Upper critical fields in granular superconductors

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Abstract
We have measured the upper critical field in granular Al-Ge samples, as a function of temperature and for different metal concentrations. For small metal concentrations, we find that the upper critical field of the sample is that of the isolated grains at all temperatures. For high metal concentrations, the upper critical field is that of a bulk dirty superconductor. For intermediate metal concentrations, one observes a crossover from the bulk type-II behavior at high temperatures to the isolated grain behavior at low temperatures, with an upturn of the critical field at the crossover temperature. We present a Landau-Ginzburg model for the critical fields in a granular system and show that it explains the experimental data.