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.

中文翻译：

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Sachdev-Ye-Kitaev 模型的电子-声子版本的 Eliashberg 方程：非费米液体超导体中的对断裂

由于超导体中的顺磁性杂质，我们提出了一个理论，它是 Abrikosov-Gor'kov 对断裂理论的非费米液体对应物。为此，我们分析了一个相互作用的电子和声子模型，它是 Sachdev-Ye-Kitaev 模型的自然概括。在大量自由度的限制下，超导的 Eliashberg 方程变得精确，并作为具有波动配对场的场论的鞍点方程出现。在正常状态下，该模型由两个非费米液体不动点控制，其特征在于不同的通用指数。在低温下，超导状态从临界正常状态出现。我们研究破对在 $T_{c}$ 上的作用，我们允许破坏时间反转对称性的无序。对于小的 Bogoliubov 准粒子权重，对于具有强非相干正常状态的系统，$T_{c}$ 作为对断裂强度的函数迅速下降，并在通过本质奇点以临界对断裂强度消失之前达到一个很小但有限的值。后者标志着非费米液体常态的紧急共形对称性的破坏。