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Symmetry-driven artificial phononic media

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Abstract

Phonons are quasiparticles associated with mechanical vibrations in materials. They are at the root of the propagation of sound and elastic waves, as well as of thermal phenomena, which are pervasive in our everyday life and in many technologies. The fundamental understanding and control of phonon responses in natural and artificial media are key in the context of communications, isolation, energy harvesting and control, sensing and imaging. It has recently been realized that controlling different symmetry classes at the microscopic and mesoscopic scales in synthetic media offers a powerful tool to precisely tailor phononic responses for advanced acoustic and elastodynamic wave control. In this Review, we survey the recent progress in the design and synthesis of artificial phononic media, namely phononic crystals and metamaterials, guided by symmetry principles. Starting from tailored broken spatial symmetries, we discuss their interplay with time symmetries for non-reciprocal and non-conservative phenomena. We also address broader concepts that combine multiple symmetry classes to induce exotic phononic wave transport. We conclude with an outlook on future research directions based on symmetry engineering for the advanced control of phononic waves.

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Fig. 1: Symmetry-driven artificial phononic media.
Fig. 2: Phononic phenomena induced by breaking spatial symmetries.
Fig. 3: Phononic phenomena induced by breaking reciprocity, time-reversal and time-translation symmetry.
Fig. 4: Phononic phenomena induced by breaking energy conservation.
Fig. 5: Generalized symmetries within families of phononic media.

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Change history

  • 08 January 2026

    In the version of the article initially published, in the “Non-reciprocal continuum phononic media” section, “\({\mathop{W}\limits^{ \sim }}_{\mathrm{ij}}={W}_{\mathrm{ij}}\)” should have read “\({\mathop{W}\limits^{ \sim }}_{\mathrm{ij}}={W}_{\mathrm{ji}}\)” and has now been corrected in the HTML and PDF versions of the article.

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Acknowledgements

A.A. and S.Y. were supported by the National Science Foundation Science and Technology Center ‘New Frontiers of Sound’, the Department of Defense and the Simons Foundation. G.S. acknowledges funding by the European Union (ERC, EXCEPTIONAL, project no. 101045494). Views and opinions expressed are, however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. M.R.H. acknowledges support from Office of Naval Research under award no. N00014-23-1-2660. R.F. acknowledges funding by the Swiss National Science Foundation under the Eccellenza Award 181232. M.F. and V.V. acknowledge partial support from the France Chicago Center through a FACCTS grant. V.V. acknowledges partial support from the Army Research Office under grant W911NF-22-2-0109 and W911NF-23-1-0212, the National Science Foundation through the Center for Living Systems (grant no. 2317138), the National Institute for Theory and Mathematics in Biology, the Chan Zuckerberg Foundation and the Simons Foundation.

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Authors and Affiliations

  1. Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, USA

    Simon Yves, Gal Shmuel & Andrea Alù

  2. Gulliver, CNRS, ESPCI Paris, Université PSL, Paris, France

    Michel Fruchart

  3. Laboratory of Wave Engineering, EPFL, Lausanne, Switzerland

    Romain Fleury

  4. Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel

    Gal Shmuel

  5. James Franck Institute, University of Chicago, Chicago, IL, USA

    Vincenzo Vitelli

  6. Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, IL, USA

    Vincenzo Vitelli

  7. Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, TX, USA

    Michael R. Haberman

  8. Physics Program, Graduate Center, City University of New York, New York, NY, USA

    Andrea Alù

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  1. Simon Yves
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Contributions

All authors contributed substantially to the discussion of the content. A.A. and M.R.H. initiated the project. S.Y., M.F., R.F., G.S. and V.V. researched the data and wrote the respective sections of the article. All authors reviewed and edited the manuscript.

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Nature Reviews Materials thanks Guancong Ma, who co-reviewed with Xulong Wang; Baile Zhang; and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Yves, S., Fruchart, M., Fleury, R. et al. Symmetry-driven artificial phononic media. Nat Rev Mater (2025). https://doi.org/10.1038/s41578-025-00860-9

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