electron interaction can satisfy all constraints and produce the odd singlet gap. A possibility which may lead to an odd gap is a strongly antiferromagnetically correlated system, such as a high-Tc material.