Abstract The paradigmatic Migdal–Eliashberg theory of the electron–phonon problem is central to the understanding of superconductivity in conventional metals. This powerful framework is justified by the smallness of the Debye frequency relative to the Fermi energy, and allows an enormous simplification of the full many-body problem. However, superconductivity is found also in many families of strongly-correlated materials, in which there is no a priori justification for the applicability of Eliashberg theory. In these systems, superconductivity emerges out of an anomalous metallic state, calling for a new theoretical framework to describe pairing out of a non-Fermi liquid. In this article, we review two model systems in which such behavior is found: a Fermi sea coupled to gapless bosonic fluctuations, and a system of fermions with local, strongly frustrated interactions. In both models, there is a well-defined limit in which the Eliashberg equations are asymptotically exact even in the strongly coupled regime. These models thus provide tractable examples of how superconductivity can emerge in the absence of coherent electronic quasiparticles; they also demonstrate the surprisingly wide applicability of the Eliashberg formalism, well beyond the conventional regime for which it was originally designed.

中文翻译：

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Eliashberg 理论对非费米液体配对的不合理有效性

摘要 电子-声子问题的范式 Migdal-Eliashberg 理论是理解常规金属超导性的核心。这个强大的框架是由德拜频率相对于费米能量的小来证明的，并且可以极大地简化完整的多体问题。然而，在许多强相关材料家族中也发现了超导性，其中没有先验证明 Eliashberg 理论的适用性。在这些系统中，超导性从异常金属状态中出现，需要一个新的理论框架来描述非费米液体的配对。在本文中，我们回顾了发现这种行为的两个模型系统：耦合到无间隙玻色子涨落的费米海，以及具有局部、强烈沮丧的互动。在这两种模型中，都有一个明确定义的极限，即使在强耦合状态下，Eliashberg 方程也是渐近精确的。因此，这些模型提供了在没有相干电子准粒子的情况下如何出现超导性的易于处理的例子。它们还证明了 Eliashberg 形式主义惊人的广泛适用性，远远超出了它最初设计的传统制度。