Cooper pairing of incoherent electrons: An electron-phonon version of the Sachdev-Ye-Kitaev model

Characterizing the interplay between non-Fermi-liquid physics and superconductivity is an important open problem in condensed matter physics. From a theoretical standpoint, the challenge stems from the difficulty in identifying controlled models where these phenomena can be simultaneously treated on equal footing. Here, the authors propose a new model of strongly interacting electrons and phonons, in close analogy with the well-known Sachdev-Ye-Kitaev model, and, via exact solution, explore how superconductivity can emerge from quantum critical and highly incoherent non-Fermi-liquid normal states. Many of the results are in qualitative agreement with observations made in iron-based, heavy-fermion, and cuprate superconductors.