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Annual Review of Materials Research

Volume 49, 2019

Topological Semimetals from First Principles

Abstract

We review recent theoretical progress in the understanding and prediction of novel topological semimetals. Topological semimetals define a class of gapless electronic phases exhibiting topologically stable crossings of energy bands. Different types of topological semimetals can be distinguished on the basis of the degeneracy of the band crossings, their codimension (e.g., point or line nodes), and the crystal space group symmetries on which the protection of stable band crossings relies. The dispersion near the band crossing is a further discriminating characteristic. These properties give rise to a wide range of distinct semimetal phases such as Dirac or Weyl semimetals, point or line node semimetals, and type I or type II semimetals. In this review we give a general description of various families of topological semimetals, with an emphasis on proposed material realizations from first-principles calculations. The conceptual framework for studying topological gapless electronic phases is reviewed, with a particular focus on the symmetry requirements of energy band crossings, and the relation between the different families of topological semimetals is elucidated. In addition to the paradigmatic Dirac and Weyl semimetals, we pay particular attention to more recent examples of topological semimetals, which include nodal line semimetals, multifold fermion semimetals, and triple-point semimetals. Less emphasis is placed on their surface state properties, their responses to external probes, and recent experimental developments.

Keyword(s): Dirac fermions, first-principles calculations, material prediction, multifold band crossings, nodal line semimetals, topological semimetals, Weyl fermions
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/content/journals/10.1146/annurev-matsci-070218-010049
2019-07-01
2024-04-25
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Literature Cited

  1. 1.
    Hasan MZ, Kane CL 2010. Topological insulators. Rev. Mod. Phys. 82:3045–67
     [Google Scholar]
  2. 2.
    Qi XL, Zhang SC 2011. Topological insulators and superconductors. Rev. Mod. Phys. 83:1057–110
     [Google Scholar]
  3. 3.
    Armitage NP, Mele EJ, Vishwanath A 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90:015001
     [Google Scholar]
  4. 4.
    Young SM, Zaheer S, Teo JCY, Kane CL, Mele EJ, Rappe AM 2012. Dirac semimetal in three dimensions. Phys. Rev. Lett. 108:140405
     [Google Scholar]
  5. 5.
    Wang Z, Sun Y, Chen XQ, Franchini C, Xu G et al. 2012. Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb). Phys. Rev. B 85:195320
     [Google Scholar]
  6. 6.
    Wan X, Turner AM, Vishwanath A, Savrasov SY 2011. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83:205101
     [Google Scholar]
  7. 7.
    Weng H, Fang C, Fang Z, Bernevig BA, Dai X 2015. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides. Phys. Rev. X 5:011029
     [Google Scholar]
  8. 8.
    Hořava P 2005. Stability of Fermi surfaces and theory. Phys. Rev. Lett. 95:016405
     [Google Scholar]
  9. 9.
    Heikkilä TT, Volovik GE 2011. Dimensional crossover in topological matter: evolution of the multiple Dirac point in the layered system to the flat band on the surface. JETP Lett. 93:59–65
     [Google Scholar]
  10. 10.
    Burkov A, Hook M, Balents L 2011. Topological nodal semimetals. Phys. Rev. B 84:235126
     [Google Scholar]
  11. 11.
    Soluyanov AA, Gresch D, Wang Z, Wu Q, Troyer M et al. 2015. Type-II Weyl semimetals. Nature 527:495–98
     [Google Scholar]
  12. 12.
    Wieder BJ, Kim Y, Rappe AM, Kane CL 2016. Double Dirac semimetals in three dimensions. Phys. Rev. Lett. 116:186402
     [Google Scholar]
  13. 13.
    Bradlyn B, Cano J, Wang Z, Vergniory M, Felser C et al. 2016. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353:aaf5037
     [Google Scholar]
  14. 14.
    Zhu Z, Winkler GW, Wu Q, Li J, Soluyanov AA 2016. Triple point topological metals. Phys. Rev. X 6:031003
     [Google Scholar]
  15. 15.
    Weng H, Fang C, Fang Z, Dai X 2016. Topological semimetals with triply degenerate nodal points in -phase tantalum nitride. Phys. Rev. B 93:241202
     [Google Scholar]
  16. 16.
    Chang G, Xu SY, Huang SM, Sanchez DS, Hsu CH et al. 2017. Nexus fermions in topological symmorphic crystalline metals. Sci. Rep. 7:1688
     [Google Scholar]
  17. 17.
    Wieder BJ 2018. Threes company. Nat. Phys. 14:329–30
     [Google Scholar]
  18. 18.
    Jeon S, Zhou BB, Gyenis A, Feldman BE, Kimchi I et al. 2014. Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal CdAs. Nat. Mater. 13:851–56
     [Google Scholar]
  19. 19.
    Feng J, Pang Y, Wu D, Wang Z, Weng H et al. 2015. Large linear magnetoresistance in Dirac semimetal Cd3As2 with Fermi surfaces close to the Dirac points. Phys. Rev. B 92:081306
     [Google Scholar]
  20. 20.
    Zhang C, Xu SY, Belopolski I, Yuan Z, Lin Z 2015. Observation of the Adler-Bell-Jackiw chiral anomaly in a Weyl semimetal. arXiv:1503.02630 [cond-mat.mes-hall]
    [Google Scholar]
  21. 21.
    Huang X, Zhao L, Long Y, Wang P, Chen D et al. 2015. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5:031023
     [Google Scholar]
  22. 22.
    Wang Y, Liu E, Liu H, Pan Y, Zhang L et al. 2016. Gate-tunable negative longitudinal magnetoresistance in the predicted Type-II Weyl semimetal WTe2. Nat. Commun. 7:13142
     [Google Scholar]
  23. 23.
    Rajamathi CR, Gupta U, Kumar N, Yang H, Sun Y et al. 2017. Weyl semimetals as hydrogen evolution catalysts. Adv. Mater. 29:1606202
     [Google Scholar]
  24. 24.
    Li J, Ma H, Xie Q, Feng S, Ullah S et al. 2018. Topological quantum catalyst: Dirac nodal line states and a potential electrocatalyst of hydrogen evolution in the TiSi family. Sci. China Mater. 61:23–29
     [Google Scholar]
  25. 25.
    Nayak C, Simon SH, Stern A, Freedman M, Das Sarma S 2008. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80:1083–159
     [Google Scholar]
  26. 26.
    Yang SA 2016. Dirac and Weyl materials: fundamental aspects and some spintronics applications. SPIN 6:1640003
     [Google Scholar]
  27. 27.
    Herring C 1937. Accidental degeneracy in the energy bands of crystals. Phys. Rev. 52:365–73
     [Google Scholar]
  28. 28.
    Yang BJ, Morimoto T, Furusaki A 2015. Topological charges of three-dimensional Dirac semimetals with rotation symmetry. Phys. Rev. B 92:165120
     [Google Scholar]
  29. 29.
    Yu R, Qi XL, Bernevig A, Fang Z, Dai X 2011. Equivalent expression of topological invariant for band insulators using the non-Abelian Berry connection. Phys. Rev. B 84:075119
     [Google Scholar]
  30. 30.
    Bansil A, Lin H, Das T 2016. Topological band theory. Rev. Mod. Phys. 88:021004
     [Google Scholar]
  31. 31.
    Yu R, Fang Z, Dai X, Weng H 2017. Topological nodal line semimetals predicted from first-principles calculations. Front. Phys. 12:127202
     [Google Scholar]
  32. 32.
    Hirayama M, Okugawa R, Murakami S 2018. Topological semimetals studied by ab initio calculations. J. Phys. Soc. Jpn. 87:041002
     [Google Scholar]
  33. 33.
    Huang SM, Xu SY, Belopolski I, Lee CC, Chang G et al. 2015. A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6:7373
     [Google Scholar]
  34. 34.
    Lv B, Feng ZL, Xu QN, Gao X, Ma JZ et al. 2017. Observation of three-component fermions in the topological semimetal molybdenum phosphide. Nature 546:627–31
     [Google Scholar]
  35. 35.
    Ma JZ, He JB, Xu YF, Lv B, Chen D et al. 2018. Three-component fermions with surface Fermi arcs in tungsten carbide. Nat. Phys. 14:349–54
     [Google Scholar]
  36. 36.
    Neupane M, Belopolski I, Hosen MM, Sanchez DS, Sankar R et al. 2016. Observation of topological nodal fermion semimetal phase in ZrSiS. Phys. Rev. B 93:201104
     [Google Scholar]
  37. 37.
    Mostofi AA, Yates JR, Lee YS, Souza I, Vanderbilt D, Marzari N 2008. wannier90: a tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178:685–99
     [Google Scholar]
  38. 38.
    Wu Q, Zhang S, Song HF, Troyer M, Soluyanov AA 2018. WannierTools: an open-source software package for novel topological materials. Comput. Phys. Commun. 224:405–16
     [Google Scholar]
  39. 39.
    Gresch D, Autes G, Yazyev OV, Troyer M, Vanderbilt D et al. 2017. Z2Pack: numerical implementation of hybrid Wannier centers for identifying topological materials. Phys. Rev. B 95:075146
     [Google Scholar]
  40. 40.
    Turner AM, Vishwanath A, Head CO 2013. Beyond band insulators: topology of semimetals and interacting phases. Topol. Insul. 6:293–324
     [Google Scholar]
  41. 41.
    Wehling T, Black-Schaffer AM, Balatsky AV 2014. Dirac materials. Adv. Phys. 63:1–76
     [Google Scholar]
  42. 42.
    Vafek O, Vishwanath A 2014. Dirac fermions in solids: from high-T cuprates and graphene to topological insulators and Weyl semimetals. Annu. Rev. Condens. Matter Phys. 5:83–112
     [Google Scholar]
  43. 43.
    Hasan MZ, Xu SY, Bian G 2015. Topological insulators, topological superconductors and Weyl fermion semimetals: discoveries, perspectives and outlooks. Phys. Scr. 2015:014001
     [Google Scholar]
  44. 44.
    Weng H, Dai X, Fang Z 2016. Topological semimetals predicted from first-principles calculations. J. Phys. Condens. Matter 28:303001
     [Google Scholar]
  45. 45.
    Fang C, Weng H, Dai X, Fang Z 2016. Topological nodal line semimetals. Chin. Phys. B 25:117106
     [Google Scholar]
  46. 46.
    Jia S, Xu SY, Hasan MZ 2016. Weyl semimetals, Fermi arcs and chiral anomalies. Nat. Mater. 15:1140–44
     [Google Scholar]
  47. 47.
    Yan B, Felser C 2017. Topological materials: Weyl semimetals. Annu. Rev. Condens. Matter Phys. 8:337–54
     [Google Scholar]
  48. 48.
    Hasan MZ, Xu SY, Belopolski I, Huang SM 2017. Discovery of Weyl fermion semimetals and topological Fermi arc states. Annu. Rev. Condens. Matter Phys. 8:289–309
     [Google Scholar]
  49. 49.
    Yang SY, Yang H, Derunova E, Parkin SS, Yan B, Ali MN 2018. Symmetry demanded topological nodal-line materials. Adv. Phys. X 3:1414631
     [Google Scholar]
  50. 50.
    Burkov A 2018. Weyl metals. Annu. Rev. Condens. Matter Phys. 9:359–78
     [Google Scholar]
  51. 51.
    Schoop LM, Pielnhofer F, Lotsch BV 2018. Chemical principles of topological semimetals. Chem. Mater. 30:3155–76
     [Google Scholar]
  52. 52.
    Bernevig A, Weng H, Fang Z, Dai X 2018. Recent progress in the study of topological semimetals. J. Phys. Soc. Jpn. 87:041001
     [Google Scholar]
  53. 53.
    Murakami S 2007. Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase. New J. Phys. 9:356
     [Google Scholar]
  54. 54.
    Neto AHC, Guinea F, Peres NMR, Novoselov KS, Geim AK 2009. The electronic properties of graphene. Rev. Mod. Phys. 81:109–62
     [Google Scholar]
  55. 55.
    Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y et al. 2004. Electric field effect in atomically thin carbon films. Science 306:666–69
     [Google Scholar]
  56. 56.
    Weng H, Dai X, Fang Z 2014. Transition-metal pentatelluride ZrTe5 and HfTe5: a paradigm for large-gap quantum spin Hall insulators. Phys. Rev. X 4:011002
     [Google Scholar]
  57. 57.
    Gibson QD, Schoop LM, Muechler L, Xie LS, Hirschberger M et al. 2015. Three-dimensional Dirac semimetals: design principles and predictions of new materials. Phys. Rev. B 91:205128
     [Google Scholar]
  58. 58.
    Manzoni G, Gragnaniello L, Autès G, Kuhn T, Sterzi A et al. 2016. Evidence for a strong topological insulator phase in . Phys. Rev. Lett. 117:237601
     [Google Scholar]
  59. 59.
    Li Q, Kharzeev DE, Zhang C, Huang Y, Pletikosić I et al. 2016. Chiral magnetic effect in ZrTe5. Nat. Phys. 12:550–54
     [Google Scholar]
  60. 60.
    Zhang Y, Wang C, Yu L, Liu G, Liang A et al. 2017. Electronic evidence of temperature-induced Lifshitz transition and topological nature in ZrTe5. Nat. Commun. 8:15512
     [Google Scholar]
  61. 61.
    Mutch J, Chen WC, Went P, Qian T, Wilson IZ 2018. Evidence for a strain tuned topological phase transition in ZrTe5. arXiv:1808.07898 [cond-mat.str-el]
    [Google Scholar]
  62. 62.
    Kane CL, Mele EJ 2005. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95:226801
     [Google Scholar]
  63. 63.
    Young SM, Kane CL 2015. Dirac semimetals in two dimensions. Phys. Rev. Lett. 115:126803
     [Google Scholar]
  64. 64.
    Zaheer S 2014.Three dimensional Dirac semimetals PhD thesis, Univ. Penn.
  65. 65.
    Steinberg JA, Young SM, Zaheer S, Kane CL, Mele EJ, Rappe AM 2014. Bulk Dirac points in distorted spinels. Phys. Rev. Lett. 112:036403
     [Google Scholar]
  66. 66.
    Wang Z, Weng H, Wu Q, Dai X, Fang Z 2013. Three-dimensional Dirac semimetal and quantum transport in CdAs. Phys. Rev. B 88:125427
     [Google Scholar]
  67. 67.
    Du Y, Wan B, Wang D, Sheng L, Duan CG, Wan X 2015. Dirac and Weyl semimetal in Bi (X = Ba, Eu; = Cu, Ag and Au). Sci. Rep. 5:14423
     [Google Scholar]
  68. 68.
    Cao W, Tang P, Xu Y, Wu J, Gu BL, Duan W 2017. Dirac semimetal phase in hexagonal LiZnBi. Phys. Rev. B 96:115203
     [Google Scholar]
  69. 69.
    Yang BJ, Nagaosa N 2014. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nat. Commun. 5:4898
     [Google Scholar]
  70. 70.
    Liu Z, Zhou B, Zhang Y, Wang Z, Weng H et al. 2014. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343:864–67
     [Google Scholar]
  71. 71.
    Liu Z, Jiang J, Zhou B, Wang Z, Zhang Y et al. 2014. A stable three-dimensional topological Dirac semimetal CdAs. Nat. Mater. 13:677–81
     [Google Scholar]
  72. 72.
    Gao Z, Hua M, Zhang H, Zhang X 2016. Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetry. Phys. Rev. B 93:205109
     [Google Scholar]
  73. 73.
    Chen C, Wang SS, Liu L, Yu ZM, Sheng XL et al. 2017. Ternary wurtzite CaAgBi materials family: a playground for essential and accidental, type-I and type-II Dirac fermions. Phys. Rev. Mater. 1:044201
     [Google Scholar]
  74. 74.
    Gao H, Kim Y, Venderbos JWF, Kane CL, Mele EJ et al. 2018. Dirac-Weyl semimetal: coexistence of Dirac and Weyl fermions in polar hexagonal crystals. Phys. Rev. Lett. 121:106404
     [Google Scholar]
  75. 75.
    Liu Q, Zunger A 2017. Predicted realization of cubic Dirac fermion in quasi-one-dimensional transition-metal monochalcogenides. Phys. Rev. X 7:021019
     [Google Scholar]
  76. 76.
    Tang P, Zhou Q, Xu G, Zhang SC 2016. Dirac fermions in an antiferromagnetic semimetal. Nat. Phys. 12:1100–4
     [Google Scholar]
  77. 77.
    Young SM, Wieder BJ 2017. Filling-enforced magnetic Dirac semimetals in two dimensions. Phys. Rev. Lett. 118:186401
     [Google Scholar]
  78. 78.
    Wang J 2017. Magnetic Dirac semimetals in three dimensions. arXiv:1701.00896 [cond-mat.mes-hall]
    [Google Scholar]
  79. 79.
    Watanabe H, Po HC, Vishwanath A 2018. Structure and topology of band structures in the 1651 magnetic space groups. Sci. Adv. 4:eaat8685
     [Google Scholar]
  80. 80.
    Hua G, Nie S, Song Z, Yu R, Xu G, Yao K 2018. Dirac semimetal in type IV magnetic space group. arXiv:1801.02806 [cond-mat.mtrl-sci]
    [Google Scholar]
  81. 81.
    Schoop LM, Topp A, Lippmann J, Orlandi F, Müchler L et al. 2018. Tunable Weyl and Dirac states in the nonsymmorphic compound CeSbTe. Sci. Adv. 4:eaar2317
     [Google Scholar]
  82. 82.
    Nielsen HB, Ninomiya M 1983. The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal. Phys. Lett. B 130:389–96
     [Google Scholar]
  83. 83.
    Xu G, Weng H, Wang Z, Dai X, Fang Z 2011. Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4. Phys. Rev. Lett. 107:186806
     [Google Scholar]
  84. 84.
    Wang Z, Vergniory M, Kushwaha S, Hirschberger M, Chulkov E et al. 2016. Time-reversal-breaking Weyl fermions in magnetic Heusler alloys. Phys. Rev. Lett. 117:236401
     [Google Scholar]
  85. 85.
    Chang G, Xu SY, Zheng H, Singh B, Hsu CH et al. 2016. Room-temperature magnetic topological Weyl fermion and nodal line semimetal states in half-metallic Heusler Co2TiX (X = Si, Ge, or Sn). Sci. Rep. 6:38839
     [Google Scholar]
  86. 86.
    Yang H, Sun Y, Zhang Y, Shi WJ, Parkin SS, Yan B 2017. Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn. New J. Phys. 19:015008
     [Google Scholar]
  87. 87.
    Xu Q, Liu E, Shi W, Muechler L, Gayles J et al. 2018. Topological surface Fermi arcs in the magnetic Weyl semimetal Co3Sn2S2. Phys. Rev. B 97:235416
     [Google Scholar]
  88. 88.
    Nayak AK, Fischer JE, Sun Y, Yan B, Karel J et al. 2016. Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn3Ge. Sci. Adv. 2:e1501870
     [Google Scholar]
  89. 89.
    Kiyohara N, Tomita T, Nakatsuji S 2016. Giant anomalous Hall effect in the chiral antiferromagnet Mn3Ge. Phys. Rev. Appl. 5:064009
     [Google Scholar]
  90. 90.
    Liu E, Sun Y, Kumar N, Muechler L, Sun A et al. 2018. Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal. Nat. Phys. 14:1125–31
     [Google Scholar]
  91. 91.
    Wang Q, Xu Y, Lou R, Liu Z, Li M et al. 2018. Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions. Nat. Commun. 9:3681
     [Google Scholar]
  92. 92.
    Burkov A, Balents L 2011. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107:127205
     [Google Scholar]
  93. 93.
    Zhang H, Wang J, Xu G, Xu Y, Zhang SC 2014. Topological states in ferromagnetic CdO/EuO superlattices and quantum wells. Phys. Rev. Lett. 112:096804
     [Google Scholar]
  94. 94.
    Liu J, Vanderbilt D 2014. Weyl semimetals from noncentrosymmetric topological insulators. Phys. Rev. B 90:155316
     [Google Scholar]
  95. 95.
    Zyuzin AA, Wu S, Burkov AA 2012. Weyl semimetal with broken time reversal and inversion symmetries. Phys. Rev. B 85:165110
     [Google Scholar]
  96. 96.
    Halász GB, Balents L 2012. Time-reversal invariant realization of the Weyl semimetal phase. Phys. Rev. B 85:035103
     [Google Scholar]
  97. 97.
    Xu SY, Alidoust N, Belopolski I, Yuan Z, Bian G et al. 2015. Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide. Nat. Phys. 11:748–54
     [Google Scholar]
  98. 98.
    Xu SY, Belopolski I, Alidoust N, Neupane M, Bian G et al. 2015. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349:613–17
     [Google Scholar]
  99. 99.
    Lv B, Weng H, Fu B, Wang X, Miao H et al. 2015. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5:031013
     [Google Scholar]
  100. 100.
    Lv B, Xu N, Weng H, Ma J, Richard P et al. 2015. Observation of Weyl nodes in TaAs. Nat. Phys. 11:724–27
     [Google Scholar]
  101. 101.
    Yang L, Liu Z, Sun Y, Peng H, Yang H et al. 2015. Weyl semimetal phase in the non-centrosymmetric compound TaAs. Nat. Phys. 11:728–32
     [Google Scholar]
  102. 102.
    Bernevig BA 2015. It's been a Weyl coming. Nat. Phys. 11:698–99
     [Google Scholar]
  103. 103.
    Ruan J, Jian SK, Zhang D, Yao H, Zhang H et al. 2016. Ideal Weyl semimetals in the chalcopyrites , , , and . Phys. Rev. Lett. 116:226801
     [Google Scholar]
  104. 104.
    Autes G, Gresch D, Troyer M, Soluyanov AA, Yazyev OV 2016. Robust type-II Weyl semimetal phase in transition metal diphosphides XP2 (X = Mo, W). Phys. Rev. Lett. 117:066402
     [Google Scholar]
  105. 105.
    Chang G, Xu SY, Sanchez DS, Huang SM, Lee CC et al. 2016. A strongly robust type II Weyl fermion semimetal state in Ta3S2. Sci. Adv. 2:e1600295
     [Google Scholar]
  106. 106.
    Koepernik K, Kasinathan D, Efremov D, Khim S, Borisenko S et al. 2016. TaIrTe4: a ternary type-II Weyl semimetal. Phys. Rev. B 93:201101
     [Google Scholar]
  107. 107.
    Wang Z, Gresch D, Soluyanov AA, Xie W, Kushwaha S et al. 2016. MoTe2: a type-II Weyl topological metal. Phys. Rev. Lett. 117:056805
     [Google Scholar]
  108. 108.
    Chang G, Wieder BJ, Schindler F, Sanchez DS, Belopolski I et al. 2018. Topological quantum properties of chiral crystals. Nat. Mater. 17:978–85
     [Google Scholar]
  109. 109.
    Morimoto T, Zhong S, Orenstein J, Moore JE 2016. Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals. Phys. Rev. B 94:245121
     [Google Scholar]
  110. 110.
    de Juan F, Grushin AG, Morimoto T, Moore JE 2017. Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun. 8:15995
     [Google Scholar]
  111. 111.
    Wu L, Patankar S, Morimoto T, Nair NL, Thewalt E et al. 2017. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13:350–55
     [Google Scholar]
  112. 112.
    Ma Q, Xu SY, Chan CK, Zhang CL, Chang G et al. 2017. Direct optical detection of Weyl fermion chirality in a topological semimetal. Nat. Phys. 13:842–47
     [Google Scholar]
  113. 113.
    Yang X, Burch K, Ran Y 2017. Divergent bulk photovoltaic effect in Weyl semimetals. arXiv:1712.09363 [cond-mat.mes-hall]
    [Google Scholar]
  114. 114.
    Flicker F, de Juan F, Bradlyn B, Morimoto T, Vergniory MG, Grushin AG 2018. Chiral optical response of multifold fermions. arXiv:1806.09642 [cond-mat.mes-hall]
    [Google Scholar]
  115. 115.
    Huang H, Zhou S, Duan W 2016. Type-II Dirac fermions in the PtSe2 class of transition metal dichalcogenides. Phys. Rev. B 94:121117
     [Google Scholar]
  116. 116.
    Xu SY, Alidoust N, Chang G, Lu H, Singh B 2016. Discovery of Lorentz-violating Weyl fermion semimetal state in LaAlGe materials. arXiv:1603.07318 [cond-mat.mes-hall]
    [Google Scholar]
  117. 117.
    Chang TR, Xu SY, Sanchez DS, Tsai WF, Huang SM et al. 2017. Type-II symmetry–protected topological Dirac semimetals. Phys. Rev. Lett. 119:026404
     [Google Scholar]
  118. 118.
    Fang C, Gilbert MJ, Dai X, Bernevig BA 2012. Multi-Weyl topological semimetals stabilized by point group symmetry. Phys. Rev. Lett. 108:266802
     [Google Scholar]
  119. 119.
    Huang SM, Xu SY, Belopolski I, Lee CC, Chang G et al. 2016. New type of Weyl semimetal with quadratic double Weyl fermions. PNAS 113:1180–85
     [Google Scholar]
  120. 120.
    Fang C, Chen Y, Kee HY, Fu L 2015. Topological nodal line semimetals with and without spin-orbital coupling. Phys. Rev. B 92:081201
     [Google Scholar]
  121. 121.
    He J, Kong X, Wang W, Kou SP 2018. Type-II nodal line semimetal. New J. Phys. 20:053019
     [Google Scholar]
  122. 122.
    Kim D, Ahn S, Jung JH, Min H, Ihm J et al. 2018. Type-II Dirac line node in strained Na3N. Phys. Rev. Mater. 2:104203
     [Google Scholar]
  123. 123.
    Bzdušek T, Wu Q, Rüegg A, Sigrist M, Soluyanov AA 2016. Nodal-chain metals. Nature 538:75–78
     [Google Scholar]
  124. 124.
    Kim Y, Wieder BJ, Kane CL, Rappe AM 2015. Dirac line nodes in inversion-symmetric crystals. Phys. Rev. Lett. 115:036806
     [Google Scholar]
  125. 125.
    Fu L, Kane CL, Mele EJ 2007. Topological insulators in three dimensions. Phys. Rev. Lett. 98:106803
     [Google Scholar]
  126. 126.
    Fu L, Kane CL 2007. Topological insulators with inversion symmetry. Phys. Rev. B 76:045302
     [Google Scholar]
  127. 127.
    Teo JCY, Kane CL 2010. Topological defects and gapless modes in insulators and superconductors. Phys. Rev. B 82:115120
     [Google Scholar]
  128. 128.
    Zhao J, Yu R, Weng H, Fang Z 2016. Topological node-line semimetal in compressed black phosphorus. Phys. Rev. B 94:195104
     [Google Scholar]
  129. 129.
    Xu N, Qian YT, Wu QS, Autès G, Matt CE 2018. Trivial topological phase of CaAgP and the topological nodal-line transition in CaAg(). Phys. Rev. B 97:161111(R)
     [Google Scholar]
  130. 130.
    Volovik GE 2015. From standard model of particle physics to room-temperature superconductivity. Phys. Scr. T164:014014
     [Google Scholar]
  131. 131.
    Heikkilä TT, Volovik GE 2016. Flat bands as a route to high-temperature superconductivity in graphite. Basic Physics of Functionalized Graphite P Esquinazi123–43 Cham, Switz.: Springer Int.
     [Google Scholar]
  132. 132.
    Yu R, Weng H, Fang Z, Dai X, Hu X 2015. Topological node-line semimetal and Dirac semimetal state in antiperovskite . Phys. Rev. Lett. 115:036807
     [Google Scholar]
  133. 133.
    Mikitik GP, Sharlai YV 1999. Manifestation of Berry's phase in metal physics. Phys. Rev. Lett. 82:2147–50
     [Google Scholar]
  134. 134.
    Mikitik GP, Sharlai YV 2006. Band-contact lines in the electron energy spectrum of graphite. Phys. Rev. B 73:235112
     [Google Scholar]
  135. 135.
    Schoop LM, Ali MN, Straßer C, Topp A, Varykhalov A et al. 2016. Dirac cone protected by non-symmorphic symmetry and three-dimensional Dirac line node in ZrSiS. Nat. Commun. 7:11696
     [Google Scholar]
  136. 136.
    Hu J, Tang Z, Liu J, Liu X, Zhu Y et al. 2016. Evidence of topological nodal-line fermions in ZrSiSe and ZrSiTe. Phys. Rev. Lett. 117:016602
     [Google Scholar]
  137. 137.
    Hosen MM, Dimitri K, Aperis A, Maldonado P, Belopolski I 2018. Observation of gapless Dirac surface states in ZrGeTe. Phys. Rev. B 97:121103(R)
     [Google Scholar]
  138. 138.
    Hosen MM, Dhakal G, Dimitri K, Maldonado P, Aperis A et al. 2018. Discovery of topological nodal-line fermionic phase in a magnetic material GdSbTe. Sci. Rep. 8:13283
     [Google Scholar]
  139. 139.
    Zhang X, Yu ZM, Sheng XL, Yang HY, Yang SA 2017. Coexistence of four-band nodal rings and triply degenerate nodal points in centrosymmetric metal diborides. Phys. Rev. B 95:235116
     [Google Scholar]
  140. 140.
    Yi CJ, Lv BQ, Wu QS, Fu BB, Gao X 2018. Observation of a nodal chain with Dirac surface states in TiB2. Phys. Rev. B 97:201107(R)
     [Google Scholar]
  141. 141.
    Chang T-R, Pletikosic I, Kong T, Bian G, Huang A 2017. Realization of a type-II nodal-line semimetal in Mg3Bi2. arXiv:1711.09167 [cond-mat.mtrl-sci]
    [Google Scholar]
  142. 142.
    Li K, Li C, Hu J, Li Y, Fang C 2017. Dirac and nodal line magnons in three-dimensional antiferromagnets. Phys. Rev. Lett. 119:247202
     [Google Scholar]
  143. 143.
    Song Z, Zhang T, Fang C 2018. Diagnosis for nonmagnetic topological semimetals in the absence of spin-orbital coupling. Phys. Rev. X 8:031069
     [Google Scholar]
  144. 144.
    Morimoto T, Furusaki A 2014. Weyl and Dirac semimetals with topological charge. Phys. Rev. B 89:235127
     [Google Scholar]
  145. 145.
    Zhao YX, Lu Y 2017. -symmetric real Dirac fermions and semimetals. Phys. Rev. Lett. 118:056401
     [Google Scholar]
  146. 146.
    Ahn J, Kim D, Kim Y, Yang BJ 2018. Band topology and linking structure of nodal line semimetals with monopole charges. Phys. Rev. Lett. 121:106403
     [Google Scholar]
  147. 147.
    Nomura T, Habe T, Sakamoto R, Koshino M 2018. Three-dimensional graphdiyne as a topological nodal-line semimetal. Phys. Rev. Mater. 2:054204
     [Google Scholar]
  148. 148.
    Yamakage A, Yamakawa Y, Tanaka Y, Okamoto Y 2016. Line-node Dirac semimetal and topological insulating phase in noncentrosymmetric pnictides CaAgX (X = P, As). J. Phys. Soc. Jpn. 85:013708
     [Google Scholar]
  149. 149.
    Nayak J, Kumar N, Wu SC, Shekhar C, Fink J et al. 2018. Electronic properties of topological insulator candidate CaAgAs. J. Phys. Condens. Matter 30:045501
     [Google Scholar]
  150. 150.
    Takane D, Nakayama K, Souma S, Wada T, Okamoto Y et al. 2018. Observation of Dirac-like energy band and ring-torus Fermi surface associated with the nodal line in topological insulator CaAgAs. NPJ Quant. Mater. 3:1
     [Google Scholar]
  151. 151.
    Sun JP 2017. Topological nodal line semimetal in non-centrosymmetric PbTaS2. Chin. Phys. Lett. 34:077101
     [Google Scholar]
  152. 152.
    Okamoto Y, Inohara T, Yamakage A, Yamakawa Y, Takenaka K 2016. Low carrier density metal realized in candidate line-node Dirac semimetals CaAgP and CaAgAs. J. Phys. Soc. Jpn. 85:123701
     [Google Scholar]
  153. 153.
    Xu CQ, Sankar R, Zhou W, Li B, Han ZD et al. 2017. Topological phase transition under pressure in the topological nodal-line superconductor PbTaSe2. Phys. Rev. B 96:064528
     [Google Scholar]
  154. 154.
    Wieder BJ, Kane CL 2016. Spin-orbit semimetals in the layer groups. Phys. Rev. B 94:155108
     [Google Scholar]
  155. 155.
    Chen Y, Lu YM, Kee HY 2015. Topological crystalline metal in orthorhombic perovskite iridates. Nat. Commun. 6:6593
     [Google Scholar]
  156. 156.
    Manes JL 2012. Existence of bulk chiral fermions and crystal symmetry. Phys. Rev. B 85:155118
     [Google Scholar]
  157. 157.
    Bradlyn B, Cano J, Wang Z, Vergniory M, Felser C et al. 2016. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353:aaf5037
     [Google Scholar]
  158. 158.
    Sharma G, Zhao Z, Sarker P, Nail BA, Wang J et al. 2016. Electronic structure, photovoltage, and photocatalytic hydrogen evolution with p-CuBi2O4 nanocrystals. J. Mater. Chem. A 4:2936–42
     [Google Scholar]
  159. 159.
    Tang P, Zhou Q, Zhang SC 2017. Multiple types of topological fermions in transition metal silicides. Phys. Rev. Lett. 119:206402
     [Google Scholar]
  160. 160.
    Chang G, Xu SY, Wieder BJ, Sanchez DS, Huang SM et al. 2017. Unconventional chiral fermions and large topological Fermi arcs in RhSi. Phys. Rev. Lett. 119:206401
     [Google Scholar]
  161. 161.
    Watanabe H, Po HC, Vishwanath A, Zaletel M 2015. Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals. PNAS 112:14551–56
     [Google Scholar]
  162. 162.
    Chadov S, Qi X, Kübler J, Fecher GH, Felser C, Zhang SC 2010. Tunable multifunctional topological insulators in ternary Heusler compounds. Nat. Mater. 9:541–45
     [Google Scholar]
  163. 163.
    Yang H, Yu J, Parkin SSP, Felser C, Liu CX, Yan B 2017. Prediction of triple point fermions in simple half-Heusler topological insulators. Phys. Rev. Lett. 119:136401
     [Google Scholar]
  164. 164.
    Gao W, Zhu X, Zheng F, Wu M, Zhang J et al. 2018. A possible candidate for triply degenerate point fermions in trigonal layered PtBi2. Nat. Commun. 9:3249
     [Google Scholar]
  165. 165.
    Bradlyn B, Elcoro L, Cano J, Vergniory M, Wang Z et al. 2017. Topological quantum chemistry. Nature 547:298–305
     [Google Scholar]
  166. 166.
    Po HC, Vishwanath A, Watanabe H 2017. Symmetry-based indicators of band topology in the 230 space groups. Nat. Commun. 8:50
     [Google Scholar]
  167. 167.
    Kruthoff J, de Boer J, van Wezel J, Kane CL, Slager RJ 2017. Topological classification of crystalline insulators through band structure combinatorics. Phys. Rev. X 7:041069
     [Google Scholar]
  168. 168.
    Song Z, Zhang T, Fang Z, Fang C 2018. Quantitative mappings between symmetry and topology in solids. Nat. Commun. 9:3530
     [Google Scholar]
  169. 169.
    Hughes TL, Prodan E, Bernevig BA 2011. Inversion-symmetric topological insulators. Phys. Rev. B 83:245132
     [Google Scholar]
  170. 170.
    Zhang T, Jiang Y, Song Z, Huang H, He Y 2018. Catalogue of topological electronic materials. arXiv:1807.08756 [cond-mat.mtrl-sci]
    [Google Scholar]
  171. 171.
    Vergniory M, Elcoro L, Felser C, Bernevig B, Wang Z 2018. The (high quality) topological materials in the world. arXiv:1807.10271 [cond-mat.mtrl-sci]
    [Google Scholar]
  172. 172.
    Tang F, Po HC, Vishwanath A, Wan X 2018. Towards ideal topological materials: comprehensive database searches using symmetry indicators. arXiv:1807.09744 [cond-mat.mes-hall]
    [Google Scholar]
/content/journals/10.1146/annurev-matsci-070218-010049
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Topological Semimetals from First Principles
Annual Review of Materials Research 49, 153 (2019); https://doi.org/10.1146/annurev-matsci-070218-010049
/content/journals/10.1146/annurev-matsci-070218-010049
/content/journals/10.1146/annurev-matsci-070218-010049
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