Screening effects in superconductors

TL;DR

This paper develops a theoretical framework for understanding how screening effects influence superconductivity in materials, especially high-$T_{C}$ superconductors, by analyzing the Hubbard model with Coulomb interactions.

Contribution

It introduces a functional integral approach to model the interplay of pairing, Coulomb repulsion, and phase fluctuations in superconductors.

Findings

Relation between $T_{C}$ and composition explained

Screening effects modify charge fluctuations

Josephson coupling influences superconducting transition

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.