Universal scaling of the self-field critical current in superconductors: from sub-nanometre to millimetre size

E F Talantsev,W P Crump,J L Tallon

doi:10.1038/s41598-017-10226-z

Abstract

Universal scaling behaviour in superconductors has significantly elucidated fluctuation and phase transition phenomena in these materials. However, universal behaviour for the most practical property, the critical current, was not contemplated because prevailing models invoke nucleation and migration of flux vortices. Such migration depends critically on pinning, and the detailed microstructure naturally differs from one material to another, even within a single material. Through microstructural engineering there have been ongoing improvements in the field-dependent critical current, thus illustrating its non-universal behaviour. But here we demonstrate the universal size scaling of the self-field critical current for any superconductor, of any symmetry, geometry or band multiplicity. Key to our analysis is the huge range of sample dimensions, from single-atomic-layer to mm-scale. These have widely variable microstructure with transition temperatures ranging from 1.2 K to the current record, 203 K. In all cases the critical current is governed by a fundamental surface current density limit given by the relevant critical field divided by the penetration depth.

Highlights

Universal scaling behaviour in superconductors has significantly elucidated fluctuation and phase transition phenomena in these materials
We showed[6] for a large range of single- or multi-band superconductors, independent of type, symmetry, size or geometry, that, in the absence of weak links and in zero external field, the transport critical current density is determined only by the penetration depth. This is referred to as the “self-field Jc” or Jc(sf). This observation provides a simple route to measure the absolute value of the penetration depth and other thermodynamic properties such as the superconducting energy gap and the relative jump in electronic specific heat at the transition temperature, Tc
We show schematically the two extremes when the wire radius, a, and film thickness, b, are either large compared with λ or small compared with λ, respectively

Summary

Introduction

Universal scaling behaviour in superconductors has significantly elucidated fluctuation and phase transition phenomena in these materials. Using a simple but compelling scaling plot we compare Jc(sf) data for nanoscale films and wires, including single-atomic-layer superconductors, with data for macroscopic samples to show that in all cases, spanning up to eight orders of magnitude in effective size, the current density across the surface, when dissipation sets in, is always Js = Bc/(μ0λ) for type I superconductors and Js = Bc1/(μ0λ) for type II superconductors.

Results

Conclusion