Effect of a Locally Repulsive Interaction on s-wave Superconductors

TL;DR

This paper rigorously analyzes how local Coulomb repulsion influences s-wave superconductors, revealing conditions under which repulsion can enhance superconductivity and coexist with ferromagnetism, and explaining the superconductor-Mott insulator transition.

Contribution

It provides a rigorous mathematical analysis of the effects of local Coulomb repulsion on s-wave superconductors, including phase transitions and coexistence phenomena.

Findings

Repulsion can increase critical temperature and condensate density.

Superconducting and ferromagnetic phases can coexist under certain conditions.

Doping is necessary for superconductor formation from insulators.

Abstract

The thermodynamic impact of the Coulomb repulsion on s-wave superconductors is analyzed via a rigorous study of equilibrium and ground states of the strong coupling BCS-Hubbard Hamiltonian. We show that the one-site electron repulsion can favor superconductivity at fixed chemical potential by increasing the critical temperature and/or the Cooper pair condensate density. If the one-site repulsion is not too large, a first or a second order superconducting phase transition can appear at low temperatures. The Mei\ss ner effect is shown to be rather generic but coexistence of superconducting and ferromagnetic phases is also shown to be feasible, for instance near half-filling and at strong repulsion. Our proof of a superconductor-Mott insulator phase transition implies a rigorous explanation of the necessity of doping insulators to create superconductors. These mathematical results are consequences of "quantum large deviation" arguments combined with an adaptation of the proof of St{\o}rmer's theorem to even states on the CAR algebra.