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


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.

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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.

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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).

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Authors and Affiliations



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.

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

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks P. Hosur, A. Soluyanov and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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

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