Charging Ultrasmall Tunnel Junctions in Electromagnetic Environment

TL;DR

This paper derives an analytical expression for the quantum admittance of ultrasmall tunnel junctions in various electromagnetic environments, and validates the results with experimental data, enhancing understanding of quantum conductance behavior.

Contribution

It provides a general analytical formula for quantum admittance in arbitrary environments and confirms theoretical predictions with numerical and experimental agreement.

Findings

Analytical expression for quantum admittance derived.

Numerical results match experimental measurements.

Confirmed theoretical conclusions across conductance ranges.

Abstract

We have investigated the quantum admittance of an ultrasmall tunnel junction with arbitrary tunneling strength under an electromagnetic environment. Using the functional integral approach a close analytical expression of the quantum admittance is derived for a general electromagnetic environment. We then consider a specific controllable environment where a resistance is connected in series with the tunneling junction, for which we derived the dc quantum conductance from the zero frequency limit of the imaginary part of the quantum admittance. For such electromagnetic environment the dc conductance has been investigated in recent experiments, and our numerical results agree quantitatively very well with the measurements. Our complete numerical results for the entire range of junction conductance and electromagnetic environmental conductance confirmed the few existing theoretical conclusions.