Observation of unconventional chiral fermions with long Fermi arcs in CoSi


Chirality—the geometric property of objects that do not coincide with their mirror image—is found in nature, for example, in molecules, crystals, galaxies and life forms. In quantum field theory, the chirality of a massless particle is defined by whether the directions of its spin and motion are parallel or antiparallel. Although massless chiral fermions—Weyl fermions—were predicted 90 years ago, their existence as fundamental particles has not been experimentally confirmed. However, their analogues have been observed as quasiparticles in condensed matter systems. In addition to Weyl fermions1,2,3,4, theorists have proposed a number of unconventional (that is, beyond the standard model) chiral fermions in condensed matter systems5,6,7,8, but direct experimental evidence of their existence is still lacking. Here, by using angle-resolved photoemission spectroscopy, we reveal two types of unconventional chiral fermion—spin-1 and charge-2 fermions—at the band-crossing points near the Fermi level in CoSi. The projections of these chiral fermions on the (001) surface are connected by giant Fermi arcs traversing the entire surface Brillouin zone. These chiral fermions are enforced at the centre or corner of the bulk Brillouin zone by the crystal symmetries, making CoSi a system with only one pair of chiral nodes with large separation in momentum space and extremely long surface Fermi arcs, in sharp contrast to Weyl semimetals, which have multiple pairs of Weyl nodes with small separation. Our results confirm the existence of unconventional chiral fermions and provide a platform for exploring the physical properties associated with chiral fermions.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Crystal structure and calculated electronic structure of CoSi.
Fig. 2: Fermi surfaces and band dispersions measured on the (111) surface.
Fig. 3: Fermi surfaces and band dispersions measured with soft X-rays on the (001) surface.
Fig. 4: Surface Fermi arcs measured with VUV light on the (001) surface.

Data availability

Materials and additional data related to this paper are available from the authors upon request.


  1. 1.

    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).

    ADS  Article  Google Scholar 

  2. 2.

    Weng, H., Fang, C., Fang, Z., Bernevig, B. A. & Dai, X. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides. Phys. Rev. X 5, 011029 (2015).

    Google Scholar 

  3. 3.

    Huang, S. M. et al. A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6, 7373 (2015).

    CAS  Article  Google Scholar 

  4. 4.

    Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

    ADS  CAS  Article  Google Scholar 

  5. 5.

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

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

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

    ADS  Article  Google Scholar 

  7. 7.

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

    ADS  Article  Google Scholar 

  8. 8.

    Pshenay-Severin, D. A., Ivanov, Y. V., Burkov, A. A. & Burkov, A. T. Band structure and unconventional electronic topology of CoSi. J. Phys. Condens. Matter 30, 135501 (2018).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Wang, Z. et al. Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb). Phys. Rev. B 85, 195320 (2012).

    ADS  Article  Google Scholar 

  10. 10.

    Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).

    ADS  CAS  Article  Google Scholar 

  11. 11.

    Wang, Z., Weng, H., Wu, Q., Dai, X. & Fang, Z. Three-dimensional Dirac semimetal and quantum transport in Cd3As2. Phys. Rev. B 88, 125427 (2013).

    ADS  Article  Google Scholar 

  12. 12.

    Heikkilä, T. T. & Volovik, G. E. Nexus and Dirac lines in topological materials. New J. Phys. 17, 093019 (2015).

    ADS  Article  Google Scholar 

  13. 13.

    Wieder, B. J., Kim, Y., Rappe, A. M. & Kane, C. L. Double Dirac semimetals in three dimensions. Phys. Rev. Lett. 116, 186402 (2016).

    ADS  Article  Google Scholar 

  14. 14.

    Weng, H., Fang, C., Fang, Z. & Dai, X. Topological semimetals with triply degenerate nodal points in θ-phase tantalum nitride. Phys. Rev. B 93, 241202 (2016).

    ADS  Article  Google Scholar 

  15. 15.

    Zhu, Z., Winkler, G. W., Wu, Q. S., Li, J. & Soluyanov, A. A. Triple point topological metals. Phys. Rev. X 6, 031003 (2016).

    Google Scholar 

  16. 16.

    Weng, H., Fang, C., Fang, Z. & Dai, X. Co-existence of Weyl fermion and massless triply degenerate nodal points. Phys. Rev. B 94, 165201 (2016).

    ADS  Article  Google Scholar 

  17. 17.

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

    Google Scholar 

  18. 18.

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

    ADS  CAS  Article  Google Scholar 

  19. 19.

    Deng, K. et al. Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2. Nat. Phys. 12, 1105 (2016).

    CAS  Article  Google Scholar 

  20. 20.

    Huang, L. et al. Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2. Nat. Mater. 15, 1155 (2016).

    ADS  CAS  Article  Google Scholar 

  21. 21.

    Liu, Z. K. et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864–867 (2014).

    ADS  CAS  Article  Google Scholar 

  22. 22.

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

    ADS  CAS  Article  Google Scholar 

  23. 23.

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

    CAS  Article  Google Scholar 

  24. 24.

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

    ADS  CAS  Article  Google Scholar 

  25. 25.

    Fang, C., Lu, L., Liu, J. & Fu, L. Topological semimetals with helicoid surface states. Nat. Phys. 12, 936–941 (2016).

    Article  Google Scholar 

  26. 26.

    Xu, S.-Y. et al. Observation of Fermi arc surface states in a topological metal. Science 347, 294–298 (2015).

    ADS  CAS  Article  Google Scholar 

  27. 27.

    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).

    ADS  CAS  Article  Google Scholar 

  28. 28.

    Qi, X.-L., Hughes, T. L. & Zhang, S.-C. Topological invariants for the Fermi surface of a time-reversal-invariant superconductor. Phys. Rev. B 81, 134508 (2010).

    ADS  Article  Google Scholar 

  29. 29.

    Dai, X., Lu, H.-Z., Shen, S.-Q. & Yao, H. Detecting monopole charge in Weyl semimetals via quantum interference transport. Phys. Rev. B 93, 161110 (2016).

    ADS  Article  Google Scholar 

  30. 30.

    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).

    ADS  Article  Google Scholar 

  31. 31.

    Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).

    ADS  MathSciNet  Article  Google Scholar 

  32. 32.

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

    ADS  CAS  Article  Google Scholar 

  33. 33.

    Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

    ADS  CAS  Article  Google Scholar 

  34. 34.

    Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847–12865 (1997).

    ADS  CAS  Article  Google Scholar 

  35. 35.

    CoSi crystal structure. Inorganic Solid Phases  https://materials.springer.com/isp/crystallographic/docs/sd_0378292 (Springer Materials, 2016).

Download references


We thank Y. Zhong and J. Guan for assistance with the RHEED measurements. We thank H. Yao, H. Lu and Z. Wang for discussions. We thank N. B. M. Schröter, A. Chikina and V. N. Strocov for assistance with the ARPES measurements at the SLS. This work was supported by the Ministry of Science and Technology of China (2016YFA0401000, 2015CB921000, 2016YFA0300600, 2016YFA0300504, 2016YFA0302400, 2018YFA0305700 and 2017YFA0302901), the National Natural Science Foundation of China (11622435, U1832202, 11474340, 11822412, 11574371, 11674369, 11574394, 11774423 and 11774399), the Chinese Academy of Sciences (QYZDB-SSW-SLH043, XDB07000000 and XDB28000000), the Science Challenge Project (TZ2016004), the K. C. Wong Education Foundation (GJTD-2018-01), the Beijing Natural Science Foundation (Z180008) and the Beijing Municipal Science and Technology Commission (Z171100002017018, Z181100004218005 and Z181100004218001). Y.H. acknowledges support by the CAS Pioneer Hundred Talents Program (type C). Z. Li acknowledges support by the National Postdoctoral Program for Innovative Talents (BX20170012).

Author information




T.Q. and Y. Sun supervised the project. Z.R., H. Li and T.Q. performed the ARPES measurements with the assistance of B.F., W.F., J.L. and Y.H.; Z.R., C.T. and Y. Sun processed the sample surfaces with the assistance of Z. Liu and Y.L.; T.Z. and H.W. performed ab initio calculations; S.T., C.L., H. Lei, L.W., Y. Shi and Z. Li synthesized the single crystals; Z.R, H. Li, T.Q. and Y. Sun analysed the experimental data; Z.R., T.Z., T.Q. and Y. Sun plotted the figures; T.Q., C.F. and H.D. wrote the manuscript.

Corresponding authors

Correspondence to Hechang Lei or Yujie Sun or Tian Qian.

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.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Rao, Z., Li, H., Zhang, T. et al. Observation of unconventional chiral fermions with long Fermi arcs in CoSi. Nature 567, 496–499 (2019). https://doi.org/10.1038/s41586-019-1031-8

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.