- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Sources of nonlinearity of a driven carbon nanotube electromechanical resonator

Sofia Sevitz1,2,*, Kushagra Aggarwal3,4, Jorge Tabanera-Bravo5,6, Juliette Monsel2, Florian Vigneau3, Federico Fedele4, Joe Dunlop7, Juan M. R. Parrondo5, Gerard J. Milburn8 et al.

Janet Anders1,7, Natalia Ares4, and Federico Cerisola7,†

  • *Contact author: sevitz@chalmers.se
  • †Contact author: f.cerisola@exeter.ac.uk
PDF

Phys. Rev. Research 8, 033237 – Published 27 August, 2026

DOI: https://doi.org/10.1103/t59c-rdnm

Abstract

Nanoelectromechanical resonators provide an ideal platform for investigating the interplay between electron transport and nonlinear mechanical motion. Externally driven suspended carbon nanotubes, containing an electrostatically defined quantum dot, are especially promising. These devices possess two main sources of nonlinearity: the electromechanical coupling and the intrinsic contributions of the resonator that induce a Duffing-like nonlinear behavior. In this work, we observe the interplay between the two sources across different driving regimes. The main nonlinear feature we observe is the emergence of archlike resonances in the electronic transport when the resonator is strongly driven. We show that our model is in good agreement with our experimental electron transport measurements on a suspended carbon nanotube. This characterization paves the way for the exploration of nonlinear phenomena using mesoscopic electromechanical resonators.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (53)

  1. A. Eichler, J. Chaste, J. Moser, and A. Bachtold, Parametric amplification and self-oscillation in a nanotube mechanical resonator, Nano Lett. 11, 2699 (2011).
  2. Y. Wen, N. Ares, F. J. Schupp, T. Pei, G. A. D. Briggs, and E. A. Laird, A coherent nanomechanical oscillator driven by single-electron tunnelling, Nat. Phys. 16, 75 (2020).
  3. C. Urgell, W. Yang, S. L. De Bonis, C. Samanta, M. J. Esplandiu, Q. Dong, Y. Jin, and A. Bachtold, Cooling and self-oscillation in a nanotube electromechanical resonator, Nat. Phys. 16, 32 (2020).
  4. J. Tabanera-Bravo, F. Vigneau, J. Monsel, K. Aggarwal, L. Bresque, F. Fedele, F. Cerisola, G. A. D. Briggs, J. Anders, A. Auffèves, Juan M. R. Parrondo, and N. Ares, Stability of long-sustained oscillations induced by electron tunneling, Phys. Rev. Res. 6, 013291 (2024).
  5. P. Belardinelli, W. Yang, A. Bachtold, M. I. Dykman, and F. Alijani, Hidden vibrational bistability revealed by intrinsic fluctuations of a carbon nanotube, Nano Lett. 25, 8443 (2025).
  6. L. Tesser, B. Bhandari, P. A. Erdman, E. Paladino, R. Fazio, and F. Taddei, Heat rectification through single and coupled quantum dots, New J. Phys. 24, 035001 (2022).
  7. A. Gusso, R. L. Viana, A. C. Mathias, and I. L. Caldas, Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes, Chaos Solit. Fractals 122, 6 (2019).
  8. M. Woolley, G. Milburn, and C. M. Caves, Nonlinear quantum metrology using coupled nanomechanical resonators, New J. Phys. 10, 125018 (2008).
  9. J. Chaste, A. Eichler, J. Moser, G. Ceballos, R. Rurali, and A. Bachtold, A nanomechanical mass sensor with yoctogram resolution, Nat. Nanotechnol. 7, 301 (2012).
  10. X. Wang, A. Miranowicz, H.-R. Li, and F. Nori, Hybrid quantum device with a carbon nanotube and a flux qubit for dissipative quantum engineering, Phys. Rev. B 95, 205415 (2017).
  11. J. Moser, A. Eichler, J. Güttinger, M. I. Dykman, and A. Bachtold, Nanotube mechanical resonators with quality factors of up to 5 million, Nat. Nanotechnol. 9, 1007 (2014).
  12. Z. Zhong, N. M. Gabor, J. E. Sharping, A. L. Gaeta, and P. L. McEuen, Terahertz time-domain measurement of ballistic electron resonance in a single-walled carbon nanotube, Nat. Nanotechnol. 3, 201 (2008).
  13. J.-Y. Park, S. Rosenblatt, Y. Yaish, V. Sazonova, H. Üstünel, S. Braig, T. A. Arias, P. W. Brouwer, and P. L. McEuen, Electron-phonon scattering in metallic single-walled carbon nanotubes, Nano Lett. 4, 517 (2004).
  14. X. Zhou, J.-Y. Park, S. Huang, J. Liu, and P. L. McEuen, Band structure, phonon scattering, and the performance limit of single-walled carbon nanotube transistors, Phys. Rev. Lett. 95, 146805 (2005).
  15. E. A. Laird, F. Kuemmeth, G. A. Steele, K. Grove-Rasmussen, J. Nygård, K. Flensberg, and L. P. Kouwenhoven, Quantum transport in carbon nanotubes, Rev. Mod. Phys. 87, 703 (2015).
  16. F. Vigneau, J. Monsel, J. Tabanera, K. Aggarwal, L. Bresque, F. Fedele, F. Cerisola, G. A. D. Briggs, J. Anders, Juan M. R. Parrondo, A. Auffèves, and N. Ares, Ultrastrong coupling between electron tunneling and mechanical motion, Phys. Rev. Res. 4, 043168 (2022).
  17. C. Samanta, S. L. De Bonis, C. B. Møller, R. Tormo-Queralt, W. Yang, C. Urgell, B. Stamenic, B. Thibeault, Y. Jin, D. A. Czaplewski, F. Pistolesi, and A. Bachtold, Nonlinear nanomechanical resonators approaching the quantum ground state, Nat. Phys. 19, 1340 (2023).
  18. G. A. Steele, A. K. Hüttel, B. Witkamp, M. Poot, H. B. Meerwaldt, L. P. Kouwenhoven, and H. S. J. van der Zant, Strong coupling between single-electron tunneling and nanomechanical motion, Science 325, 1103 (2009).
  19. C. Samanta, N. Arora, and A. K. Naik, Tuning of geometric nonlinearity in ultrathin nanoelectromechanical systems, Appl. Phys. Lett. 113, 113101 (2018).
  20. P. G. Steeneken, R. J. Dolleman, D. Davidovikj, F. Alijani, and H. S. J. van der Zant, Dynamics of 2D material membranes, 2D Mater. 8, 042001 (2021).
  21. H. B. Meerwaldt, G. Labadze, B. H. Schneider, A. Taspinar, Y. M. Blanter, H. S. J. van der Zant, and G. A. Steele, Probing the charge of a quantum dot with a nanomechanical resonator, Phys. Rev. B 86, 115454 (2012).
  22. H. B. Meerwaldt, G. A. Steele, and H. S. J. van der Zant, 12 carbon nanotubes: Nonlinear high-Q resonators with strong coupling to single-electron tunneling, in Fluctuating Nonlinear Oscillators: From Nanomechanics to Quantum Superconducting Circuits, edited by M. Dykman (Oxford University Press, Oxford, 2012).
  23. X. Wang, L. Cong, D. Zhu, Z. Yuan, X. Lin, W. Zhao, Z. Bai, W. Liang, X. Sun, G.-W. Deng, and K. Jiang, Visualizing nonlinear resonance in nanomechanical systems via single-electron tunneling, Nano Res. 14, 1156 (2021).
  24. K. Willick, X. S. Tang, and J. Baugh, Probing the non-linear transient response of a carbon nanotube mechanical oscillator, Appl. Phys. Lett. 111, 223108 (2017).
  25. G. Luo, Z.-Z. Zhang, G.-W. Deng, H.-O. Li, G. Cao, M. Xiao, G.-C. Guo, and G.-P. Guo, Coupling graphene nanomechanical motion to a single-electron transistor, Nanoscale 9, 5608 (2017).
  26. L. Cong, G.-W. Deng, X. Lin, W. Liang, Z. Bai, W. Zhao, K. Jiang, and X. Wang, Multi-order nonlinearities and resulting coherent oscillations of the states in quantum dot-mechanical resonator hybrid system, in 2021 IEEE 16th International Conference on Nano/Micro Engineered and Molecular Systems (NEMS) (IEEE, Xiamen, China, 2021), pp. 1084–1087.
  27. P. G. Kirton and A. D. Armour, Nonlinear dynamics of a driven nanomechanical single-electron transistor, Phys. Rev. B 87, 155407 (2013).
  28. B. Witkamp, M. Poot, and H. S. J. Van Der Zant, Bending-mode vibration of a suspended nanotube resonator, Nano Lett. 6, 2904 (2006).
  29. S. Sapmaz, Y. M. Blanter, L. Gurevich, and H. S. J. van der Zant, Carbon nanotubes as nanoelectromechanical systems, Phys. Rev. B 67, 235414 (2003).
  30. C.-H. Ho, R. Scott, and J. Eisley, Non-planar, non-linear oscillations of a beam—I. Forced motions, Int. J. Non Linear Mech. 10, 113 (1975).
  31. W. G. Conley, A. Raman, C. M. Krousgrill, and S. Mohammadi, Nonlinear and nonplanar dynamics of suspended nanotube and nanowire resonators, Nano Lett. 8, 1590 (2008).
  32. H. J. R. Westra, M. Poot, H. S. J. van der Zant, and W. J. Venstra, Nonlinear modal interactions in clamped-clamped mechanical resonators, Phys. Rev. Lett. 105, 117205 (2010).
  33. A. Eichler, M. del Álamo Ruiz, J. A. Plaza, and A. Bachtold, Strong coupling between mechanical modes in a nanotube resonator, Phys. Rev. Lett. 109, 025503 (2012).
  34. I. Kozinsky, H. W. C. Postma, I. Bargatin, and M. L. Roukes, Tuning nonlinearity, dynamic range, and frequency of nanomechanical resonators, Appl. Phys. Lett. 88, 253101 (2006).
  35. I. Katz, A. Retzker, R. Straub, and R. Lifshitz, Signatures for a classical to quantum transition of a driven nonlinear nanomechanical resonator, Phys. Rev. Lett. 99, 040404 (2007).
  36. K. F. Albrecht, A. Martin-Rodero, R. C. Monreal, L. Mühlbacher, and A. Levy Yeyati, Long transient dynamics in the Anderson-Holstein model out of equilibrium, Phys. Rev. B 87, 085127 (2013).
  37. A. Mitra, I. Aleiner, and A. J. Millis, Phonon effects in molecular transistors: Quantal and classical treatment, Phys. Rev. B 69, 245302 (2004).
  38. G. Piovano, F. Cavaliere, E. Paladino, and M. Sassetti, Coherent properties of nanoelectromechanical systems, Phys. Rev. B 83, 245311 (2011).
  39. A. Moulhim, B. Tripathi, and M. Kumar, Nonequilibrium Green function technique for analyzing electron transport through single and two levels of interacting quantum dot, Phys. Scr. 96, 125802 (2021).
  40. P. P. Potts, Quantum thermodynamics, SciPost Phys. Lect. Notes 126 (2026).
  41. G. Schaller, Open Quantum Systems Far From Equilibrium, Lecture Notes in Physics, Vol. 881 (Springer International Publishing, Cham, 2014).
  42. A. A. Clerk and S. Bennett, Quantum nanoelectromechanics with electrons, quasi-particles and Cooper pairs: Effective bath descriptions and strong feedback effects, New J. Phys. 7, 238 (2005).
  43. We neglect thermal fluctuations here because they are orders of magnitude smaller than the external drive.
  44. This has to do with the sign chosen for β, a negative β would result in a sharp drop for ωex<ω (see Appendix pp4).
  45. C. W. J. Beenakker, Theory of Coulomb-blockade oscillations in the conductance of a quantum dot, Phys. Rev. B 44, 1646 (1991).
  46. B. Lassagne, Y. Tarakanov, J. Kinaret, D. Garcia-Sanchez, and A. Bachtold, Coupling mechanics to charge transport in carbon nanotube mechanical resonators, Science 325, 1107 (2009).
  47. The conversion from the experimental driving power Pex to the driving force Fex considered in the model is nontrivial; thus, we estimate their values based on the observed features in the current.
  48. O. Culhane, M. T. Mitchison, and J. Goold, Extractable work in quantum electromechanics, Phys. Rev. E 106, L032104 (2022).
  49. S. Sevitz, K. Aggarwal, J. Tabanera-Bravo, J. Monsel, F. Vigneau, F. Fedele, J. Dunlop, J. Parrondo, G. J. Milburn, J. Anders, N. Ares, and F. Cerisola, sofsevitz/NonlinearDynamicsQDCNT: Publication version (Version Publication) [Computer software], [dataset] Zenodo, 2026, https://doi.org/10.5281/zenodo.20747566.
  50. C. Rackauckas and Q. Nie, DifferentialEquations.jl—A performant and feature-rich ecosystem for solving differential equations in Julia, J. Open Res. Software 5, 15 (2017).
  51. F. Cerisola and F. Fedele, spin-mechanical-coupling-2025-data-model, 2025, https://github.com/oxquantum-repo/spin-mechanical-coupling-2025-data-model.
  52. R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Spins in few-electron quantum dots, Rev. Mod. Phys. 79, 1217 (2007).
  53. M. Poot and H. S. van der Zant, Mechanical systems in the quantum regime, Phys. Rep. 511, 273 (2012).

Outline

Information

Phys. Rev. Research 8, 033237– Published 27 August, 2026
  • Received 10 October 2025
  • Accepted 8 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation