Effective capacitance in a single-electron transistor

TL;DR

This paper calculates the frequency-dependent response of a single-electron transistor using the Kubo formula, revealing a finite reactive component under Coulomb blockade due to virtual processes, which can be measured via microwave reflection.

Contribution

It introduces a method to compute the effective capacitance in a SET considering virtual tunneling processes, extending understanding of its reactive response.

Findings

Finite reactive part exists under Coulomb blockade due to virtual processes

Effective capacitance can be measured with rf-SET via microwave reflection

Method valid across a wide range of parameters

Abstract

Starting from the Kubo formula for conductance, we calculate the frequency-dependent response of a single-electron transistor (SET) driven by an ac signal. Treating tunneling processes within the lowest order approximation, valid for a wide range of parameters, we discover a finite reactive part even under Coulomb blockade due to virtual processes. At low frequencies this can be described by an effective capacitance. This effect can be probed with microwave reflection measurements in radio-frequency (rf) SET provided that the capacitance of the surroundings does not completely mask that of the SET.