Quantum Shuttle Phenomena in a Nanoelectromechanical Single-Electron Transistor

TL;DR

This paper analyzes quantum shuttle phenomena in a nanoelectromechanical single-electron transistor, revealing a transition from classical to quantum regimes of shuttle vibrations influenced by electric field strength and dissipation levels.

Contribution

It provides an analytical study of quantum shuttle behavior in realistic conditions, identifying the instability of the vibrational ground state and characterizing the quantum regime of shuttle vibrations.

Findings

Instability of the vibrational ground state below a dissipation threshold.

Recovery of classical shuttle behavior at high electric fields.

Existence of a quantum regime with large fluctuations at low electric fields.

Abstract

An analytical analysis of quantum shuttle phenomena in a nanoelectromechanical single-electron transistor has been performed in the realistic case, when the electron tunnelling length is much greater than the amplitude of the zero point oscillations of the central island. It is shown that when the dissipation is below a certain threshold value, the vibrational ground state of the central island is unstable. The steady-state into which this instability develops is studied. It is found that if the electric field ${\cal E}$ between the leads is much greater than a characteristic value ${\cal E}_q$, the quasiclassical shuttle picture is recovered, while if ${\cal E}\ll{\cal E}_q$ a new quantum regime of shuttle vibrations occurs. We show that in the latter regime small quantum fluctuations result in large (i.e. finite in the limit $\hbar \to 0$) shuttle vibrations.