Quantum Description of Shuttle Instability in Nanoelectromechanical Single Electron Transistor

TL;DR

This paper presents a quantum mechanical analysis of shuttle instability in nanoelectromechanical single-electron transistors, revealing voltage-dependent regimes where the system transitions from stable to unstable oscillations.

Contribution

It introduces a quantum description of shuttle instability, identifying the critical voltage threshold and characterizing the quantum regime of mechanical vibrations.

Findings

Below threshold, the mechanical state remains near ground state.

Above threshold, the system exhibits exponentially growing oscillations.

The study interprets these oscillations as a quantum shuttle instability.

Abstract

The voltage dependence of nanoelectromechanical effects in a system where the quantized mechanical vibrations of a quantum dot are coupled to coherent tunneling of electrons through a single level in the dot is studied. It is found that there are two different regimes depending on the value of an applied voltage. If the bias voltage is below a certain threshold value, then the state of the mechanical subsystem is located near its ground state. If the bias voltage is above the threshold value then the system becomes unstable which manifests itself in the expectation value of the displacement being an oscillating function of time with an exponentially increasing amplitude. This can be interpreted as a shuttle instability in a quantum regime.