Scaling Behavior in the Current-Voltage Characteristic of One- and Two-Dimensional Arrays of Small Metallic Islands

We have measured the current-voltage ( $I$- $V$) characteristics of one- and two-dimensional arrays of normal metal islands linked by small tunnel junctions. The tunneling resistance is large compared to the resistance quantum, and a ground plane reduces the screening length to much less than the interisland spacing. At temperatures well below the island charging energy, we find a threshold voltage $V_T$ below which little current flows. For $V>\mathrm{}{V}_T$, $I$ scales as $({V/V}_T-1\mathrm{}{)}^{\zeta }$ where $\zeta =1.36\mathrm{}\pm 0.1$ (1D) and $1.80\pm 0.16$ (2D). We interpret this behavior as a dynamic critical phenomenon.