Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Observation of three-component fermions in the topological semimetal molybdenum phosphide

Abstract

In quantum field theory, Lorentz invariance leads to three types of fermion—Dirac, Weyl and Majorana. Although the existence of Weyl and Majorana fermions as elementary particles in high-energy physics is debated, all three types of fermion have been proposed to exist as low-energy, long-wavelength quasiparticle excitations in condensed-matter systems1,2,3,4,5,6,7,8,9,10,11,12. The existence of Dirac and Weyl fermions in condensed-matter systems has been confirmed experimentally13,14,15,16,17,18, and that of Majorana fermions is supported by various experiments19,20. However, in condensed-matter systems, fermions in crystals are constrained by the symmetries of the 230 crystal space groups rather than by Lorentz invariance, giving rise to the possibility of finding other types of fermionic excitation that have no counterparts in high-energy physics21,22,23,24,25,26,27,28,29. Here we use angle-resolved photoemission spectroscopy to demonstrate the existence of a triply degenerate point in the electronic structure of crystalline molybdenum phosphide. Quasiparticle excitations near a triply degenerate point are three-component fermions, beyond the conventional Dirac–Weyl–Majorana classification, which attributes Dirac and Weyl fermions to four- and two-fold degenerate points, respectively. We also observe pairs of Weyl points in the bulk electronic structure of the crystal that coexist with the three-component fermions. This material thus represents a platform for studying the interplay between different types of fermions. Our experimental discovery opens up a way of exploring the new physics of unconventional fermions in condensed-matter systems.

This is a preview of subscription content

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Crystal structure and band structure of MoP along the Γ–A line in the Brillouin zone.
Figure 2: Overall electronic structure of MoP in the three-dimensional Brillouin zone of the bulk.
Figure 3: Electronic structure near TP1.
Figure 4: Electronic structure near the Weyl points.

References

  1. 1

    Castro Neto, A. H. et al. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008)

    ADS  Article  Google Scholar 

  3. 3

    Lutchyn, R. M., Sau, J. D. & Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010)

    ADS  Article  Google Scholar 

  4. 4

    Oreg, Y., Refael, G. & Von Oppen, F. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010)

    ADS  Article  Google Scholar 

  5. 5

    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 

  6. 6

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

    ADS  CAS  Article  Google Scholar 

  7. 7

    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 

  8. 8

    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 

  9. 9

    Xu, G., Weng, H., Wang, Z., Dai, X. & Fang, Z. Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4 . Phys. Rev. Lett. 107, 186806 (2011)

    ADS  Article  Google Scholar 

  10. 10

    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 

  11. 11

    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)

    ADS  CAS  Article  Google Scholar 

  12. 12

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

    ADS  CAS  Article  Google Scholar 

  13. 13

    Liu, Z. K. et al. A stable three-dimensional topological Dirac semimetal Cd3As2 . Nat. Mater. 13, 677–681 (2014)

    ADS  CAS  Article  Google Scholar 

  14. 14

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

    ADS  CAS  Article  Google Scholar 

  15. 15

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

    Google Scholar 

  16. 16

    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 

  17. 17

    Lv, B. Q. et al. Observation of Weyl nodes in TaAs. Nat. Phys. 11, 724–727 (2015)

    Article  Google Scholar 

  18. 18

    Yang, L. X. et al. Weyl semimetal phase in the non-centrosymmetric compound TaAs. Nat. Phys. 11, 728–732 (2015)

    CAS  Article  Google Scholar 

  19. 19

    Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003–1007 (2012)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014)

    ADS  CAS  Article  Google Scholar 

  21. 21

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

    ADS  Article  Google Scholar 

  22. 22

    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 

  23. 23

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

    MathSciNet  Article  Google Scholar 

  24. 24

    Winkler, G. W., Wu, Q., Troyer, M., Krogstrup, P. & Soluyanov, A. A. Topological phases in InAs1−xSbx: from novel topological semimetal to Majorana wire. Phys. Rev. Lett. 117, 076403 (2016)

    ADS  Article  Google Scholar 

  25. 25

    Hyart, T. & Heikkilä, T. T. Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines. Phys. Rev. B 93, 235147 (2016)

    ADS  Article  Google Scholar 

  26. 26

    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 

  27. 27

    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 

  28. 28

    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 

  29. 29

    Chang, G. et al. New fermions on the line in topological symmorphic metals. Preprint at https://arXiv.org/abs/1605.06831 (2016)

  30. 30

    Strocov, V. N. et al. Three-dimensional electron realm in VSe2 by soft X-ray photoelectron spectroscopy: origin of charge-density waves. Phys. Rev. Lett. 109, 086401 (2012)

    ADS  Article  Google Scholar 

  31. 31

    Strocov, V. N. et al. Soft-X-ray ARPES facility at the ADRESS beamline of the SLS: concepts, technical realisation and scientific applications. J. Synchrotron Radiat. 21, 32–44 (2014)

    CAS  Article  Google Scholar 

  32. 32

    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 

  33. 33

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

Download references

Acknowledgements

We thank B.-B. Fu, N. Xu and A. Chikina for assistance with the ARPES experiments. We thank Y. Shao and Y.-L. Wang for examining the topography of the (100) cleavage surface using scanning tunnelling microscopy, although the results are not shown. This work was supported by the National Natural Science Foundation of China (11622435, 11474330, 11422428, 11674369, 11474340, 11674371 and 11234014), the Ministry of Science and Technology of China (2016YFA0401000, 2016YFA0300600, 2015CB921300, 2013CB921700, 2016YFA0302400 and 2016YFA0300300) and the Chinese Academy of Sciences (XDB07000000). Y.-B.H. acknowledges support by the CAS Pioneer ‘Hundred Talents Program’ (type C).

Author information

Affiliations

Authors

Contributions

H.D. and T.Q. conceived the experiments; B.Q.L., X.G. and T.Q. performed the ARPES measurements with assistance from J.-Z.M., L.-Y.K., Y.-B.H. and V.N.S.; Q.-N.X. and H.-M.W. performed the ab initio calculations; B.Q.L., T.Q. and H.D. analysed the experimental data; B.Q.L., Q.-N.X. and T.Q. made the figures; T.Q., C.F., H.D., B.Q.L. and P.R. wrote the manuscript; and Z.-L.F. and Y.-G.S. synthesized the single crystals.

Corresponding authors

Correspondence to Y.-G. Shi, T. Qian or H. Ding.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks P. Hosur, A. Soluyanov 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.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Lv, B., Feng, ZL., Xu, QN. et al. Observation of three-component fermions in the topological semimetal molybdenum phosphide. Nature 546, 627–631 (2017). https://doi.org/10.1038/nature22390

Download citation

Comments

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.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing