Critical Currents of Josephson-Coupled Wire Arrays

TL;DR

This paper calculates the critical current and current-voltage characteristics of a Josephson-coupled wire array under a magnetic field, revealing sharp peaks in critical current related to flux quantization and array size.

Contribution

It introduces a model for Josephson wire arrays with two layers and analyzes how magnetic flux affects critical currents, highlighting the role of vortex lattice commensurability.

Findings

Critical current peaks occur at small integer q values.

Critical current scales as (n/q)^{1/2} for large arrays.

Sharp peaks are linked to vortex lattice commensurability.

Abstract

We calculate the current-voltage characteristics and critical current I_c^{array} of an array of Josephson-coupled superconducting wires. The array has two layers, each consisting of a set of parallel wires, arranged at right angles, such that an overdamped resistively-shunted junction forms wherever two wires cross. A uniform magnetic field equal to f flux quanta per plaquette is applied perpendicular to the layers. If f = p/q, where p and q are mutually prime integers, I_c^{array}(f) is found to have sharp peaks when q is a small integer. To an excellent approximation, it is found in a square array of n^2 plaquettes, that I_c^{array}(f) \propto (n/q)^{1/2} for sufficiently large n. This result is interpreted in terms of the commensurability between the array and the assumed q \times q unit cell of the ground state vortex lattice.