Current-oscillator correlation and Fano factor spectrum of quantum shuttle with finite bias voltage and temperature

TL;DR

This paper develops a master equation for a quantum shuttle system considering bias voltage and temperature, revealing how current and noise characteristics depend on vibrational states and thermal effects.

Contribution

It introduces a comprehensive master equation incorporating Fermi functions and vibrational dynamics, enabling detailed analysis of current and noise in quantum shuttles under various conditions.

Findings

Current exhibits step-like features at low temperature depending on phonon number.

Thermal noise emerges and current steps vanish at higher temperatures.

Fano factor indicates sub-Poissonian noise in ground state and super-Poissonian in excited states.

Abstract

A general master equation is derived to describe an electromechanical single-dot transistor in the Coulomb blockade regime. In the equation, Fermi distribution functions in the two leads are taken into account, which allows one to study the system as a function of bias voltage and temperature of the leads. Furthermore, we treat the coherent interaction mechanism between electron tunneling events and the dynamics of excited vibrational modes. Stationary solutions of the equation are numerically calculated. We show current through the oscillating island at low temperature appears step like characteristics as a function of the bias voltage and the steps depend on mean phonon number of the oscillator. At higher temperatures the current steps would disappear and this event is accompanied by the emergence of thermal noise of the charge transfer. When the system is mainly in the ground state, zero frequency Fano factor of current manifests sub-Poissonian noise and when the system is partially driven into its excited states it exhibits super-Poissonian noise. The difference in the current noise would almost be removed for the situation in which the dissipation rate of the oscillator is much larger than the bare tunneling rates of electrons.