Abstract

The superfluid density is a key parameter in describing the thermodynamic and electrodynamic properties of superconductors and governs for example the fluctuation amplitude near Tc. If fluctuations are sufficiently strong the transition temperature Tc can be reduced below its mean-field value. Firstly, it is shown that the transport critical current density of all superconductors in zero external field is, rather surprisingly, a universal parameter governed only by the superfluid density. Using what must be close to the entire inventory of available data (98 data sets), this is demonstrated for all superconductors of any type, symmetry or anisotropy, including single atomic-layer superconductors. This leads to a remarkable scaling behaviour as a function of sample size for both films and round wires which is found to be applicable over some eight orders of magnitude in sample dimension – from single atomic layer to mm scale. The superfluid density is determined in this way for highly compressed H2S with Tc = 203 K (_{150 GPa) and the fluctuation temperature scale is estimated. It is} 1400 K for phase fluctuations but as low as 300 K for amplitude fluctuations suggesting that already the mean-field Tc value exceeds the observed 203 K and any attempts to raise Tc further are likely to be increasingly hampered by strong fluctuations.