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Engineering nanoscale hypersonic phonon transport


Controlling vibrations in solids is crucial to tailor their elastic properties and interaction with light. Thermal vibrations represent a source of noise and dephasing for many physical processes at the quantum level. One strategy to avoid these vibrations is to structure a solid such that it possesses a phononic stop band, that is, a frequency range over which there are no available elastic waves. Here we demonstrate the complete absence of thermal vibrations in a nanostructured silicon membrane at room temperature over a broad spectral window, with a 5.3-GHz-wide bandgap centred at 8.4 GHz. By constructing a line-defect waveguide, we directly measure gigahertz guided modes without any external excitation using Brillouin light scattering spectroscopy. Our experimental results show that the shamrock crystal geometry can be used as an efficient platform for phonon manipulation with possible applications in optomechanics and signal processing transduction.

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Fig. 1: Shamrock phononic insulator.
Fig. 2: Brillouin light scattering spectroscopy.
Fig. 3: Hypersonic phononic waveguide.

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Data supporting the results and conclusions are available at


  1. Krause, A. G., Winger, M., Blasius, T. D., Lin, Q. & Painter, O. A high-resolution microchip optomechanical accelerometer. Nat. Photon. 6, 768–772 (2012).

    Article  CAS  Google Scholar 

  2. Chaste, J. et al. A nanomechanical mass sensor with yoctogram resolution. Nat. Nanotechnol. 7, 301–304 (2012).

    Article  CAS  Google Scholar 

  3. Gavartin, E., Verlot, P. & Kippenberg, T. J. A hybrid on-chip optomechanical transducer for ultrasensitive force measurements. Nat. Nanotechnol. 7, 509–514 (2012).

    Article  CAS  Google Scholar 

  4. Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011).

    Article  CAS  Google Scholar 

  5. Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).

    Article  CAS  Google Scholar 

  6. Sigalas, M. & Economou, E. N. Band structure of elastic waves in two dimensional systems. Solid State Commun. 86, 141–143 (1993).

    Article  CAS  Google Scholar 

  7. Kushwaha, M. S., Halevi, P., Dobrzynski, L. & Djafari-Rouhani, B. Acoustic band structure of periodic elastic composites. Phys. Rev. Lett. 71, 2022 (1993).

    Article  CAS  Google Scholar 

  8. Martínez-Sala, R. et al. Sound attenuation by sculpture. Nature 378, 241 (1995).

    Article  Google Scholar 

  9. Gorishnyy, T., Ullal, C. K., Maldovan, M., Fytas, G. & Thomas, E. L. Hypersonic phononic crystals. Phys. Rev. Lett. 94, 115501 (2005).

    Article  CAS  Google Scholar 

  10. Zen, N., Puurtinen, T. A., Isotalo, T. J., Chaudhuri, S. & Maasilta, I. J. Engineering thermal conductance using a two-dimensional phononic crystal. Nat. Commun. 5, 3435 (2014).

    Article  Google Scholar 

  11. Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J. & Painter, O. Optomechanical crystals. Nature 462, 78–82 (2009).

    Article  CAS  Google Scholar 

  12. Djafari-Rouhani, B., El-Jallal, S. & Pennec, Y. Phoxonic crystals and cavity optomechanics. C. R. Phys. 17, 555–564 (2016).

    Article  CAS  Google Scholar 

  13. MacCabe, G. S. et al. Nano-acoustic resonator with ultralong phonon lifetime. Science 370, 840–843 (2020).

    Article  CAS  Google Scholar 

  14. Fang, K., Matheny, M. H., Luan, X. & Painter, O. Optical transduction and routing of microwave phonons in cavity-optomechanical circuits. Nat. Photon. 10, 489–496 (2016).

    Article  CAS  Google Scholar 

  15. Patel, R. N. et al. Single mode phononic wire. Phys. Rev. Lett. 121, 040501 (2018).

    Article  CAS  Google Scholar 

  16. Ren, H. et al. Two-dimensional optomechanical crystal cavity with high quantum cooperativity. Nat. Commun. 11, 3373 (2020).

    Article  Google Scholar 

  17. Gomis-Bresco, J. et al. A one-dimensional optomechanical crystal with a complete phononic band gap. Nat. Commun. 5, 4452 (2014).

    Article  CAS  Google Scholar 

  18. Mohammadi, S., Eftekhar, A. A., Khelif, A., Hunt, W. D. & Adibi, A. Evidence of large high frequency complete phononic band gaps in silicon phononic crystal plates. Appl. Phys. Lett. 92, 221905 (2008).

    Article  Google Scholar 

  19. Soliman, Y. M. et al. Phononic crystals operating in the gigahertz range with extremely wide band gaps. Appl. Phys. Lett. 97, 193502 (2010).

    Article  Google Scholar 

  20. Gorisse, M. et al. Observation of band gaps in the gigahertz range and deaf bands in a hypersonic aluminum nitride phononic crystal slab. Appl. Phys. Lett. 98, 234103 (2011).

    Article  Google Scholar 

  21. Benchabane, S. et al. Guidance of surface waves in a micron-scale phononic crystal line-defect waveguide. Appl. Phys. Lett. 106, 081903 (2015).

    Article  Google Scholar 

  22. Otsuka, P. H. et al. Broadband evolution of phononic-crystal-waveguide eigenstates in real- and k-spaces. Sci. Rep. 3, 3351 (2013).

    Article  CAS  Google Scholar 

  23. Cheng, W., Wang, J., Jonas, U., Fytas, G. & Stefanou, N. Observation and tuning of hypersonic bandgaps in colloidal crystals. Nat. Mater. 5, 830–836 (2006).

    Article  CAS  Google Scholar 

  24. Graczykowski, B. et al. Phonon dispersion in hypersonic two-dimensional phononic crystal membranes. Phys. Rev. B 91, 075414 (2015).

    Article  Google Scholar 

  25. Liu, Q., Li, H. & Li, M. Electromechanical Brillouin scattering in integrated optomechanical waveguides. Optica 6, 778–785 (2019).

    Article  CAS  Google Scholar 

  26. Söllner, I., Midolo, L. & Lodahl, P. Deterministic single-phonon source triggered by a single photon. Phys. Rev. Lett. 116, 234301 (2016).

    Article  Google Scholar 

  27. Arregui, G., Navarro-Urrios, D., Kehagias, N., SotomayorTorres, C. M. & García, P. D. All-optical radio-frequency modulation of Anderson-localized modes. Phys. Rev. B 98, 180202 (2018).

  28. COMSOL Multiphysics v.5.1 (COSMOL Inc., 2022).

  29. Safavi-Naeini, A. H. & Painter, O. Design of optomechanical cavities and waveguides on a simultaneous bandgap phononic-photonic crystal slab. Opt. Express 18, 14926–14943 (2010).

    Article  CAS  Google Scholar 

  30. Kargar, F. & Balandin, A. A. Advances in Brillouin–Mandelstam light-scattering spectroscopy. Nat. Photon. 15, 720–731 (2021).

    Article  CAS  Google Scholar 

  31. Carlotti, G. Elastic characterization of transparent and opaque films, multilayers and acoustic resonators by surface Brillouin scattering: a review. Appl. Sci. 8, 124 (2018).

    Article  Google Scholar 

  32. Boyd, R. W. Nonlinear Optics 3rd edn (Academic Press, 2008).

  33. Johnson, S. G. et al. Perturbation theory for Maxwell’s equations with shifting material boundaries. Phys. Rev. E 65, 066611 (2002).

    Article  Google Scholar 

  34. Van Laer, R., Kuyken, B., Van Thourhout, D. & Baets, R. Interaction between light and highly confined hypersound in a silicon photonic nanowire. Nat. Photon. 9, 199–203 (2015).

    Article  CAS  Google Scholar 

  35. Florez, O. et al. Brillouin scattering self-cancellation. Nat. Commun. 7, 11759 (2016).

    Article  CAS  Google Scholar 

  36. Cuffe, J. et al. Phonons in slow motion: dispersion relations in ultrathin Si membranes. Nano Lett. 12, 3569–3573 (2012).

    Article  CAS  Google Scholar 

  37. Brillouin, L. Diffusion de la lumière et des rayons X par un corps transparent homogène. Ann. Phys. 9, 88–122 (1922).

    Article  Google Scholar 

  38. Loudon, R. & Sandercock, J. R. Analysis of the light-scattering cross section for surface ripples on solids. J. Phys. C 13, 2609 (1980).

    Article  CAS  Google Scholar 

  39. Shin, H. et al. Control of coherent information via on-chip photonic-phononic emitter-receivers. Nat. Commun. 6, 6427 (2015).

    Article  CAS  Google Scholar 

  40. Gurlek, B., Sandoghdar, V. & Martin-Cano, D. Engineering long-lived vibrational states for an organic molecule. Phys. Rev. Lett. 127, 123603 (2021).

    Article  CAS  Google Scholar 

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This project has received funding from the European Union’s H2020 FET Proactive project TOCHA (No. 824140) and Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement (No. 754558). The ICN2 authors acknowledge funding from the Severo Ochoa programme from Spanish MINECO (No. SEV-2019-0706), Plan Nacional (RTI2018-093921-A-C44 - SMOOTH) and MCIN project SIP (PGC2018-101743-B-100), as well as by the CERCA Programme Generalitat de Catalunya. O.F. and G.A. are supported by BIST PhD Fellowships, R.C.N. by a Marie Sklodowska-Curie fellowship (No. 897148) and P.D.G. by a Ramon y Cajal fellowship (No. RyC-2015-18124). M.A. and S.S. gratefully acknowledge funding from the Villum Foundation Young Investigator Programme (No. 13170), the Danish National Research Foundation (No. DNRF147 – NanoPhoton), Innovation Fund Denmark (No. 0175-00022 – NEXUS) and Independent Research Fund Denmark (No. 0135-00315 – VAFL).

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Authors and Affiliations



O.F. designed, simulated and characterized the samples. M.A. and S.S. fabricated the samples. G.A., R.C.N. and J.G.-B. contributed to the data analysis. C.M.S.-T. and P.D.G. supervised the work. P.D.G. conceived the idea and the project. O.F. and P.D.G. wrote the manuscript with contributions and input from all authors.

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Correspondence to O. Florez or P. D. García.

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Nature Nanotechnology thanks Ilari Maasilta and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Figs. 1–11 and a Supplementary Discussion divided into five sections: Section 1. Crystal design, fabrication and characterization; Section 2. Numerical calculations; Section 3. Brillouin light scattering spectroscopy; Section 4. Scattering efficiency; Section 5. Spectral tunability.

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Florez, O., Arregui, G., Albrechtsen, M. et al. Engineering nanoscale hypersonic phonon transport. Nat. Nanotechnol. 17, 947–951 (2022).

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