Josephson-junction arrays with long-range interactions

Abstract

We calculate the current-voltage (IV) characteristics of a Josephson-junction array with long-range interactions. The array consists of two sets of equally spaced parallel superconducting wires placed at right angles. A Josephson junction is formed at every point wherever the wires cross. We treat each such junction as an overdamped resistively shunted junction, and each wire segment between two junctions as a similar resistively shunted junction with a much higher critical current. The IV characteristics are obtained by solving the coupled Josephson equations numerically. We find that, for a sufficiently large number of wires, the critical current saturates at a finite value because of the wire inductance, in excellent agreement with experiment. The calculated IV characteristics also show a striking hysteresis, even though each of the individual junctions is nonhysteretic. The hysteresis results from a global redistribution of current flow on the upper and lower voltage branches, and is also in excellent agreement with experiment.

Mean-field theory for arrays of Josephson-coupled wires

“…4 In that work ͑carried out only at f ϭ0), the array critical current I c array was also found to be affected by finite ; specifically, I c array /I c;xy ϳ Ϫ1/2 , where was defined as the ratio of junction critical currents I c;xy /I c;z ͑equivalent to the coupling constant ratio in this paper͒. Thus, I c array behaves, for large , just like T c ( f ϭ0), and for the same reason.…”

“…In an earlier paper, 4 we showed that the saturation behavior could be accounted for by a simple dynamical model, in which the wire segments were treated as overdamped Josephson junctions with a critical current much larger than that of the junctions connecting different wires. This gives the wires an effective inductance per unit length of ប/(2eI c a), where I c is the critical current of the Josephson junctions used to model the wires.…”

Critical currents of Josephson-coupled wire arrays

“…3 For very large arrays, the assumption that each wire is a locus of constant phase breaks down, and the meanfield theory has to be corrected to take account of the phase variation along the array. 4 This same effect causes the critical current of the array to saturate at a finite value which depends on the Josephson penetration depth, even as N → ∞. 5,6 The exactness of mean-field theory is believed to have an analog in the dynamics of these arrays.…”