Theory of Percolative Conduction in Polycrystaline High-temperature Superconductors

TL;DR

This paper develops a model for conduction in polycrystalline high-temperature superconductors, linking microscopic weak links at grain boundaries to macroscopic electrical behavior using analytical and numerical methods.

Contribution

It introduces a nonlinear resistor network model and a novel variational numerical technique to analyze percolative conduction in high-Tc superconductors.

Findings

Established a connection between I-V characteristics and macroscopic properties.

Demonstrated the effectiveness of the variational numerical technique.

Provided insights into limiting factors for high-current applications.

Abstract

Conduction in bulk polycrystalline high-T$_c$ superconductors with relatively high critical currents has been shown to be percolative. This phenomenon is due to weak links at grain boundaries. These weak links are the major limiting factor for technological applications which require high current densities. We formulate a model of these materials which can be reduced to a nonlinear resistor network. The model is solved by analytical approximations and a new numerical technique. The numerical technique is variational, which makes it capable of solving a wide variety of nonlinear problems. The results show that an unambiguous connection can be made between the I-V characteristics at the microscopic level and the macroscopic electrical properties.