Coulomb blockade for an oscillating tunnel junction

TL;DR

This paper investigates how a nano-mechanical oscillator influences Coulomb blockade phenomena in a voltage-biased tunnel junction, revealing modifications to the $I$-$V$ characteristics due to quantum fluctuations.

Contribution

It introduces a simple method to incorporate mechanical oscillators into Coulomb blockade models by modifying the circuit's effective impedance.

Findings

Quantum fluctuations alter the $I$-$V$ characteristics in strong Coulomb blockade.

The oscillator's effect can be modeled by an effective impedance modification.

The theory applies to various impedance types, including inductance and resistance.

Abstract

We consider a tunnel junction formed between a fixed electrode and an oscillating one. Accumulation of the charge on the junction capacitor induces a force on the nano-mechanical oscillator. The junction is voltage biased and connected in series with an impedance $Z(\omega)$. We discuss how the picture of Coulomb blockade is modified by the presence of the oscillator. Quantum fluctuations of the mechanical oscillator modify the $I$-$V$ characteristics particularly in the strong Coulomb blockade limit. We show that the oscillator can be taken into account by a simple modification of the effective impedance of the circuit. We discuss in some details the case of a single inductance $Z(\omega)=iL\omega$ and of a constant resistance $Z(\omega)=R$. With little modifications the theory applies also to incoherent transport in Josephson junctions in the tunneling limit.