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Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene

Nature Nanotechnology volume 6, pages 339–342 (2011)Cite this article

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Abstract

The theory of damping is discussed in Newton's Principia1 and has been tested in objects as diverse as the Foucault pendulum, the mirrors in gravitational-wave detectors and submicrometre mechanical resonators. In general, the damping observed in these systems can be described by a linear damping force. Advances in nanofabrication mean that it is now possible to explore damping in systems with one or more atomic-scale dimensions. Here we study the damping of mechanical resonators based on carbon nanotubes2,3,4,5,6,7,8,9,10,11 and graphene sheets12,13,14,15. The damping is found to strongly depend on the amplitude of motion, and can be described by a nonlinear rather than a linear damping force. We exploit the nonlinear nature of damping in these systems to improve the figures of merit for both nanotube and graphene resonators. For instance, we achieve a quality factor of 100,000 for a graphene resonator.

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Figure 1: Devices and measurement setup.
Figure 2: Nonlinear damping in nanotube resonators.
Figure 3: Nonlinear damping in a graphene resonator.
Figure 4: Quality factor and force sensitivity at low driving force.

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Acknowledgements

The authors acknowledge support from the European Union (RODIN, FP7), the Spanish ministry (FIS2009-11284), the Catalan government (AGAUR, SGR), the Swiss National Science Foundation (PBBSP2-130945) and a Marie Curie grant (271938). I.W.-R. acknowledges financial support from the Nanosystems Initiative Munich. The authors also thank B. Thibeault (Santa Barbara) for help in fabrication and P. Gambardella, S. Roche and S. Valenzuela for a critical reading of the manuscript.

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Author notes

  1. A. Eichler and J. Moser: These authors contributed equally to this work

Authors and Affiliations

  1. CIN2 (ICN-CSIC), Catalan Institute of Nanotechnology, Campus de la UAB 08193 Bellaterra, Barcelona, Spain

    A. Eichler, J. Moser, J. Chaste, M. Zdrojek & A. Bachtold

  2. Technische Universität München, Garching, 85748, Germany

    I. Wilson-Rae

Authors
  1. A. Eichler
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  2. J. Moser
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  3. J. Chaste
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  4. M. Zdrojek
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  5. I. Wilson-Rae
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  6. A. Bachtold
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Contributions

A.E., J.M. and M.Z. fabricated the devices. J.M. and A.E. developed the measurement setup and performed the measurements. J.C. and A.B. provided measurement support. A.E., J.M., A.B. and I.W.-R. analysed the data. I.W.-R. established equations (2) and (3). A.B. conceived and designed the experiment. All authors contributed to writing the manuscript.

Corresponding author

Correspondence to A. Bachtold.

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The authors declare no competing financial interests.

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Eichler, A., Moser, J., Chaste, J. et al. Nonlinear damping in mechanical resonators made from carbon nanotubes and graphene. Nature Nanotech 6, 339–342 (2011). https://doi.org/10.1038/nnano.2011.71

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