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

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 nonuniversal 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.

arXiv comment15 pages, 6 figures

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• Universal Fermi velocity in highly compressed hydride superconductors
• Quantifying the nonadiabaticity strength constant in recently discovered highly-compressed superconductors
• Current distribution across type II superconducting films: a new vortex-free critical state
• New scaling laws for pinning force density in superconductors
• The onset of dissipation in high-temperature superconductors: magnetic hysteresis and field dependence
• Peak in the critical current density in (Ca${}_x$Sr${}_{1-x}$)${}_3$Rh${}_4$Sn${}_{13}$ tuned towards the structural quantum critical point
• Spinning superconductors and ferromagnets
• Quantum Phase Transition as a Promising Route to Enhance the Critical Current in Kagome Superconductor CsV${}_3$Sb${}_5$