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Observation of a phononic higher-order Weyl semimetal

Nature Materials volume 20, pages 794–799 (2021)Cite this article

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Abstract

Weyl semimetals (WSMs)1 exhibit phenomena such as Fermi arc surface states, pseudo-gauge fields and quantum anomalies that arise from topological band degeneracy in crystalline solids for electrons1 and metamaterials for photons2 and phonons3. Here we report a higher-order Weyl semimetal (HOWSM) in a phononic system that exhibits topologically protected boundary states in multiple dimensions. We created the physical realization of the HOWSM in a chiral phononic crystal with uniaxial screw symmetry. Using acoustic pump–probe spectroscopies, we observed coexisting chiral Fermi arc states on two-dimensional surfaces and dispersive hinge arc states on one-dimensional hinge boundaries. These topological boundary states link the projections of the Weyl points (WPs) in different dimensions and directions, and hence demonstrate the higher-order topological physics4,5,6,7,8 in WSMs. Our study further establishes the fundamental connection between higher-order topology and Weyl physics in crystalline materials and should stimulate further work on other potential materials, such as higher-order topological nodal-line semimetals.

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Fig. 1: WSMs and HOWSMs.
Fig. 2: A phononic HOWSM.
Fig. 3: Topological surface states of the HOWSM.
Fig. 4: Higher-order hinge arc states.

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Data availability

All data are available in the main text and the Supplementary Information. Additional information is available from the corresponding authors upon reasonable request.

Code availability

We used the commercial software COMSOL MULTIPHYSICS to perform the acoustic wave simulations and eigenstates calculations. Requests for the computation details can be addressed to the corresponding authors.

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Acknowledgements

Z.-K.L., B.J. and J.-H.J. are supported by the National Natural Science Foundation of China (Grant no. 12074281) and Jiangsu Province Specially-Appointed Professor Funding. H.-X.W. is supported by the National Natural Science Foundation of China (Grant no. 11904060). L.L., Y.W. and F.L. are supported by the Natural Science Foundation of Guangdong Province (no. 2020A1515010549) and China Postdoctoral Science Foundation (no. 2020M672615).

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Author notes

  1. These authors contributed equally: Li Luo, Hai-Xiao Wang, Zhi-Kang Lin.

Authors and Affiliations

  1. School of Physics and Optoelectronics, South China University of Technology, Guangzhou, China

    Li Luo & Ying Wu

  2. School of Physical Science and Technology, and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou, China

    Hai-Xiao Wang, Zhi-Kang Lin, Bin Jiang & Jian-Hua Jiang

  3. School of Physical Science and Technology, Guangxi Normal University, Guilin, China

    Hai-Xiao Wang

  4. School of Physics, Beijing Institute of Technology, Beijing, China

    Feng Li

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  1. Li Luo
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Contributions

J.-H.J. initiated the project. J.-H.J. and F.L. guided the research. J.-H.J., H.-X.W., B.J. and Z.-K.L. established the theory. H.-X.W. and L.L. performed the numerical calculations and simulations. L.L., Y.W., J.-H.J. and F.L. designed and achieved the experimental set-up and the measurements. All the authors contributed to the discussions of the results and the manuscript preparation. J.-H.J., H.-X.W., Z.K.L. and F.L. wrote the manuscript and the Supplementary Information.

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Correspondence to Feng Li or Jian-Hua Jiang.

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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.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–20 and Notes 1–9.

Supplementary Video 1

We show the propagation of the hinge states dynamically in the video.

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Luo, L., Wang, HX., Lin, ZK. et al. Observation of a phononic higher-order Weyl semimetal. Nat. Mater. 20, 794–799 (2021). https://doi.org/10.1038/s41563-021-00985-6

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