Current-Voltage Hyperscaling in Arrays of Josephson Junctions

Abstract

We measure the voltage-supercurrent (V-Is) characteristic of three-dimensional arrays of point contacts and find V ∼ Isa with a = 2.1 ± 0.2 at the critical coherence temperature Tc. This behaviour results from the following properties of the coherence transition: i) hyperscaling of critical exponents; ii) general relations satisfied by relevant parameters, in this case the supercurrent, in phase transitions; iii) the crossover exponent is 2β + ν; iv) the paracoherent excess conductivity has the same critical exponent γ as the related X-Y model susceptibility. Previously published data on granular superconductors are compatible with this description.