Application of Percolation Theory to Current Transfer in Granular Superconductors

TL;DR

This paper explores how percolation theory models current transfer in granular superconductors, highlighting its successes and limitations, and proposes new relations and a scaling law to bridge the gap between theory and experiment.

Contribution

It introduces a new scaling law between current and probability and discusses the limitations of existing percolation models in describing superconducting behavior.

Findings

Percolation theory can describe some properties of granular superconductors.

A conceptual gap exists between experimental data and theoretical models.

A new scaling law between current and probability is proposed.

Abstract

We investigate the description of current transfer in polycrystalline superconductors by percolation theory and its limitations. Various computer models that have been proposed are reviewed and related to the experimental and theoretical framework. While some conductor properties can be well described by percolation theory and models, we argue that a conceptual gap exists between experiment and theory. This gap has to be bridged by finding relations between electromagnetic and statistical parameters. We derive various such relations and compare them with recent simulation data. In particular, we suggest a new scaling law between the two fundamental variables current and probability.