Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such as a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model, is unsolvable in any dimension we really care about.
To address this problem, I will start by pointing out that Fermi surfaces possess an overlooked emergent symmetry. Mott insulators break this emergent symmetry. The simplest model that breaks the emergent symmetry of a Fermi surface is the Hatsugai/Kohmoto constructed in 1992. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly that this model, when appended with a weak pairing interaction, exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity.
The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are 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. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.