Stiffness and coherence length measurements of ultra-thin superconductor, and implications to layered superconductors

Based on the London equation, we use a rotor-free vector potential ${\bf A}$, and current measurements by a SQUID, to determine the superconducting Pearl length $\Lambda$, and coherence length $\xi$, of ultra-thin, ring shaped, MoSi films, as a function of thickness $d$ and temperature $T$. We find that $\xi$ is a function of $d$ with a jump at $\xi \sim d \sim 5$nm. At base temperature the superconducting stiffness, defined by $1/\lambda^2=1/(\Lambda d)$, is an increasing function of $T_c$. Similar behavior, known as the Uemura plot, exist in bulk layered superconductors, but with doping as an implicit parameter. We also provide the critical exponents of $\Lambda (T)$.