# Intrinsic superconducting instabilities of a solvable model for an incoherent metal

## TL;DR

This paper introduces solvable lattice models with large orbital numbers exhibiting unconventional superconducting instabilities originating from incoherent metals, independent of Fermi surface nesting.

## Contribution

It constructs a family of solvable models with SYK-like interactions showing novel superconducting phases from incoherent metals.

## Key findings

- Discovery of non-BCS superconductivity from incoherent non-Fermi liquids
- Superconductivity with transition temperatures comparable to bandwidth
- Pairing instabilities not reliant on Fermi surface nesting

## Abstract

We construct a family of translationally invariant lattice models with a large number ($N$) of orbitals at every site coupled together via single electron tunneling. By tuning the relative strength of the electronic bandwidth and on-site interactions, that have a modified Sachdev-Ye-Kitaev (SYK) form, we demonstrate a number of unusual features at strong coupling and in the large$-N$ limit. We find examples of (i) an intrinsic non-BCS superconducting instability arising out of an incoherent non-Fermi liquid metal, and, (ii) an instability of an incipient heavy Fermi liquid metal to superconductivity with transition temperatures comparable to its renormalized bandwidth. At strong-coupling, these solvable models display pairing instabilities that are not driven by any special "nesting" properties associated with an underlying Fermi surface.