Dynamics and Current Fluctuations in AC driven Charge Shuttle

TL;DR

This paper reviews the dynamics and current fluctuations of an AC-driven charge shuttle, highlighting its rectification behavior, frequency-dependent dynamics, and correlated transport signatures in current noise.

Contribution

It provides a comprehensive analysis of the charge shuttle's behavior under AC driving, including dynamics, transition to self-oscillation, and full counting statistics of current fluctuations.

Findings

The device acts as a rectifier transforming AC into DC under asymmetry.

Current noise shows signatures of correlated transport at locking frequencies.

Explicit expressions for full-counting statistics are derived in the adiabatic limit.

Abstract

The behavior of a charge shuttle under a pure AC field has been recently considered theoretically and experimentally. If the system presents an asymmetry in the tunneling amplitudes the device acts as a nano-electromechanical rectifier, transforming a pure AC voltage field into a direct curren. In this paper we first review the model and the appearance of the rectifying effect for bias voltages below the threshold of self-oscillation. We discuss in some details the dynamics of the central island that, like the current, presents strong dependence on the forcing AC field frequency. In presence of both a constant and a small oscillating bias voltage we analyze the transition from the static to self-oscillating solution. We then consider current fluctuations (full counting statistics) for periodic motion of the grain. We explicitly evaluate the current noise numerically and we find that it shows clear signatures of correlated transport at certain locking frequencies. In the adiabatic limit we obtain a simple expression for the full-counting statistics and calculate explicitly the first four moments.