Phase transition in current-biased arrays of small Josephson junctions

We present a variational approach to treat the metastable superconducting state in an array of small Josephson junctions driven by an applied current. Using this approach, we calculate an approximate phase diagram of such an array with a current bias. Our approach is a generalization of one previously used for such an array at zero applied current. We find that, for a given array, a superconducting to nonsuperconducting transition at zero temperature can be achieved either by varying the magnitude of the applied current at fixed direction or by varying the direction of the applied current at fixed magnitude. We examine this transition in two-dimensional arrays on both square and triangular lattices, and in a simple cubic array. We also calculate the dependence of this transition on the direction of the applied current. For a given array and bias current, a superconductor-to-insulator transition also takes place as the temperature is increased. Using the variational approach, we calculate critical values of the junction parameters, temperature, and current for this transition on three different lattices.