An analytical approach to the thermal instability of superconducting films under high current densities

TL;DR

This paper presents an analytical model for the thermal instability of superconducting films under high current densities, predicting the critical current density with high accuracy and supporting the thermal breakdown hypothesis.

Contribution

It introduces a new analytical approach using Green's functions to predict thermal stability and critical current density in superconducting films.

Findings

Predicted critical current densities agree with experiments within 5%.

Thermal instability is confirmed as the main cause of superconductivity breakdown.

Model applies to YBCO films near their critical temperature.

Abstract

Using the Green's function of the 3D heat equation, we develop an analytical account of the thermal behaviour of superconducting films subjected to electrical currents larger than their critical current in the absence of an applied magnetic field. Our model assumes homogeneity of films and current density, and besides thermal coefficients employs parameters obtained by fitting to experimental electrical field - current density characteristics at constant bath temperature. We derive both a tractable dynamic equation for the real temperature of the film up to the supercritical current density J^\ast (the lowest current density inducing transition to the normal state), and a thermal stability criterion that allows prediction of J^\ast . For two typical YBCO films, J^\ast predictions agree with observations to within 5%. These findings strongly support the hypothesis that a current-induced thermal instability is generally the origin of the breakdown of superconductivity under high electrical current densities, at least at temperatures not too far from Tc.