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Topological triply degenerate point with double Fermi arcs


Unconventional chiral particles have recently been predicted to appear in certain three-dimensional crystal structures containing three- or more-fold linear band degeneracy points (BDPs)1,2,3,4. These BDPs carry topological charges, but are distinct from the standard twofold Weyl points or fourfold Dirac points, and cannot be described in terms of an emergent relativistic field theory1. Here we report on the experimental observation of a topological threefold BDP in a three-dimensional phononic crystal. Using direct acoustic field mapping, we demonstrate the existence of the threefold BDP in the bulk band structure, as well as doubled Fermi arcs of surface states consistent with a topological charge of 2. Another novel BDP, similar to a Dirac point but carrying non-zero topological charge, is connected to the threefold BDP via the doubled Fermi arcs. The Fermi arcs form double helicoids spanning a broad frequency range (relative bandwidth >25%). We show that the non-contractibility of these arcs gives rise to the phenomenon of topologically protected negative refraction of surface states on all surfaces of the sample. Our work paves the way to using these unconventional particles for exploring new emergent physical phenomena, and may find applications in symmetry-stabilized three-dimensional zero-index metamaterials.

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Fig. 1: 3D phononic crystal with a charge-2 triple point and a charge-2 quadruple point.
Fig. 2: Experimental observation of a charge-2 triple point and a charge-2 quadruple point.
Fig. 3: Experimental observation of the double-helicoid topological surface states.
Fig. 4: Negative refraction of topological surface states.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


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We thank H. S. Tan at Nanyang Technological University for helpful discussions. This work was sponsored by the Singapore Ministry of Education under grant numbers MOE2018-T2-1-022 (S), MOE2015-T2-1-070, MOE2015-T2-2-008, MOE2016-T3-1-006 and Tier 1 RG174/16 (S). H.-x.S. acknowledges support of the National Natural Science Foundation of China (11774137).

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Authors and Affiliations



All authors contributed extensively to this work. Y.Y. designed the phononic crystal and performed the simulations. Y.Y., H.X., Z.G., S.-q.Y. and H.-x.S. fabricated the sample and designed the experiments. H.-x.S., J.-p.X., Y.G. and D.J. performed measurements. Y.Y., Y.C. and B.Z. analysed data and wrote the paper. Y.C. and B.Z. supervised the project.

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Correspondence to Yidong Chong or Baile Zhang.

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The authors declare no competing interests.

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Supplementary text, Figs. 1–5 and references.

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Yang, Y., Sun, Hx., Xia, Jp. et al. Topological triply degenerate point with double Fermi arcs. Nat. Phys. 15, 645–649 (2019).

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