Symmetry Analysis of Odd- and Even-Frequency Superconducting Gaps for Time-Reversal Symmetric Interactions*

We present a general formalism for the classification of superconducting states of matter incorporating time-reversal symmetry. The analysis is based on a group theoretical classification of the Bethe-Salpeter equation. Our approach extends previous ground-laying work [2] by including both even- and odd-frequency superconducting states [1].
Since the combination of spin interchange, parity and time-reversal has to be odd for a pair of electrons, the possible odd-frequency gaps are either both, even under spin and even under parity or odd under spin and odd under parity. Furthermore, our investigation reveals that odd-frequency solutions do not require a time-reversal breaking potential, but can arise naturally for a time-reversal symmetric interaction as symmetry breaking ground states of the system. As such, the phenomenon of odd-frequency superconductivity is similar to other symmetry breaking transitions.

[1] R. M. Geilhufe & A. V. Balatsky, arXiv preprint: arXiv:1709.07650, (2017).
[2] M. Sigrist & K. Ueda, Reviews of Modern physics, 63(2), 239, (1991).