Skip to main content
SpringerLink
Log in

Topological triply degenerate point with double Fermi arcs

  • Letter
  • Published:

From Nature Physics

View current issue Submit your manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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.

Similar content being viewed by others

Data availability

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

References

  1. Bradlyn, B. et al. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353, aaf5037 (2016).

    Article  MathSciNet  Google Scholar 

  2. Zhang, T. et al. Double-Weyl phonons in transition-metal monosilicides. Phys. Rev. Lett. 120, 016401 (2018).

    Article  ADS  Google Scholar 

  3. Chang, G. et al. Unconventional chiral Fermions and large topological Fermi arcs in RhSi. Phys. Rev. Lett. 119, 206401 (2017).

    Article  ADS  Google Scholar 

  4. Tang, P., Zhou, Q. & Zhang, S.-C. Multiple types of topological fermions in transition metal silicides. Phys. Rev. Lett. 119, 206402 (2017).

    Article  ADS  Google Scholar 

  5. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    Article  ADS  Google Scholar 

  6. Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).

    Article  ADS  Google Scholar 

  7. Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).

    Article  ADS  Google Scholar 

  8. Lu, L. et al. Experimental observation of Weyl points. Science 349, 622–624 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  9. Lv, B. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).

    Google Scholar 

  10. Xiao, M., Chen, W.-J., He, W.-Y. & Chan, C. T. Synthetic gauge flux and Weyl points in acoustic systems. Nat. Phys. 11, 920–924 (2015).

    Article  Google Scholar 

  11. Noh, J. et al. Experimental observation of optical Weyl points and Fermi arc-like surface states. Nat. Phys. 13, 611–617 (2017).

    Article  Google Scholar 

  12. Armitage, N., Mele, E. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  13. Yang, B. et al. Ideal Weyl points and helicoid surface states in artificial photonic crystal structures. Science 359, 1013–1016 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  14. Li, F., Huang, X., Lu, J., Ma, J. & Liu, Z. Weyl points and Fermi arcs in a chiral phononic crystal. Nat. Phys. 14, 30–34 (2018).

    Article  Google Scholar 

  15. Kargarian, M., Randeria, M. & Lu, Y.-M. Are the surface Fermi arcs in Dirac semimetals topologically protected? Proc. Natl Acad. Sci. USA 113, 8648–8652 (2016).

    Article  ADS  Google Scholar 

  16. Fang, C., Gilbert, M. J., Dai, X. & Bernevig, B. A. Multi-Weyl topological semimetals stabilized by point group symmetry. Phys. Rev. Lett. 108, 266802 (2012).

    Article  ADS  Google Scholar 

  17. Huang, S.-M. et al. New type of Weyl semimetal with quadratic double Weyl fermions. Proc. Natl Acad. Sci. USA 113, 1180–1185 (2016).

    Article  ADS  Google Scholar 

  18. Chen, W. J., Xiao, M. & Chan, C. T. Photonic crystals possessing multiple Weyl points and the experimental observation of robust surface states. Nat. Commun. 7, 13038 (2016).

    Article  ADS  Google Scholar 

  19. Manes, J. L. Existence of bulk chiral fermions and crystal symmetry. Phys. Rev. B 85, 155118 (2012).

    Article  ADS  Google Scholar 

  20. Lv, B. et al. Observation of three-component fermions in the topological semimetal molybdenum phosphide. Nature 546, 627–631 (2017).

    Article  ADS  Google Scholar 

  21. Ma, J.-Z. et al. Three-component fermions with surface Fermi arcs in tungsten carbide. Nat. Phys. 14, 349–354 (2018).

    Article  Google Scholar 

  22. Miao, H. et al. Observation of double Weyl phonons in parity-breaking FeSi. Phys. Rev. Lett. 121, 035302 (2018).

    Article  ADS  Google Scholar 

  23. Yu, R., Qi, X. L., Bernevig, A., Fang, Z. & Dai, X. Equivalent expression of Z2 topological invariant for band insulators using the non-Abelian Berry connection. Phys. Rev. B 84, 075119 (2011).

    Article  ADS  Google Scholar 

  24. Nielsen, H. B. & Ninomiya, M. A no-go theorem for regularizing chiral fermions. Phys. Lett. B 105, 219–223 (1981).

    Article  ADS  Google Scholar 

  25. He, H. et al. Topological negative refraction of surface acoustic waves in a Weyl phononic crystal. Nature 560, 61–64 (2018).

    Article  ADS  Google Scholar 

  26. Jia, H. et al. Observation of chiral zero mode in inhomogeneous three-dimensional Weyl metamaterials. Science 363, 148–151 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  27. Peri, V., Serra-Garcia, M., Ilan, R. & Huber, S. D. Axial-field-induced chiral channels in an acoustic Weyl system. Nat. Phys. https://doi.org/10.1038/s41567-019-0415-x (2019).

    Article  ADS  Google Scholar 

  28. Saba, M., Hamm, J. M., Baumberg, J. J. & Hess, O. Group theoretical route to deterministic Weyl points in chiral photonic lattices. Phys. Rev. Lett. 119, 227401 (2017).

    Article  ADS  Google Scholar 

  29. Huang, X., Lai, Y., Hang, Z. H., Zheng, H. & Chan, C. Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nat. Mater. 10, 582–586 (2011).

    Article  ADS  Google Scholar 

  30. Sanchez, D. S. et al. Topological chiral crystals with helicoid-arc quantum states. Nature 567, 500–505 (2019).

    Article  ADS  Google Scholar 

  31. Schröter, N. et al. Topological semimetal in a chiral crystal with large Chern numbers, multifold band crossings, and long Fermi-arcs. Preprint at https://arxiv.org/abs/1812.03310 (2018).

  32. Rao, Z.-C. et al. Observation of unconventional chiral fermions with long Fermi arcs in CoSi. Nature 567, 496–499 (2019).

    Article  ADS  Google Scholar 

  33. Takane, D. et al. Observation of chiral fermions with a large topological charge and associated Fermi-arc surface states in CoSi. Phys. Rev. Lett. 122, 076402 (2019).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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).

Author information

Author notes

  1. These authors contributed equally: Yihao Yang, Hong-xiang Sun.

Authors and Affiliations

  1. Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Yihao Yang, Haoran Xue, Zhen Gao, Yidong Chong & Baile Zhang

  2. Centre for Disruptive Photonic Technologies, The Photonics Institute, Nanyang Technological University, Singapore, Singapore

    Yihao Yang, Haoran Xue, Zhen Gao, Yidong Chong & Baile Zhang

  3. Research Center of Fluid Machinery Engineering and Technology, Faculty of Science, Jiangsu University, Zhenjiang, China

    Hong-xiang Sun, Jian-ping Xia, Yong Ge, Ding Jia & Shou-qi Yuan

Authors
  1. Yihao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong-xiang Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jian-ping Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Haoran Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zhen Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Yong Ge
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Ding Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Shou-qi Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Yidong Chong
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Baile Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Corresponding authors

Correspondence to Yidong Chong or Baile Zhang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary text, Figs. 1–5 and references.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, Y., Sun, Hx., Xia, Jp. et al. Topological triply degenerate point with double Fermi arcs. Nat. Phys. 15, 645–649 (2019). https://doi.org/10.1038/s41567-019-0502-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-019-0502-z

  • Springer Nature Limited

This article is cited by

Search

Navigation