Exact Superconducting Instability in a Doped Mott Insulator

TL;DR

This paper presents an exact solution to a model of doped Mott insulators showing a superconducting instability with unique properties, providing insights into non-Fermi liquid behavior and spectral weight transfer in high-temperature superconductors.

Contribution

It introduces an exactly solvable model demonstrating superconductivity in a doped Mott insulator with non-BCS features and unconventional excitations.

Findings

Superconducting instability occurs upon doping or reducing interaction strength.

The superconductor exhibits a gap-to-transition temperature ratio exceeding BCS limit.

Spectral weight shifts from high to low energies during superconductivity.

Abstract

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.