Activated transport and scaling behavior in the current-voltage characteristics and Coulomb-blockade oscillations of two-dimensional arrays of metallic islands

We have investigated the transport properties of two-dimensional arrays of normal islands interconnected by tunnel junctions fabricated close to a conducting ground plane. For bias voltages $V$ below a threshold voltage $V_{\mathrm{th}},$ the current $I$ is thermally activated with an activation energy proportional to $V_{\mathrm{th}}-V.\mathrm{}$ For $V>\mathrm{}{V}_{\mathrm{th}},$ $I$ scales as $(V-V_{\mathrm{th}}{)}^{\zeta },$ where $\zeta =2.01\mathrm{}\pm 0.04$ and $1.58\pm 0.04$ for two samples. For constant $V,$ $I$ exhibits Coulomb-blockade oscillations as a function of the voltage of the ground plane. The amplitude of these oscillations scales as $(V-V_{\mathrm{th}}{)}^{\chi },$ where $\chi =0.68\mathrm{}\pm 0.18$ and $0.31\pm 0.10$ for the same samples, respectively. These values are consistent with our theoretical prediction $\chi =\left(\zeta -1\right)/2.$