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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Data supporting the results and conclusions are available at https://doi.org/10.5281/zenodo.6610862.
Krause, A. G., Winger, M., Blasius, T. D., Lin, Q. & Painter, O. A high-resolution microchip optomechanical accelerometer. Nat. Photon. 6, 768–772 (2012).
Chaste, J. et al. A nanomechanical mass sensor with yoctogram resolution. Nat. Nanotechnol. 7, 301–304 (2012).
Gavartin, E., Verlot, P. & Kippenberg, T. J. A hybrid on-chip optomechanical transducer for ultrasensitive force measurements. Nat. Nanotechnol. 7, 509–514 (2012).
Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011).
Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).
Sigalas, M. & Economou, E. N. Band structure of elastic waves in two dimensional systems. Solid State Commun. 86, 141–143 (1993).
Kushwaha, M. S., Halevi, P., Dobrzynski, L. & Djafari-Rouhani, B. Acoustic band structure of periodic elastic composites. Phys. Rev. Lett. 71, 2022 (1993).
Martínez-Sala, R. et al. Sound attenuation by sculpture. Nature 378, 241 (1995).
Gorishnyy, T., Ullal, C. K., Maldovan, M., Fytas, G. & Thomas, E. L. Hypersonic phononic crystals. Phys. Rev. Lett. 94, 115501 (2005).
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).
Eichenfield, M., Chan, J., Camacho, R. M., Vahala, K. J. & Painter, O. Optomechanical crystals. Nature 462, 78–82 (2009).
Djafari-Rouhani, B., El-Jallal, S. & Pennec, Y. Phoxonic crystals and cavity optomechanics. C. R. Phys. 17, 555–564 (2016).
MacCabe, G. S. et al. Nano-acoustic resonator with ultralong phonon lifetime. Science 370, 840–843 (2020).
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).
Patel, R. N. et al. Single mode phononic wire. Phys. Rev. Lett. 121, 040501 (2018).
Ren, H. et al. Two-dimensional optomechanical crystal cavity with high quantum cooperativity. Nat. Commun. 11, 3373 (2020).
Gomis-Bresco, J. et al. A one-dimensional optomechanical crystal with a complete phononic band gap. Nat. Commun. 5, 4452 (2014).
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).
Soliman, Y. M. et al. Phononic crystals operating in the gigahertz range with extremely wide band gaps. Appl. Phys. Lett. 97, 193502 (2010).
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).
Benchabane, S. et al. Guidance of surface waves in a micron-scale phononic crystal line-defect waveguide. Appl. Phys. Lett. 106, 081903 (2015).
Otsuka, P. H. et al. Broadband evolution of phononic-crystal-waveguide eigenstates in real- and k-spaces. Sci. Rep. 3, 3351 (2013).
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).
Graczykowski, B. et al. Phonon dispersion in hypersonic two-dimensional phononic crystal membranes. Phys. Rev. B 91, 075414 (2015).
Liu, Q., Li, H. & Li, M. Electromechanical Brillouin scattering in integrated optomechanical waveguides. Optica 6, 778–785 (2019).
Söllner, I., Midolo, L. & Lodahl, P. Deterministic single-phonon source triggered by a single photon. Phys. Rev. Lett. 116, 234301 (2016).
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).
COMSOL Multiphysics v.5.1 (COSMOL Inc., 2022).
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).
Kargar, F. & Balandin, A. A. Advances in Brillouin–Mandelstam light-scattering spectroscopy. Nat. Photon. 15, 720–731 (2021).
Carlotti, G. Elastic characterization of transparent and opaque films, multilayers and acoustic resonators by surface Brillouin scattering: a review. Appl. Sci. 8, 124 (2018).
Boyd, R. W. Nonlinear Optics 3rd edn (Academic Press, 2008).
Johnson, S. G. et al. Perturbation theory for Maxwell’s equations with shifting material boundaries. Phys. Rev. E 65, 066611 (2002).
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).
Florez, O. et al. Brillouin scattering self-cancellation. Nat. Commun. 7, 11759 (2016).
Cuffe, J. et al. Phonons in slow motion: dispersion relations in ultrathin Si membranes. Nano Lett. 12, 3569–3573 (2012).
Brillouin, L. Diffusion de la lumière et des rayons X par un corps transparent homogène. Ann. Phys. 9, 88–122 (1922).
Loudon, R. & Sandercock, J. R. Analysis of the light-scattering cross section for surface ripples on solids. J. Phys. C 13, 2609 (1980).
Shin, H. et al. Control of coherent information via on-chip photonic-phononic emitter-receivers. Nat. Commun. 6, 6427 (2015).
Gurlek, B., Sandoghdar, V. & Martin-Cano, D. Engineering long-lived vibrational states for an organic molecule. Phys. Rev. Lett. 127, 123603 (2021).
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).
The authors declare no competing interests.
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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). https://doi.org/10.1038/s41565-022-01178-1
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