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

Abstract

We have used modern supercomputer facilities to carry out extensive numerical simulations of statistical properties of 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 r.m.s. width \(\delta V_t\) growing as \(<V_t > \propto N^{1/2}\) with the array size \(N\). On the contrary, in square 2D arrays of large size the distribution around \(<V_t> \propto N\) becomes relatively narrow \((\delta V_t/< V_t> \propto 1/N)\), and the dc \(I\)-\(V\) curves are virtually universal. At low voltages, the slope \(G_0(T)\) of \(I\)-\(V\) curves obeys the Arrhenius law. The corresponding activation energy \(U_0\) grows only slowly with \(N\) and is considerably lower than the formally calculated "lowest pass" energy \(E_{max}\) of the potential profile, thus indicating the profile "softness".