Realization of practical eightfold fermions and fourfold van Hove singularity in TaCo2Te2
Source abstract
Abstract
Abstract Space groups describing the symmetry of lattice structure allow the emergence of fermionic quasiparticles with various degeneracy in the band structure. Theoretical efforts have predicted many materials hosting fermions with the highest degeneracy, i.e., eightfold fermions, yet lacking experimental realization. Here, we explore the band degeneracies in TaCo 2 Te 2 crystals. Through systematic experimental and theoretical analyses, we establish TaCo 2 Te 2 as a nonsymmorphic crystal with negligible spin–orbit coupling (SOC) and long-range magnetic order. These critical properties guarantee the realization of practical eightfold fermions and fourfold van Hove singularity, as directly observed by photoemission spectroscopy. TaCo 2 Te 2 serves as a topological quantum critical platform, which can be tuned into various magnetic, topologically trivial, and nontrivial phases by adding strain, magnetic field, or SOC. The latter is demonstrated by our first-principles calculations, which show that enhancing SOC in TaCo 2 Te 2 will promote the experimental observation of bulk hourglass fermions. Our results establish TaCo 2 Te 2 as a platform to explore the interplay between symmetry and band topology.
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Research context
OpenAlex topics: Topological Materials and Phenomena · Advanced Condensed Matter Physics · 2D Materials and Applications
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References (74)
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1. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).10.1038/nature04233 ↗
2. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).10.1126/science.1102896 ↗
3. Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008).10.1038/nature06843 ↗
4. Chen, Y. L. et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178–181 (2009).10.1126/science.1173034 ↗
5. Hsieh, D. et al. A tunable topological insulator in the spin helical Dirac transport regime. Nature 460, 1101–1105 (2009).10.1038/nature08234 ↗
6. Xia, Y. et al. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nat. Phys. 5, 398–402 (2009).10.1038/nphys1274 ↗
7. Lv, B. Q. et al. Observation of Weyl nodes in TaAs. Nat. Phys. 11, 724–727 (2015).10.1038/nphys3426 ↗
8. Xu, S. Y. et al. Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide. Nat. Phys. 11, 748–754 (2015).10.1038/nphys3437 ↗
9. Xu, S. Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).10.1126/science.aaa9297 ↗
10. Xu, S. Y. et al. Observation of Fermi arc surface states in a topological metal. Science 347, 294–298 (2015).10.1126/science.1256742 ↗
11. Yang, L. X. et al. Weyl semimetal phase in the non-centrosymmetric compound TaAs. Nat. Phys. 11, 728–732 (2015).10.1038/nphys3425 ↗
12. Liu, Z. K. et al. A stable three-dimensional topological Dirac semimetal Cd3As2. Nat. Mater. 13, 677–681 (2014).10.1038/nmat3990 ↗
13. Liu, Z. K. et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864–867 (2014).10.1126/science.1245085 ↗
14. Alexandradinata, A., Wang, Z. & Bernevig, B. A. Topological insulators from group cohomology. Phys. Rev. X 6, 021008 (2016).
15. Bradlyn, B. et al. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353, aaf5037 (2016).10.1126/science.aaf5037 ↗
16. Huang, S. M. et al. New type of Weyl semimetal with quadratic double Weyl fermions. Proc. Natl Acad. Sci. USA 113, 1180–1185 (2016).10.1073/pnas.1514581113 ↗
17. Wang, Z., Alexandradinata, A., Cava, R. J. & Bernevig, B. A. Hourglass fermions. Nature 532, 189–194 (2016).10.1038/nature17410 ↗
18. 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).10.1103/PhysRevB.93.241202 ↗
19. Wieder, B. J., Kim, Y., Rappe, A. M. & Kane, C. L. Double Dirac semimetals in three dimensions. Phys. Rev. Lett. 116, 186402 (2016).10.1103/PhysRevLett.116.186402 ↗
20. Zhu, Z., Winkler, G. W., Wu, Q., Li, J. & Soluyanov, A. A. Triple point topological metals. Phys. Rev. X 6, 031003 (2016).
21. Liu, Q. & Zunger, A. Predicted realization of cubic Dirac fermion in quasi-one-dimensional transition-metal monochalcogenides. Phys. Rev. X 7, 021019 (2017).
22. Wieder, B. J. et al. Wallpaper fermions and the nonsymmorphic Dirac insulator. Science 361, 246–251 (2018).10.1126/science.aan2802 ↗
23. Wu, W., Yu, Z. M., Zhou, X., Zhao, Y. X. & Yang, S. A. Higher-order Dirac fermions in three dimensions. Phys. Rev. B 101, 205134 (2020).10.1103/PhysRevB.101.205134 ↗
24. Guo, P. J., Wei, Y. W., Liu, K., Liu, Z. X. & Lu, Z. Y. Eightfold degenerate fermions in two dimensions. Phys. Rev. Lett. 127, 176401 (2021).10.1103/PhysRevLett.127.176401 ↗
25. Cano, J., Bradlyn, B. & Vergniory, M. G. Multifold nodal points in magnetic materials. APL Mater. 7, 101125 (2019).10.1063/1.5124314 ↗
26. Schoop, L. M. et al. Tunable Weyl and Dirac states in the nonsymmorphic compound CeSbTe. Sci. Adv. 4, eaar2317 (2018).10.1126/sciadv.aar2317 ↗
27. Xu, C. Z. et al. Elemental topological Dirac semimetal: α-Sn on InSb(111). Phys. Rev. Lett. 118, 146402 (2017).10.1103/PhysRevLett.118.146402 ↗
28. Kumar, N. et al. Signatures of sixfold degenerate exotic fermions in a superconducting metal PdSb2. Adv. Mater. 32, e1906046 (2020).10.1002/adma.201906046 ↗
29. Sun, Z. P. et al. Direct observation of sixfold exotic fermions in the pyrite-structured topological semimetal PdSb2. Phys. Rev. B 101, 155114 (2020).10.1103/PhysRevB.101.155114 ↗
30. Yáng, X. et al. Observation of sixfold degenerate fermions in PdSb2. Phys. Rev. B 101, 201105 (2020).10.1103/PhysRevB.101.201105 ↗
31. Chapai, R. et al. Superconducting properties of the spin Hall candidate Ta3Sb with eightfold degeneracy. Phys. Rev. B 105, 184510 (2022).10.1103/PhysRevB.105.184510 ↗
32. Zhang, X. et al. Eightfold fermionic excitation in a charge density wave compound. Phys. Rev. B 102, 035125 (2020).10.1103/PhysRevB.102.035125 ↗
33. Berry, T., Pressley, L. A., Phelan, W. A., Tran, T. T. & McQueen, T. M. Laser-enhanced single crystal growth of non-symmorphic materials: applications to an eight-fold fermion candidate. Chem. Mater. 32, 5827–5834 (2020).10.1021/acs.chemmater.0c01721 ↗
34. Yuan, N. F. Q., Isobe, H. & Fu, L. Magic of high-order van Hove singularity. Nat. Commun. 10, 5769 (2019).10.1038/s41467-019-13670-9 ↗
35. Yuan, N. F. Q. & Fu, L. Classification of critical points in energy bands based on topology, scaling, and symmetry. Phys. Rev. B 101, 125120 (2020).10.1103/PhysRevB.101.125120 ↗
36. Singha, R. et al. TaCo2Te2: an air‐stable, high mobility Van der Waals material with probable magnetic order. Adv. Funct. Mater. 32, 2108920 (2021).10.1002/adfm.202108920 ↗
37. Wang, Q. et al. Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions. Nat. Commun. 9, 3681 (2018).10.1038/s41467-018-06088-2 ↗
38. Liu, E. et al. Giant anomalous Hall effect in a ferromagnetic Kagome-lattice semimetal. Nat. Phys. 14, 1125–1131 (2018).10.1038/s41567-018-0234-5 ↗
39. Bilbao Crystallographic Server. https://www.cryst.ehu.es/ (2023).
40. Ma, J. et al. Experimental evidence of hourglass fermion in the candidate nonsymmorphic topological insulator KHgSb. Sci. Adv. 3, e1602415 (2017).10.1126/sciadv.1602415 ↗
41. Wang, L., Jian, S.-K. & Yao, H. Hourglass semimetals with nonsymmorphic symmetries in three dimensions. Phys. Rev. B 96, 075110 (2017).10.1103/PhysRevB.96.075110 ↗
42. Li, S. et al. Nonsymmorphic-symmetry-protected hourglass Dirac loop, nodal line, and Dirac point in bulk and monolayer X3SiTe6 (X = Ta, Nb). Phys. Rev. B 97, 045131 (2018).10.1103/PhysRevB.97.045131 ↗
43. Weng, H. et al. Topological node-line semimetal in three-dimensional graphene networks. Phys. Rev. B 92, 045108 (2015).10.1103/PhysRevB.92.045108 ↗
44. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).10.1103/PhysRevB.54.11169 ↗
45. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758 (1999).10.1103/PhysRevB.59.1758 ↗
46. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953 (1994).10.1103/PhysRevB.50.17953 ↗
47. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).10.1103/PhysRevLett.77.3865 ↗
48. Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188 (1976).10.1103/PhysRevB.13.5188 ↗
49. Souza, I., Marzari, N. & Vanderbilt, D. Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001).10.1103/PhysRevB.65.035109 ↗
50. Pizzi, G. et al. Wannier90 as a community code: new features and applications. J. Phys. Condens. Matter 32, 165902 (2020).10.1088/1361-648X/ab51ff ↗
51. Wu, Q., Zhang, S., Song, H.-F., Troyer, M. & Soluyanov, A. A. WannierTools: an open-source software package for novel topological materials. Comput. Phys. Commun. 224, 405 (2018).10.1016/j.cpc.2017.09.033 ↗
52. Deng, K. et al. Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2. Nat. Phys. 12, 1105–1110 (2016).10.1038/nphys3871 ↗
53. Huang, L. et al. Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2. Nat. Mater. 15, 1155–1160 (2016).10.1038/nmat4685 ↗
54. Jiang, J. et al. Signature of type-II Weyl semimetal phase in MoTe2. Nat. Commun. 8, 13973 (2017).10.1038/ncomms13973 ↗
55. Xu, S. Y. et al. Discovery of Lorentz-violating type II Weyl fermions in LaAlGe. Sci. Adv. 3, e1603266 (2017).10.1126/sciadv.1603266 ↗
56. Belopolski, I. et al. Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points. Nat. Commun. 8, 942 (2017).10.1038/s41467-017-00938-1 ↗
57. Borisenko, S. et al. Time-reversal symmetry breaking type-II Weyl state in YbMnBi2. Nat. Commun. 10, 3424 (2019).10.1038/s41467-019-11393-5 ↗
58. Belopolski, I. et al. Discovery of topological Weyl fermion lines and drumhead surface states in a room temperature magnet. Science 365, 1278–1281 (2019).10.1126/science.aav2327 ↗
59. Liu, D. F. et al. Magnetic Weyl semimetal phase in a Kagomé crystal. Science 365, 1282–1285 (2019).10.1126/science.aav2873 ↗
60. Lv, B. Q. et al. Observation of three-component fermions in the topological semimetal molybdenum phosphide. Nature 546, 627–631 (2017).10.1038/nature22390 ↗
61. Ma, J. Z. et al. Three-component fermions with surface Fermi arcs in tungsten carbide. Nat. Phys. 14, 349–354 (2018).10.1038/s41567-017-0021-8 ↗
62. Li, Y. et al. Topological origin of the type-II Dirac fermions in PtSe2. Phys. Rev. Mater. 1, 074202 (2017).10.1103/PhysRevMaterials.1.074202 ↗
63. Zhang, K. et al. Experimental evidence for type-II Dirac semimetal in PtSe2. Phys. Rev. B 96, 125102 (2017).10.1103/PhysRevB.96.125102 ↗
64. Bahramy, M. S. et al. Ubiquitous formation of bulk Dirac cones and topological surface states from a single orbital manifold in transition-metal dichalcogenides. Nat. Mater. 17, 21–28 (2018).10.1038/nmat5031 ↗
65. Fei, F. et al. Nontrivial Berry phase and type-II Dirac transport in the layered material PdTe2. Phys. Rev. B 96, 041201 (2017).10.1103/PhysRevB.96.041201 ↗
66. Noh, H. J. et al. Experimental realization of type-II Dirac fermions in a PdTe2 Superconductor. Phys. Rev. Lett. 119, 016401 (2017).10.1103/PhysRevLett.119.016401 ↗
67. Yan, M. et al. Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe2. Nat. Commun. 8, 257 (2017).10.1038/s41467-017-00280-6 ↗
68. Miao, H. et al. Observation of double Weyl phonons in parity-breaking FeSi. Phys. Rev. Lett. 121, 035302 (2018).10.1103/PhysRevLett.121.035302 ↗
69. Rao, Z. et al. Observation of unconventional chiral fermions with long Fermi arcs in CoSi. Nature 567, 496–499 (2019).10.1038/s41586-019-1031-8 ↗
70. Sanchez, D. S. et al. Topological chiral crystals with helicoid-arc quantum states. Nature 567, 500–505 (2019).10.1038/s41586-019-1037-2 ↗
71. Schröter, N. B. M. et al. Chiral topological semimetal with multifold band crossings and long Fermi arcs. Nat. Phys. 15, 759–765 (2019).10.1038/s41567-019-0511-y ↗
72. 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).10.1103/PhysRevLett.122.076402 ↗
73. Schroter, N. B. M. et al. Observation and control of maximal Chern numbers in a chiral topological semimetal. Science 369, 179–183 (2020).10.1126/science.aaz3480 ↗
74. Lv, B. Q. et al. Observation of multiple types of topological fermions in PdBiSe. Phys. Rev. B 99, 241104 (2019).10.1103/PhysRevB.99.241104 ↗