Abstract

Migdal-Eliashberg theory (METh) of boson-mediated superconductivity contains a √λ divergence in the critical temperature Tc at strong electron-boson coupling λ. In conventional METh, the strong-coupling regime can be accessed only in the limit that λE=λ ωD/EF << 1, where ωD is the Debye frequency and EF is the Fermi energy. Here [1], 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≈0.18ωD√λ for large λ, provided λE remains small, and crosses over to a universal value of Tc≈0.04EF 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 METh saturates to a universal value (independent of λ and ωD), providing an upper bound on the critical temperature at strong electron-boson coupling.

[1] N. V. Gnezdilov and R. Boyack, arXiv:2505.02894 [cond-mat.str-el], (2025)