From superconductor stability and relaxation to Andreev reflections

TL;DR

This paper introduces an unconventional electrical resistance network approach to determine the critical temperature of superconductors, refining a dynamic relaxation model and highlighting limitations in analyzing superconductor/normal conductor junctions with non-Ohmic effects.

Contribution

It extends a dynamic relaxation model for superconductor stability analysis and proposes an alternative thermal fluctuations solution, revealing a transition boundary layer and limitations in current calculations.

Findings

Refined the relaxation model for superconductor stability.

Identified a transition boundary layer near critical temperature.

Highlighted limitations in current calculations involving non-Ohmic effects.

Abstract

How exactly can critical temperature be determined from results obtained in resistivity measurements? An unconventional approach using an electrical resistance network is presented in this paper to find an answer to this question. In a first step, a recently suggested, dynamic relaxation model is refined and extended beyond its proper applicability and competence range (superconductor stability against quench). This step addresses bending of the resistivity vs. temperature curves near critical temperature. In a second step, an alternative solution of the thermal fluctuations problem is presented. From both results, existence of a non-local, transition boundary layer can be postulated, a temperature uncertainty around critical temperature. Finally, severe limitations to calculate total current through superconductor/normal conductor thin film junctions become obvious from this approach if any non-Ohmic contributions (like Andreev reflection or Josephson currents) have to be taken into account. This problem is a parallel to multi-component heat transfer.