Magnetic response and enhanced Tc in the 1D to 2D crossover regime of mesoscopic superconducting aluminum rings.

We have studied more than 40 mesoscopic Aluminum rings by positioning a scannable SQUID susceptometer over each ring individually, and have found a striking non-monotonic dependence of Tc on linewidth. By measuring the magnetic response, or current in the ring, as a function of applied flux and temperature, it is possible to extract $\lambda(T)$ and $\xi(T)$. The rings vary in width (40-350nm) and diameter (1-4um) with a nominal thickness of 35nm. For rings with linewidths above 150nm ($\approx 2 \xi(T = 0)$), the extracted superfluid density shows a high-temperature tail up to temperatures as high as 15\% above the 1D and bulk thin film critical temperatures. In this regime, we also find evidence for the saturation of $\xi(T)$ on the order of the ring's linewidth. We speculate that these results indicate the particular importance of Tc disorder in the crossover from quasi-1D to 2D superconductivity.