Solvable strong-coupling models for pairing and charge-4e superconductivity in non-Fermi liquids

We present Sachdev-Ye-Kitaev-like models that captures the interplay between fermionic incoherence and strong attractive interaction in the pairing instability of non-Fermi liquids. The first class of models feature random all-to-all interactions among fermions and bosons. We show that this model exhibits ``self-tuned quantum criticality" for a range of fermion filling independent on the bare boson mass. Unlike BCS instability, the pairing phase of electrons occur at T=0 only for some range of parameters, which is separated by the non-Fermi liquid phase via an infinite-order Kosterliz-Thouless critical point. In the second class of models, we consider a solvable Sachdev-Ye-Kitaev-like model for charge-4e superconductivity. We determine spectral properties, the superfluid density, and the pairing instability of a charge-4e superconductor, which applies even in the strong-coupling regime.