Self-tuned criticality and non-Fermi liquid pairing in a Yukawa-SYK model

We present a Sachdev-Ye-Kitaev-like model describing random Yukawa interactions between localized fermions and dynamical bosons in quantum dots. We show that by varying the fermion density the system undergoes a transition between a gapped insulating phase and a quantum-critical non-Fermi liquid phase. The non-Fermi liquid phase displays exotic pairing behavior — depending on parameters, the system either develops superconductivity or persists as a non-Fermi liquid down to zero temperature, despite the strong attractive interaction mediated by the critical boson. We supplement our analytical large-$N$ results with quantum Monte Carlo simulations, showing excellent agreement.