On the nature of self-field critical current in superconductors and its use as a probe of the superfluid density
Authors:   , Crump Wayne Philip 
Published: December 2021

<p>Superconductors are used in many applications where large electrical currents are needed. This is due to their ability to transport an electric current without resistance. There is however a limit to the magnitude of current that can be conducted before dissipation starts to occur. This is known as the critical current and is a topic of great interest in applied superconductivity.  For type II superconductors, it is well known that vortex motion plays a role in the determination of the in-field critical current. This has led great effort in engineering the microstructure of these superconductors to hinder the motion of vortices and enhance their critical currents. However the self-field critical current (when there is no applied external field) generally does not see any enhancement due to efforts to pin vortex motion.  The work here examines the behaviour of the self-field critical current in thin-film and cylindrical wire superconductors of many different superconductor types and sizes. It is found that a critical state is reached when the current density at the surface of the sample reaches the magnitude of Bc/μ₀λ for type I and Bc₁/μ₀λ for type II superconductors regardless of the size and material type. This finding shows that there is a fundamental limit to the self-field current density that cannot be enhanced by engineering the microstructure and is essentially of thermodynamic origin.  The result also sets up the self-field critical current density as a probe of the superfluid density. This was explored in many different superconductor types by considering the temperature dependence of the self-field critical current. The ground-state magnetic penetration depth, groundstate energy gap and specific heat jump at the critical temperature were key thermodynamic parameters extracted from the critical current data. For a very large number of superconductors the extracted parameters in general matched well with literature values measured using conventional but much more complex techniques.  A result inferred from the critical state was that the current distribution across the width of a rectangular superconductor would be uniform, contrary to expectations of the Meissner state. This was tested by measuring the perpendicular magnetic field resulting from a transport current in a superconducting tape as it reached the critical state. It was indeed found that the current distribution is uniform across the width.  The self-field critical current was also measured in YBa₂Cu₃Oy samples with Zn impurities to measure the superfluid density and further test the self-field critical current as a measure of superfluid density and in particular explore whether it follows the canonical dependence on the transition temperature observed for superconductors with d-wave symmetry. Here the critical current was found to reduce as more impurities were added and indeed this matched its expected canonical reduction, following the superfluid density as Jc(sf) ∝p³/².  These results taken together support the unexpected existence of a fundamental limit in the self-field critical current, which is thermodynamic in origin.</p>