Positional disorder in superconducting wire networks and Josephson junction arrays

We report the results of mean-field simulations of superconducting wire networks with positional disorder. The nodes of square wire arrays were displaced with either Gaussian or truncated uniform distributions on two different types of unit cells. Using the linearized Ginzburg-Landau equations we have numerically determined the transition temperature, $T_c$, as a function of the average number of magnetic-flux quanta per unit cell, $f_0$, for different amounts of disorder. $T_c\left(f_0\right)$ exhibits decaying oscillations, periodic in $f_0$, whose amplitude goes to zero at a disorder-dependent critical field, $f_c$. Our calculated value of this critical magnetic field is in good agreement with our experimental magnetoresistance measurements on Josephson junction arrays.