Screening effects in superconductors

The partition function of the Hubbard model with local attraction and long-range Coulomb repulsion between electrons is written as a functional integral with an action A involving a pairing field Δ and a local potential V. After integration over V and over fluctuations in \Δ\2, the final form of A involves a Josephson coupling between the local phases of Δ and a "kinetic energy" term, representing the screened Coulomb interaction between charge fluctuations. The competition between Josephson coupling and charging energy allows to understand the relation between TC and composition in high-TC materials, in particular superlattices, alloys and bulk systems of low doping.