Topological Mechanical Metamaterials Revealed By Higher-order Coordinate Transformations

Résumé : 

The field of condensed matter physics has advanced considerably with the recent discovery of topological quantum matter, including topological insulating and superconducting materials. Many topological phenomena have also moved from the quantum to the classical domain1,2. Either in quantum or classical topological matter, the bulk-boundary correspondence is a central concept which associates a non-trivial bulk topology of the material with the existence of localized topological states at its boundaries.

In particular for finite-frequency mechanical metamaterials3, the bulk-boundary correspondence has so far been described in terms of displacements, which requires fixed boundaries to support topologically protected edge modes. Here4, we present a new family of finite-frequency mechanical metamaterials whose topological properties emerge in deformation coordinates and for free boundaries. We present two examples, the first being the canonical mass-dimer, for which the bulk-boundary correspondence in deformation coordinates reveals the previously unknown topological origin of its edge modes. Second, we present a new mechanical analog of the Kitaev chain. We show theoretically and experimentally that this mechanical chain supports edge states for both free and fixed boundaries, where the bulk-boundary correspondence is established in deformations and displacements, respectively. Our results suggest the existence of a class of topological edge modes not previously discovered for more complex and tailored boundaries.

References

1. T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys. 91, 015006 (2019).
2. R. Susstrunk and S. D. Huber, Classification of topological phonons in linear mechanical metamaterials, Proc. Natl. Acad. Sci. USA 113, EA767 (2016).
3. S. D. Huber, Topological mechanics, Nat. Phys. 12, 621 (2016); Y. Barlas and E. Prodan, Topological classification table implemented with classical passive metamaterials, Phys.Rev. B 98 , 094310 (2018).
4. F. Allein, A. Anastasiadis, R. Chaunsali, I. Frank, N. Boechler, F. Diakonos, G. Theocharis, Strain Topological Metamaterials and revealing hidden topology in higher-order coordinates, Nature Communications 14, 6633 (2023)

Le 12 décembre 2023  à 11h00 / Amphithéâtre François Canac, LMA

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