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Universal scaling behaviour in superconductors has significantly elucidatedfluctuation and phase transition phenomena in these materials. However,universal behaviour for the most practical property, the critical current, wasnot contemplated because prevailing models invoke nucleation and migration offlux vortices. Such migration depends critically on pinning, and the detailedmicrostructure naturally differs from one material to another, even within asingle material. Through microstructural engineering there have been ongoingimprovements in the field-dependent critical current, thus illustrating itsnonuniversal behaviour. But here we demonstrate the universal size scaling ofthe self-field critical current for any superconductor, of any symmetry,geometry or band multiplicity. Key to our analysis is the huge range of sampledimensions, from single-atomic-layer to mm-scale. These have widely variablemicrostructure with transition temperatures ranging from 1.2 K to the currentrecord, 203 K. In all cases the critical current is governed by a fundamentalsurface current density limit given by the relevant critical field divided bythe penetration depth.

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