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.
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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).
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).
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).
Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).
Bradlyn, B. et al. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353, aaf5037 (2016).
Tang, P., Zhou, Q. & Zhang, S.-C. Multiple types of topological fermions in transition metal silicides. Phys. Rev. Lett. 119, 206402 (2017).
Chang, G. et al. Unconventional chiral fermions and large topological Fermi arcs in RhSi. Phys. Rev. Lett. 119, 206401 (2017).
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).
Wang, Z. et al. Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb). Phys. Rev. B 85, 195320 (2012).
Young, S. M. et al. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108, 140405 (2012).
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).
Heikkilä, T. T. & Volovik, G. E. Nexus and Dirac lines in topological materials. New J. Phys. 17, 093019 (2015).
Wieder, B. J., Kim, Y., Rappe, A. M. & Kane, C. L. Double Dirac semimetals in three dimensions. Phys. Rev. Lett. 116, 186402 (2016).
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).
Zhu, Z., Winkler, G. W., Wu, Q. S., Li, J. & Soluyanov, A. A. Triple point topological metals. Phys. Rev. X 6, 031003 (2016).
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).
Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).
Deng, K. et al. Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2. Nat. Phys. 12, 1105 (2016).
Huang, L. et al. Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2. Nat. Mater. 15, 1155 (2016).
Liu, Z. K. et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864–867 (2014).
Lv, B. Q. et al. Observation of three-component fermions in the topological semimetal molybdenum phosphide. Nature 546, 627–631 (2017).
Ma, J.-Z. et al. Three-component fermions with surface Fermi arcs in tungsten carbide. Nat. Phys. 14, 349–354 (2018).
Zhang, T. et al. Double-Weyl phonons in transition-metal monosilicides. Phys. Rev. Lett. 120, 016401 (2018).
Fang, C., Lu, L., Liu, J. & Fu, L. Topological semimetals with helicoid surface states. Nat. Phys. 12, 936–941 (2016).
Xu, S.-Y. et al. Observation of Fermi arc surface states in a topological metal. Science 347, 294–298 (2015).
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).
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).
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).
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).
Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
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).
Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847–12865 (1997).
CoSi crystal structure. Inorganic Solid Phases https://materials.springer.com/isp/crystallographic/docs/sd_0378292 (Springer Materials, 2016).
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).
The authors declare no competing interests.
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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
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