Thermodynamic Parameters of Single- or Multi-Band Superconductors Derived from Self-Field Critical Currents

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, using an extended BCS-like model, we calculate the penetration depth from the temperature dependence of the superconducting energy gap thus allowing us to fit self-field critical current data. In this way we extract from the T-dependent gap a set of key thermodynamic parameters, the ground-state penetration depth, energy gap and jump in electronic specific heat. Our fits to 79 available data sets, from zinc nanowires to compressed sulphur hydride with critical temperatures of 0.65 to 203 K, respectively, are excellent and the extracted parameters agree well with reported bulk values. Samples include thin films, wires or nanowires of single- or multi-band s-wave and d-wave superconductors of either type I or type II. For multiband or multiphase samples we accurately recover individual band contributions and phase fractions.