  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.
