Upper bound on Tc in a strongly coupled electron-boson superconductor

Abstract

Migdal-Eliashberg theory of boson-mediated superconductivity contains a λ divergence in the critical temperature Tc for strong electron-boson coupling λ. In the conventional Migdal-Eliashberg theory, the strong-coupling regime can be accessed only in the limit that λE=λωD/ɛF≪1, where ωD is the Debye frequency and ɛF is the Fermi energy. Here we go beyond this restriction in the context of the two-dimensional Yukawa-SYK (Y-SYK) model, which is solvable for arbitrary values of λE. We find that Tc≈0.18ωDλ for large λ, provided λE remains small, and crosses over to a universal value of Tc≈0.04ɛF for large λE. The saturation of Tc is due to a self-consistent account of the boson dynamics for large λE and remains valid provided the vertex corrections are negligible. Depending on the value of λ, this self-consistent approach leads to pairing that describes multiple classes of quantum critical electronic systems. These results demonstrate how the λ growth of Tc in Migdal-Eliashberg theory saturates to a universal value independent of λ and ωD, providing an upper bound on the critical temperature at strong electron-boson coupling.

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