Eliashberg equations for an electron-phonon version of the Sachdev-Ye-Kitaev model: Pair Breaking in non-Fermi liquid superconductors

TL;DR

This paper develops a non-Fermi-liquid theory of superconductivity based on an electron-phonon model generalizing the Sachdev-Ye-Kitaev model, analyzing pair-breaking effects and their impact on critical temperature and symmetry.

Contribution

It introduces an Eliashberg framework for a non-Fermi-liquid superconductor derived from a SYK-like model, revealing new fixed points and pair-breaking phenomena.

Findings

Superconducting transition temperature drops rapidly with pair-breaking strength.

Critical normal state exhibits two distinct non-Fermi-liquid fixed points.

Superconductivity vanishes at a critical pair-breaking strength with an essential singularity.

Abstract

We present a theory that is a non-Fermi-liquid counterpart of the Abrikosov-Gor'kov pair-breaking theory due to paramagnetic impurities in superconductors. To this end we analyze a model of interacting electrons and phonons that is a natural generalization of the Sachdev-Ye-Kitaev-model. In the limit of large numbers of degrees of freedom, the Eliashberg equations of superconductivity become exact and emerge as saddle-point equations of a field theory with fluctuating pairing fields. In its normal state the model is governed by two non-Fermi liquid fixed points, characterized by distinct universal exponents. At low temperatures a superconducting state emerges from the critical normal state. We study the role of pair-breaking on $T_{c}$, where we allow for disorder that breaks time-reversal symmetry. For small Bogoliubov quasi-particle weight, relevant for systems with strongly incoherent normal state, $T_{c}$ drops rapidly as function of the pair breaking strength and reaches a small but finite value before it vanishes at a critical pair-breaking strength via an essential singularity. The latter signals a breakdown of the emergent conformal symmetry of the non-Fermi liquid normal state.