Nonharmonic oscillations of nanosized cantilevers due to quantum-size effects

TL;DR

This paper predicts that quantum-size effects cause nanoscale cantilevers to exhibit nonharmonic oscillations with amplitude-dependent resonance frequencies, due to changes in electron states affecting the spring constant.

Contribution

It introduces a model linking quantum electron states to mechanical oscillations, revealing oscillatory behavior in the spring constant of nanowire cantilevers.

Findings

Spring constant oscillates with bending due to quantum effects

Resonance frequency depends on oscillation amplitude

Quantum-size effects are detectable in nanoscale mechanical systems

Abstract

Using a one-dimensional jellium model and standard beam theory we calculate the spring constant of a vibrating nanowire cantilever. By using the asymptotic energy eigenvalues of the standing electron waves over the nanometer-sized cross-section area, the change in the grand canonical potential is calculated and hence the force and the spring constant. As the wire is bent more electron states fits in its cross section. This has an impact on the spring"constant" which oscillates slightly with the bending of the wire. In this way we obtain an amplitude-dependent resonance frequency of the oscillations that should be detectable.