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 Vₜₕ, the current I is thermally activated with an activation energy proportional to Vₜₕ-V. For V>Vₜₕ, I scales as (V-Vₜₕ)^ζ, where ζ=2.01±0.04 and 1.58±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-Vₜₕ)^χ, where χ=0.68±0.18 and 0.31±0.10 for the same samples, respectively. These values are consistent with our theoretical prediction χ=(ζ-1)/2.