Josephson Junction Arrays with Positional Disorder: Experiments and Simulations

We present the results of a study of Josephson junction arrays with positional disorder, using both experiments and Monte Carlo simulations. We have fabricated 50 x 50 arrays of PbCu proximity-effects junctions, with controlled positional disorder characterized by a parameter delta-star. The zero-field resistive transitions of these samples are well described by the Kosterlitz- Thouless-Halperin-Nelson vortex-unbinding theory. Measurements of resistance vs. magnetic field reveal rich structure, with pronounced minima at integer fields, as well as higher-order structure. In samples with disorders the principal oscillations are found to decay linearly with field, after accounting for the effect of the magnetic field on the critical currents of the individual junctions. We can quantify the destruction of phase-coherence on length-scales of order q times the lattice parameter by defining critical fields, fcq approx. 1delta-star, by the disappearance of structures at fields fo pq, where fo is the average number of flux quanta per plaquette, and p and q are integers. Extrapolation to q infinity yields an estimate of the critical field, f c, for the destruction of quasi-long-range phase coherence which is in good agreement with the theoretical prediction of Granato and Kosterlitz. However, our experiments show no evidence for the predicted reentrant phase transition.