Dissipative and conservative nonlinearity in carbon nanotube and graphene mechanical resonators

TL;DR

This paper reviews the highly nonlinear mechanical behaviors of graphene and carbon nanotube resonators, highlighting nonlinear damping, parametric excitation, and electron transport coupling, with implications for advanced nonlinear dynamics studies.

Contribution

It provides a comprehensive review of nonlinear behaviors in nanotube and graphene resonators, emphasizing nonlinear damping and coupling effects not extensively covered before.

Findings

Nonlinear damping described by a power-law dependence of quality factor.

Absence of hysteresis in some resonators at large driving forces.

Strong coupling between mechanical motion and electron transport leads to highly nonlinear forces.

Abstract

Graphene and carbon nanotubes represent the ultimate size limit of one and two-dimensional nanoelectromechanical resonators. Because of their reduced dimensionality, graphene and carbon nanotubes display unusual mechanical behavior; in particular, their dynamics is highly nonlinear. Here, we review several types of nonlinear behavior in resonators made from nanotubes and graphene. We first discuss an unprecedented scenario where damping is described by a nonlinear force. This scenario is supported by several experimental facts: (i) the quality factor varies with the amplitude of the motion as a power law whose exponent coincides with the value predicted by the nonlinear damping model, (ii) hysteretic behavior (of the motional amplitude as a function of driving frequency) is absent in some of our resonators even for large driving forces, as expected when nonlinear damping forces are large, and (iii) when we quantify the linear damping force (by performing parametric excitation measurements) we find that it is significantly smaller than the nonlinear damping force. We then review parametric excitation measurements, an alternative actuation method which is based on nonlinear dynamics. Finally, we discuss experiments where the mechanical motion is coupled to electron transport through a nanotube. The coupling can be made so strong that the associated force acting on the nanotube becomes highly nonlinear with displacement and velocity. Overall, graphene and nanotube resonators hold promise for future studies on classical and quantum nonlinear dynamics.