Coulomb gap, Coulomb blockade, and dynamic activation energy in frustrated single-electron arrays

We have used modern supercomputer facilities to carry out extensive numerical simulations of statistical properties of one-dimensional (1D) and 2D arrays of single-electron islands with random background charges, in the limit of small island self-capacitance. In particular, the spectrum of single-electron addition energies shows a clear Coulomb gap that, in 2D arrays, obeys the Efros-Shklovskii theory modified for the specific electron-electron interaction law. The Coulomb blockade threshold voltage statistics for 1D arrays is very broad, with the rms width δVₜ growing as 〈Vₜ〉∝N1/2 with the array size N. On the contrary, in square 2D arrays of large size the distribution around 〈Vₜ〉∝N becomes relatively narrow (δVₜ/〈Vₜ〉∝1/N), and the dc I-V curves are virtually universal. At low voltages, the slope G₀(T) of I-V curves obeys the Arrhenius law. The corresponding activation energy U₀ grows only slowly with N and is considerably lower than the formally calculated ``lowest pass'' energy Eₘₐₓ of the potential profile, thus indicating the profile ``softness.''