Superconducting instability in an exactly solvable model of a doped Mott insulator

Regarding the cuprate superconductors as doped Mott insulators, we solve a toy model that exhibits both Mottness and superconductivity. We show that the Hatsugai-Kohmoto model, an exactly solvable model exhibiting a non-trivial Mott insulator-to-non-Fermi liquid metal transition, exhibits a superconducting instability. The instability is present in the non-Fermi liquid metal phase at half-filling, persists for a wide range of dopings away from half-filling, and terminates once the Mott parameter exceeds a critical strength.