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

TL;DR

This study uses advanced simulations to analyze the statistical properties of 1D and 2D single-electron arrays, revealing Coulomb gaps, blockade threshold behaviors, and temperature-dependent conduction characteristics.

Contribution

It provides detailed numerical insights into Coulomb gaps, blockade thresholds, and activation energies in disordered single-electron arrays, extending understanding of their electronic properties.

Findings

Coulomb gap in 2D arrays follows Efros-Shklovskii theory.

1D array threshold voltage distribution broadens with size.

2D array threshold voltage distribution narrows as size increases.

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".