## Abstract

We review recent theoretical progress in understanding spatially uniform s-wave superconductivity which arises from a fermion–fermion interaction, which is repulsive on the Matsubara axis, where it is real, but does depend on the transferred frequency. Such a situation holds, e.g., for systems with a screened Coulomb and retarded electron–phonon interaction. We show that despite repulsion, superconductivity is possible in a certain range of system parameters. However, at T=0 the gap function on the Matsubara axis, Δ(ω_{m}), must pass through zero and change sign at least once. These zeros of Δ(ω_{m}) have a topological interpretation in terms of dynamical vortices, and their presence imposes a constraint on the variation of the phase of the gap function along the real frequency axis, which can potentially be extracted from ARPES and other measurements. We discuss how superconductivity vanishes when the repulsion becomes too strong, and obtain a critical line which terminates at T=0 at a quantum-critical point for superconductivity. We show that the behavior of the gap function near this point is highly non-trivial. In particular, an infinitesimally small Δ(ω_{m}) contains a singular δ-function piece ω_{m}δ(ω_{m}). We argue that near the critical point superconductivity may be a mixed state with even-frequency and odd-frequency gap components.

Original language | English (US) |
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Article number | 169049 |

Journal | Annals of Physics |

Volume | 447 |

DOIs | |

State | Published - Dec 2022 |

### Bibliographical note

Funding Information:We thank A. Balatsky, I. Esterlis, S. Kivelson, E. Langmann, J. Schmalian, and S.-S. Zhang for useful discussions and suggestions. The work by A.V.C was supported by the NSFDMR-1834856, United States. 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, United States under Grant No. NSF PHY-1748958.

Funding Information:

We thank A. Balatsky, I. Esterlis, S. Kivelson, E. Langmann, J. Schmalian, and S.-S. Zhang for useful discussions and suggestions. The work by A.V.C was supported by the NSF DMR-1834856 , United States. 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, United States under Grant No. NSF PHY-1748958 .

Publisher Copyright:

© 2022 Elsevier Inc.

## Keywords

- Dynamical superconductivity
- Dynamical vortices
- Repulsive interactions
- Vortex-unbinding transition