  Because the cuprate superconductors are doped Mott insulators, it would be
advantageous to solve even a toy model that exhibits both Mottness and
superconductivity. We consider the Hatsugai-Kohmoto model, an exactly solvable
system that is a prototypical Mott insulator above a critical interaction
strength at half filling. Upon doping or reducing the interaction strength, our
exact calculations show that the system becomes a non-Fermi liquid metal with a
superconducting instability. In the presence of a weak pairing interaction, the
instability produces a thermal transition to a superconducting phase, which is
distinct from the BCS state, as evidenced by a gap-to-transition temperature
ratio exceeding the universal BCS limit. The elementary excitations of this
superconductor are not Bogoliubov quasiparticles but rather superpositions of
doublons and holons, composite excitations signaling that the superconducting
ground state of the doped Mott insulator inherits the non-Fermi liquid
character of the normal state. An unexpected feature of this model is that it
exhibits a superconductivity-induced transfer of spectral weight from high to
low energies as seen in the cuprates as well as a suppression of the superfluid
density relative to that in BCS theory.
