Shuttle instabilities: semiclassical phase analysis

TL;DR

This paper provides a semiclassical analysis of electron shuttle instabilities involving quantum dots, revealing insights into resonances and device instabilities when the central dot oscillates beyond quantum zero point motion.

Contribution

It introduces a semiclassical framework to analyze the instability phenomena in a quantum dot-based electron shuttle system.

Findings

Identifies the conditions under which resonances lead to instabilities.

Links the amplitude of the central dot's oscillation to device stability.

Provides a deeper understanding of quantum-classical transition effects in nanoscale systems.

Abstract

We present a semiclassical analysis of the instability of an electron shuttle composed of three quantum dots: two are fixed and coupled via leads to electron resevoirs at different chemical potentials, while the central dot is mounted on a classical harmonic oscillator. The semiclassical analysis, which is valid if the central dot oscillation amplitude is larger than the quantum mechanical zero point motion, can be used to gain additional insight about the relationship of resonances and instabilities of the device.