Abstract
We study the pairing of fermions by an interaction consisting of a Hubbard repulsion, mimicking a screened Coulomb potential, and a dynamical phonon-mediated attraction. For such interaction, the gap equation allows even- and odd-frequency solutions Δe and Δo. We show that odd-frequency pairing does not develop within the Eliashberg approximation due to over-critical pair breaking from the self-energy. When vertex corrections are included, the pairing interaction gets stronger, and Δo can develop. We argue that even in this case keeping the self-energy is still a must as it cancels out the thermal piece in the gap equation. We further argue that Δo is not affected by Hubbard repulsion and for strong repulsion is comparable to a reduced Δe. The resulting superconducting state is a superposition Δe±iΔo, which spontaneously breaks the time-reversal symmetry, despite that the pairing symmetry is an ordinary s wave.
| Original language | English (US) |
|---|---|
| Article number | 104515 |
| Journal | Physical Review B |
| Volume | 106 |
| Issue number | 10 |
| DOIs | |
| State | Published - Sep 1 2022 |
Bibliographical note
Funding Information:We thank Shang-Shun Zhang, Prachi Sharma, and Zhentao Wang for useful discussions. The work by A.V.C. was supported by the NSF DMR-1834856. A.V.C. acknowledges the hospitality of KITP at UCSB, where part of the work has been conducted. The research at KITP is supported by the National Science Foundation under Grant No. NSF PHY-1748958.
Publisher Copyright:
© 2022 American Physical Society.