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Higher-order topological semimetal in acoustic crystals

Abstract

The notion of higher-order topological insulators has endowed materials with topological states beyond the first order. Particularly, a three-dimensional (3D) higher-order topological insulator can host topologically protected 1D hinge states, referred to as the second-order topological insulator, or 0D corner states, referred to as the third-order topological insulator. Similarly, a 3D higher-order topological semimetal can be envisaged if it hosts states on the 1D hinges. Here we report the realization of a second-order topological Weyl semimetal in a 3D-printed acoustic crystal, which possesses Weyl points in 3D momentum space, 2D Fermi arc states on surfaces and 1D gapless states on hinges. Like the arc surface states, the hinge states also connect the projections of the Weyl points. Our experimental results evidence the existence of the higher-order topological semimetal, which may pave the way towards innovative acoustic devices.

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Fig. 1: SOTSM for a 3D stacked breathing kagomé lattice.
Fig. 2: 3D acoustic crystal with Weyl points and Fermi arcs.
Fig. 3: Hinge state and acoustic pressure fields.
Fig. 4: Hinge states and response spectra for different structural parameters.

Data availability

Owing to their larger size, the data represented in Fig. 3 and Supplementary Fig. 10 are available on Zenodo at https://zenodo.org/record/4441748#.YAFkdznisuV. Source data are provided with this paper.

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Acknowledgements

This work is supported by the National Key R & D Program of China (Grant no. 2017YFA0304203), the National Natural Science Foundation of China (Grant nos 11890701, 11674200, 11704128, 11774275, 11804101, 11974120, 11974005, 12034012, 12074128, and 12074232) and the Shanxi ‘1331 Project’ Key Subjects Construction.

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Contributions

G.C., Z.L. and S.J. conceived the idea. Q.W. and X.Z. calculated the theoretical results, designed the experiments and carried out the numerical simulations. Q.W., X.Z. and M.Y. performed the experiments. W.D., J.L. and X.H. guided the experimental measurement and analysed the experimental data. G.C. and Z.L. supervised the project. All the authors contributed to the preparation of the manuscript.

Corresponding authors

Correspondence to Gang Chen or Zhengyou Liu.

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The authors declare no competing interests.

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Peer review information Nature Materials thanks Alexander Khanikaev and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

Supplementary information

Supplementary Information

Supplementary Sections I–VIII and Figs. 1–13.

Source data

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Source Data Fig. 2

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Source Data Fig. 4

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Supplementary Data 1

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Supplementary Data 2

Source Data for Supplementary Fig. 2.

Supplementary Data 3

Source Data for Supplementary Fig. 3.

Supplementary Data 4

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Supplementary Data 5

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Supplementary Data 6

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Supplementary Data 7

Source Data for Supplementary Fig. 7.

Supplementary Data 8

Source Data for Supplementary Fig. 9.

Supplementary Data 9

Source Data for Supplementary Fig. 12.

Supplementary Data 10

Source Data for Supplementary Fig. 13.

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Wei, Q., Zhang, X., Deng, W. et al. Higher-order topological semimetal in acoustic crystals. Nat. Mater. 20, 812–817 (2021). https://doi.org/10.1038/s41563-021-00933-4

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