Dissipative and conservative nonlinearity in carbon nanotube and graphene mechanical resonators

J. Moser, A. Eichler, B. Lassagne, J. Chaste, Y. Tarakanov, J. Kinaret, I. Wilson‐Rae and A. Bachtold

in Fluctuating Nonlinear Oscillators

Published in print July 2012 | ISBN: 9780199691388
Published online September 2012 | e-ISBN: 9780191742255 | DOI:
Dissipative and conservative nonlinearity in carbon nanotube and graphene mechanical resonators

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This chapter reviews several types of nonlinear behaviour in nanotubes and graphene resonators. It first discusses a scenario where damping is described by a nonlinear force. Several experimental facts support this: the quality factor varies with the motional amplitude as a power law whose exponent coincides with the value predicted by the nonlinear damping model, hysteretic behaviour (of the motional amplitude vs. driving frequency) is absent in some resonators even for large driving forces, as expected when nonlinear damping forces are large, and the linear damping force extracted from parametric excitation measurements is significantly smaller than the nonlinear damping force. The chapter then reviews parametric excitation measurements, an alternative actuation method based on nonlinear dynamics. Finally, it discusses experiments where the mechanical motion is coupled to electron transport through a nanotube. The coupling is so strong that the associated force acting on the nanotube is highly nonlinear with displacement and velocity.

Keywords: nanoelectromechanical; mechanical resonator; carbon nanotubes; graphene; nonlinear damping; parametric excitation; Coulomb blockade; electron-vibration coupling

Chapter.  9354 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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