High temperature superconductivity induced by incipient magnetism

We consider the BCS gap equation, with an attractive interaction λ with an upper cutoff ω₀ and lower cutoff ω₁, and a repulsive interaction μ with cutoffΓ. We consider parameters such that a superconducting solution does not exist. We add a repulsive interaction ν eith cutoff ω₁ (ω₁ < ω₀), and show that this repulsive interaction (that we attribute to incipient magnetism) induces a superconducting state possessing a high transition temperature. In this state, the gap function Δ(ε) oscillates as function of ε, with a period of order ω₀. We also find solutions antisymmetric in energy [ Δ(ε) = - Δ(-ε) ], which turn out to be almost degenerate with the normal, symmetric ones. We discuss the physical implications of this model. Our model thus combines a low frequency repulsion due to antiferromagnetic interactions, with excitonic attraction at intermediate frequencies, and ordinary Coulomb repulsion above that. All frequency ranges, and coupling strengths, are comparable with the bandwidth.