Key questions for any superconductor include: what is its maximum dissipation-free electrical current (its 'critical current') and can this be used to extract fundamental thermodynamic parameters? Present models focus on depinning of magnetic vortices and implicate materials engineering to maximise pinning performance. But recently we showed that the self-field critical current for thin films is a universal property, independent of microstructure, controlled only by the penetration depth. Here we generalise this observation to include thin films, wires or nanowires of singleor multi-band s-wave and d-wave superconductors. Using extended BCS equations we consider dissipation-free self-field transport currents as London-Meissner currents, avoiding the concept of pinning altogether. We find quite generally, for type I or type II superconductors, the current is limited by the relevant critical field divided by the penetration depth. Our fits to 64 available data sets, from zinc nanowires to compressed sulphur hydride with critical temperatures of 0.65 to 203 K, respectively, are excellent. Extracted London penetration depths, superconducting energy gaps and specific heat jumps agree well with reported bulk values. For multiband or multiphase samples we accurately recover individual band contributions and phase fractions.

Recent experiments showed that thinning gallium, iron selenide and 2H tantalum disulfide to single/several monoatomic layer(s) enhances their superconducting critical temperatures.Here, we characterize these superconductors by extracting the absolute values of the London penetration depth, the superconducting energy gap, and the relative jump in specific heat at the transition temperature from their self-field critical currents. Our central finding is that the enhancement in transition temperature for these materials arises from the opening of an additional superconducting gap, while retaining a largely unchanged "bulk" superconducting gap. Literature data reveals that ultrathin niobium films similarly develop a second 2 superconducting gap. Based on the available data, it seems that, for type-II superconductors, a new superconducting band appears when the film thickness becomes smaller than the out-ofplane coherence length. The same mechanism may also be the cause of enhanced interface superconductivity.

Recently, compressed H 2 S has been shown to become superconducting at 203 K under a pressure of 155 GPa. One might expect fluctuations to dominate at such temperatures. Using the magnetisation critical current, we determine the ground-state London penetration depth, λ 0 =189 nm, and the superconducting energy gap, 0 =27.8 meV, and find these parameters are similar to those of cuprate superconductors. We also determine the fluctuation temperature scale, T fluc = 1470 K, which shows that, unlike the cuprates, T c of the hydride is not limited by fluctuations. This is due to its three dimensionality and suggests the search for better superconductors should refocus on threedimensional systems where the inevitable thermal fluctuations are less likely to reduce the observed T

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.