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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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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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.
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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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DOI: https://doi.org/10.1038/nnano.2011.71
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