Vortices and critical current in disordered arrays of Josephson junctions

The breakdown phenomena of disordered arrays of two-dimensional resistively shunted Josephson junctions driven by dc external current are studied numerically at zero temperature and zero magnetic field. First we report on perfect arrays with large linear defects (rows of missing junctions). We show the formation of vortices on the defect tips, the depinning of these vortices at the critical current, the production of Josephson oscillations by the motion of these vortices and additional transitions as breakdown occurs row by row in adjacent rows. Next we study the funnel defect to show that, in this model, local confined (nonspanning) regions of the sample cannot become normal until an entire spanning or global region or vortex path across the sample can be found. In randomly disordered samples, global breakdown means that the most critical defect region of the sample cannot become normal until a connected global path of such regions across the sample can become normal and develop a voltage. This point of global breakdown defines the critical current ${\mathit{i}}_{\mathit{c}}$ in randomly disordered arrays. At currents just below ${\mathit{i}}_{\mathit{c}}$, large regions of the sample may be critical or near critical, with vortices ready to depin from their defects in a form of self-organized criticality. It may be possible to stimulate this near depinning by external probes in this situation. We also study the statistics of an ensemble of 800 arrays of 25×25 junctions at p=0.90 to observe the failure distribution F(i) (or critical current distribution) within the ensemble. We find consistency with the modified Gumbel form for F(i), as in the case of linear problems, despite the nonlinearity. Finally we observe the average voltage 〈V〉 versus applied current i for the samples in the ensemble and find that 〈V〉 varies as (i-${\mathit{i}}_{\mathrm{〈}\mathit{V}\mathrm{〉}}$ ${)}^{\mathit{x}}$, where x=3.10±0.10.