Electron-Electron Interaction in Linear Arrays of Small Tunnel Junctions

TL;DR

This paper analyzes the electrostatic potential distribution caused by a charge in a linear array of small tunnel junctions, revealing a new crossover behavior in the potential profile that improves understanding of single-electron solitons.

Contribution

It provides an analytical solution for the potential distribution in tunnel junction arrays, highlighting a crossover behavior not captured by previous exponential models.

Findings

Derived an analytical potential distribution for tunnel junction arrays.

Identified a crossover from linear to Coulomb potential with a hump feature.

Validated the model with geometrical simulations.

Abstract

We have calculated the spatial distribution of the electrostatic potential created by an unbalanced charge $q$ in one of the conducting electrodes of a long, uniform, linear array of small tunnel junctions. The distribution describes, in particular, the shape of a topological single-electron soliton in such an array. An analytical solution obtained for a circular cross section model is compared with results of geometrical modeling of a more realistic structure with square cross section. These solutions are very close to one another, and can be reasonably approximated by a simple phenomenological expression. In contrast to the previously accepted exponential approximation, the new result describes the crossover between the linear change of the potential near the center of the soliton to the unscreened Coulomb potential far from the center, with an unexpected ``hump'' near the crossover point.