Perpendicular upper critical field of granular Pb films near the superconductor-to-insulator transition.

Abstract

We have measured the perpendicular upper critical field, ${\mathit{H}}_{\mathit{c}2}$(T), in ultrathin granular Pb films with normal-state sheet resistances, ${\mathit{R}}_{\mathit{N}}$, that range from 10 \ensuremath{\Omega} to 11 k\ensuremath{\Omega}. The films with the highest ${\mathit{R}}_{\mathit{N}}$ are near the threshold for the superconductor-to-insulator (S-I) transition. We compare our results to calculations for granular superconductors and obtain values for the grain size and coherence length characteristic of a single grain. In addition, we present a measurement of the ratio of the intergrain Josephson-coupling energy to the single-grain condensation energy near the S-I transition in these films. The small value of this ratio, 0.05, at ${\mathit{R}}_{\mathit{N}}$=11 k\ensuremath{\Omega} is consistent with the picture that fluctuations in the phase of the order parameter dominate the S-I transition in these films.