Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Electrical tuning of elastic wave propagation in nanomechanical lattices at MHz frequencies

Nature Nanotechnology volume 13, pages 1016–1020 (2018)Cite this article

Subjects

Abstract

Nanoelectromechanical systems (NEMS) that operate in the megahertz (MHz) regime allow energy transducibility between different physical domains. For example, they convert optical or electrical signals into mechanical motions and vice versa1. This coupling of different physical quantities leads to frequency-tunable NEMS resonators via electromechanical non-linearities2,3,4. NEMS platforms with single- or low-degrees of freedom have been employed to demonstrate quantum-like effects, such as mode cooling5, mechanically induced transparency5, Rabi oscillation6,7, two-mode squeezing8 and phonon lasing9. Periodic arrays of NEMS resonators with architected unit cells enable fundamental studies of lattice-based solid-state phenomena, such as bandgaps10,11, energy transport10,11,12, non-linear dynamics and localization13,14, and topological properties15, directly transferrable to on-chip devices. Here we describe one-dimensional, non-linear, nanoelectromechanical lattices (NEML) with active control of the frequency band dispersion in the radio-frequency domain (10–30 MHz). The design of our systems is inspired by NEMS-based phonon waveguides10,11 and includes the voltage-induced frequency tuning of the individual resonators2,3,4. Our NEMLs consist of a periodic arrangement of mechanically coupled, free-standing nanomembranes with circular clamped boundaries. This design forms a flexural phononic crystal with a well-defined bandgap, 1.8 MHz wide. The application of a d.c. gate voltage creates voltage-dependent on-site potentials, which can significantly shift the frequency bands of the device. Additionally, a dynamic modulation of the voltage triggers non-linear effects, which induce the formation of a phononic bandgap in the acoustic branch, analogous to Peierls transition in condensed matter16. The gating approach employed here makes the devices more compact than recently proposed systems, whose tunability mostly relies on materials’ compliance17,18 and mechanical non-linearities19,20,21,22.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Non-linear NEML.
Fig. 2: Static tuning with a d.c. gate voltage.
Fig. 3: Tunable phonon propagation velocity.
Fig. 4: Dynamic modulation and formation of a non-linear bandgap.

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Craighead, H. G. Nanoelectromechanical systems. Science 290, 1532–1535 (2000).

    Article  CAS  Google Scholar 

  2. Chen, C. et al. Performance of monolayer graphene nanomechanical resonators with electrical readout. Nat. Nanotech. 4, 861–867 (2009).

    Article  CAS  Google Scholar 

  3. Chen, C. et al. Graphene mechanical oscillators with tunable frequency. Nat. Nanotech. 8, 923–927 (2013).

    Article  CAS  Google Scholar 

  4. Bagci, T. et al. Optical detection of radio waves through a nanomechanical transducer. Nature 507, 81–85 (2014).

    Article  CAS  Google Scholar 

  5. Mahboob, I., Nishiguchi, K., Okamoto, H. & Yamaguchi, H. Phonon-cavity electromechanics. Nat. Phys. 8, 387–392 (2012).

    Article  CAS  Google Scholar 

  6. Okamoto, H. et al. Coherent phonon manipulation in coupled mechanical resonators. Nat. Phys. 9, 480–484 (2013).

    Article  CAS  Google Scholar 

  7. Faust, T., Rieger, J., Seitner, M. J., Kotthaus, J. P. & Weig, E. M. Coherent control of a classical nanomechanical two-level system. Nat. Phys. 9, 485–488 (2013).

    Article  CAS  Google Scholar 

  8. Mahboob, I., Okamoto, H., Onomitsu, K. & Yamaguchi, H. Two-mode thermal-noise squeezing in an electromechanical resonator. Phys. Rev. Lett. 113, 167203 (2014).

    Article  CAS  Google Scholar 

  9. Mahboob, I., Nishiguchi, K., Fujiwara, A. & Yamaguchi, H. Phonon lasing in an electromechanical resonator. Phys. Rev. Lett. 110, 127202 (2013).

    Article  CAS  Google Scholar 

  10. Hatanaka, D., Mahboob, I., Onomitsud, K. & Yamaguchi, H. Phonon waveguides for electromechanical circuits. Nat. Nanotech. 9, 520–524 (2014).

    Article  CAS  Google Scholar 

  11. Hatanaka, D., Dodel, A., Mahboob, I., Onomitsud, K. & Yamaguchi, H. Phonon propagation dynamics in band-engineered one-dimensional phononic crystal waveguides. New J. Phys. 17, 113032 (2015).

    Article  Google Scholar 

  12. Yu, S. et al. Surface phononic graphene. Nat. Mater. 15, 1243–1247 (2016).

    Article  CAS  Google Scholar 

  13. Sato, M. et al. Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array. Phys. Rev. Lett. 90, 044102 (2003).

    Article  CAS  Google Scholar 

  14. Sato, M., Hubbard, B. E. & Sievers, A. J. Colloquium: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays. Rev. Mod. Phys. 78, 137–157 (2006).

    Article  CAS  Google Scholar 

  15. Cha, J., Kim, K. W. & Daraio, C. Experimental realization of on-chip topological nanoelectromechanical metamaterials. Preprint at https://arXiv.org/abs/1806.10680 (2018)

  16. Gruener, G. The dynamics of charge-density waves. Rev. Mod. Phys. 60, 1129 (1988).

    Article  CAS  Google Scholar 

  17. Babaee, S., Viard, N., Wang, P., Fang, N. X. & Bertoldi, K. Harnessing deformation to switch on and off the propagation of sound. Adv. Mater. 28, 1631–1635 (2016).

    Article  CAS  Google Scholar 

  18. Wang, P., Casadei, F., Shan, S., Weaver, J. C. & Bertoldi, K. Harnessing buckling to design tunable locally resonant acoustic metamaterials. Phys. Rev. Lett. 113, 014301 (2014).

    Article  Google Scholar 

  19. Boechler, N., Yang, J., Theocharis, G., Kevrekidis, P. G. & Daraio, C. Tunable vibrational band gaps in one-dimensional diatomic granular crystal with three-particle unit cells. J. Apply. Phys. 109, 074906 (2011).

    Article  Google Scholar 

  20. Spadoni, A. & Daraio, C. Generation and control of sound bullets with a nonlinear acoustic lens. Proc. Natl Acad. Sci. USA 107, 7230–7234 (2010).

    Article  CAS  Google Scholar 

  21. Lydon, J., Serra-Garcia, M. & Daraio, C. Local to extended transitions of resonant defect modes. Phys. Rev. Lett. 113, 185503 (2014).

    Article  Google Scholar 

  22. Bilal, O. R., Foehr, A. & Daraio, C. Reprogrammable phononic metasurfaces. Adv. Mater. 29, 1700628 (2017).

    Article  Google Scholar 

  23. Seitner, M. J., Gajo, K. & Weig, E. M. Damping of metallized bilayer nanomechanical resonators at room temperature. Appl. Phys. Lett. 105, 213101 (2014).

    Article  Google Scholar 

  24. Sounas, D. L. & Alu, A. Non-reciprocal photonics based on time modulation. Nat. Photon. 11, 774–783 (2017).

    Article  CAS  Google Scholar 

  25. Bachelard, N. et al. Emergence of an enslaved phononic bandgap in a non-equilibrium pseudo-crystal. Nat. Mater. 16, 808–813 (2017).

    Article  CAS  Google Scholar 

  26. Eichler, A., Moser, J., Dykman, M. I. & Bachtold, A. Symmetry breaking in a mechanical resonator made from a carbon nanotube. Nat. Commun. 4, 2843 (2013).

    Article  CAS  Google Scholar 

  27. Biswas, T. S. et al. Remote sensing in hybridized arrays of nanostrings. Nano. Lett. 14, 2541–2545 (2014).

    Article  CAS  Google Scholar 

  28. Kharrat, C. et al. Modal control of mechanically coupled NEMS arrays for tunable RF filters. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57, 1285–1295 (2010).

    Article  Google Scholar 

  29. Olsson, R. H. III & El-Kady, I. Microfabricated phononic crystal devices and applications. Meas. Sci. Technol. 20, 012002 (2009).

    Article  Google Scholar 

  30. Tsaturyan, Y., Barg, A., Polzik, E. S. & Schliesser, A. Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution. Nat. Nanotech. 12, 776–783 (2017).

    Article  CAS  Google Scholar 

  31. Vermersch, B., Guimond, P.-O., Pichler, H. & Zoller, P. Quantum state transfer via noisy photonic and phononic waveguides. Phys. Rev. Lett. 118, 133601 (2017).

    Article  CAS  Google Scholar 

  32. Lee, S. et al. Graphene metallization of high-stress silicon nitride resonators for electrical integration. Nano. Lett. 13, 4275–4279 (2013).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge partial support for this project from NSF EFRI Award no. 1741565, Binnig and Rohrer Nanotechnology Center at IBM Zurich and the Kavli Nanoscience Institute at Caltech. We thank E. Togan at ETH Zurich for his advice on interferometers.

Author information

Authors and Affiliations

  1. Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland

    Jinwoong Cha

  2. Engineering and Applied Science, California Institute of Technology, Pasadena, CA, USA

    Jinwoong Cha & Chiara Daraio

Authors
  1. Jinwoong Cha
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chiara Daraio
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.C. and C.D. conceived the idea for the research. J.C. designed and fabricated the samples. J.C. built the experimental set-ups and performed the experiments. J.C. developed the analytical models and performed the numerical simulations. J.C. and C.D. analysed the data and wrote the manuscript.

Corresponding author

Correspondence to Chiara Daraio.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Supplementary Information

Supplementary Figures 1–13

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cha, J., Daraio, C. Electrical tuning of elastic wave propagation in nanomechanical lattices at MHz frequencies. Nature Nanotech 13, 1016–1020 (2018). https://doi.org/10.1038/s41565-018-0252-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-018-0252-6

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing