Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence*

One of the major obstacles in understanding unconventional superconductivity is the lack of a controlled theoretical framework to treat the competing effects of non-Fermi liquids and superconductivity born out of strong electronic correlations. As a solvable example of  superconductors in the strong coupling limit, we study the pairing instabilities of the Yukawa-Sachdev-Ye-Kitaev (Yukawa-SYK) model, where spinful fermions are coupled to bosons by random all-to-all Yukawa-type interactions. In contrast to the previously studied models, the random Yukawa couplings are sampled from a collection of Gaussian ensembles whose variances follow a continuous distribution rather than a fixed constant. The continuous distribution of the variances offers a new tool that can be used to control the fermion incoherence or the "non-Fermi liquidness". This allows a systematic investigation of different normal states ranging from the Fermi liquid to non-Fermi liquids. With this novel control knob for the fermion incoherence, we demonstrate how non-Fermi liquids may  show stronger tendency to form Cooper pairs in such Yukawa-SYK models.