Interactions for odd-omega gap singlet superconductors

TL;DR

This paper investigates the conditions under which odd-frequency, odd-momentum singlet superconductivity can occur, highlighting the role of electron interactions and magnetic correlations, especially in high-temperature superconductors.

Contribution

It clarifies the constraints on interaction strengths for odd-gap pairing and proposes that strong antiferromagnetic correlations can enable such pairing.

Findings

Positive scattering matrix elements constrain odd pairing.

General spin-dependent interactions can support odd-gap superconductivity.

Strong antiferromagnetic correlations may facilitate odd-gap pairing in high-$T_c$ materials.

Abstract

A class of singlet superconductors with a gap function $\Delta({\bf k}, \omega_n)$ which is {\it odd} in both momentum and Matsubara frequency was proposed recently \cite{ba}. To show an instability in the {\it 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 $p$- and $s$-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-$T_c$ material.