Single Electron Tunneling at Large Conductance: The Semiclassical Approach

TL;DR

This paper develops a semiclassical approach to analyze the linear conductance of single electron devices with Coulomb blockade, incorporating environmental effects and comparing theoretical predictions with experimental data.

Contribution

It introduces a nonperturbative path integral method for conductance calculation in high conductance regimes, extending analysis to arrays and transistors.

Findings

Agreement with experimental data for large conductance junctions

Conductance dependence on array length and impedance

Validation of semiclassical approach for single electron transistors

Abstract

We study the linear conductance of single electron devices showing Coulomb blockade phenomena. Our approach is based on a formally exact path integral representation describing electron tunneling nonperturbatively. The electromagnetic environment of the device is treated in terms of the Caldeira-Leggett model. We obtain the linear conductance from the Kubo formula leading to a formally exact expression which is evaluated in the semiclassical limit. Specifically we consider three models. First, the influence of an electromagnetic environment of arbitrary impedance on a single tunnel junction is studied focusing on the limits of large tunneling conductance and high to moderately low temperatures. The predictions are compared with recent experimental data. Second, the conductance of an array of N tunnel junctions is determined in dependence on the length N of the array and the environmental impedance. Finally, we consider a single electron transistor and compare our results for large tunneling conductance with experimental findings.