Screening effects in superconductors

Abstract

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 $\Delta$ and a local potential $V$. After integration over $V$ and over fluctuations in $|\Delta {|}^2$, the final form of $A$ involves a Josephson coupling between the local phases of $\Delta$ 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 $T_C$ and composition in high-$T_C$ materials, in particular superlattices, alloys and bulk systems of low doping.

4 pages, revtex, no figures, submitted to Physica B (Proceedings of SCES '96 International Conference, held in Zurich from 19th to 21st of August)