1932

Abstract

Three-dimensional (3D) topological semimetals represent a new class of topological matters. The study of this family of materials has been at the frontiers of condensed matter physics, and many breakthroughs have been made. Several topological semimetal phases, including Dirac semimetals (DSMs), Weyl semimetals (WSMs), nodal-line semimetals (NLSMs), and triple-point semimetals, have been theoretically predicted and experimentally demonstrated. The low-energy excitation around the Dirac/Weyl nodal points, nodal line, or triply degenerated nodal point can be viewed as emergent relativistic fermions. Experimental studies have shown that relativistic fermions can result in a rich variety of exotic transport properties, e.g., extremely large magnetoresistance, the chiral anomaly, and the intrinsic anomalous Hall effect. In this review, we first briefly introduce band structural characteristics of each topological semimetal phase, then review the current studies on quantum oscillations and exotic transport properties of various topological semimetals, and finally provide a perspective of this area.

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2019-07-01
2024-04-14
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Literature Cited

  1. 1.
    Wilczek F. 1998. Why are there analogies between condensed matter and particle theory?. Phys. Today 51:11
    [Google Scholar]
  2. 2.
    Volovik GE. 2009. The Universe in a Helium Droplet Oxford, UK: Oxford Univ. Press
  3. 3.
    Geim AK, Novoselov KS. 2007. The rise of graphene. Nat. Mater. 6:183–91
    [Google Scholar]
  4. 4.
    Hasan MZ, Kane CL. 2010. Topological insulators. Rev. Mod. Phys. 82:3045–67
    [Google Scholar]
  5. 5.
    Qi X-L, Zhang S-C. 2011. Topological insulators and superconductors. Rev. Mod. Phys. 83:1057–110
    [Google Scholar]
  6. 6.
    Vafek O, Vishwanath A. 2014. Dirac fermions in solids: from high-Tc cuprates and graphene to topological insulators and Weyl semimetals. Annu. Rev. Condens. Matter Phys. 5:83–112
    [Google Scholar]
  7. 7.
    Jia S, Xu S-Y, Hasan MZ 2016. Weyl semimetals, Fermi arcs and chiral anomalies. Nat. Mater 15:1140–44
    [Google Scholar]
  8. 8.
    Yan B, Felser C. 2017. Topological materials: Weyl semimetals. Annu. Rev. Condens. Matter Phys. 8:337–54
    [Google Scholar]
  9. 9.
    Burkov AA. 2018. Weyl metals. Annu. Rev. Condens. Matter Phys. 9:359–78
    [Google Scholar]
  10. 10.
    Armitage NP, Mele EJ, Vishwanath A 2018. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys 90:015001
    [Google Scholar]
  11. 11.
    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]
  12. 12.
    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]
  13. 13.
    Wang Z, Sun Y, Chen X-Q, 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]
  14. 14.
    Wang Z, Weng H, Wu Q, Dai X, Fang Z 2013. Three-dimensional Dirac semimetal and quantum transport in Cd3As2. Phys. Rev. B 88:125427
    [Google Scholar]
  15. 15.
    Weyl H. 1929. Elektron und Gravitation. I. Z. Phys. 56:330–52
    [Google Scholar]
  16. 16.
    Herring C. 1937. Accidental degeneracy in the energy bands of crystals. Phys. Rev. 52:365–73
    [Google Scholar]
  17. 17.
    Nielsen HB, Ninomiya M. 1983. The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal. Phys. Lett. B 130:389–96
    [Google Scholar]
  18. 18.
    Abrikosov AA, Beneslavskii SD. 1971. Some properties of gapless semiconductors of the second kind. J. Low Temp. Phys. 5:141–54
    [Google Scholar]
  19. 19.
    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]
  20. 20.
    Burkov AA, Balents L. 2011. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107:127205
    [Google Scholar]
  21. 21.
    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]
  22. 22.
    Huang S-M, Xu S-Y, Belopolski I, Lee C-C, 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]
  23. 23.
    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]
  24. 24.
    Dirac PAM. 1928. The quantum theory of the electron. Proc. R. Soc. A 117:610–24
    [Google Scholar]
  25. 25.
    Xu S-Y, 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]
  26. 26.
    Lu L, Wang Z, Ye D, Ran L, Fu L et al. 2015. Experimental observation of Weyl points. Science 349:622–24
    [Google Scholar]
  27. 27.
    Lv BQ, Weng HM, Fu BB, Wang XP, Miao H et al. 2015. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5:031013
    [Google Scholar]
  28. 28.
    Soluyanov AA, Gresch D, Wang Z, Wu Q, Troyer M et al. 2015. Type-II Weyl semimetals. Nature 527:495–98
    [Google Scholar]
  29. 29.
    Chang T-R, Xu S-Y, Sanchez DS, Tsai W-F, Huang S-M et al. 2017. Type-II symmetry-protected topological Dirac semimetals. Phys. Rev. Lett. 119:026404
    [Google Scholar]
  30. 30.
    Burkov AA, Hook MD, Balents L 2011. Topological nodal semimetals. Phys. Rev. B 84:235126
    [Google Scholar]
  31. 31.
    Bradlyn B, Cano J, Wang Z, Vergniory MG, Felser C et al. 2016. Beyond Dirac and Weyl fermions: unconventional quasiparticles in conventional crystals. Science 353:aaf5037
    [Google Scholar]
  32. 32.
    Wieder BJ, Kim Y, Rappe AM, Kane CL 2016. Double Dirac semimetals in three dimensions. Phys. Rev. Lett. 116:186402
    [Google Scholar]
  33. 33.
    Weng H, Fang C, Fang Z, Dai X 2016. Topological semimetals with triply degenerate nodal points in q-phase tantalum nitride. Phys. Rev. B 93:241202
    [Google Scholar]
  34. 34.
    Zhu Z, Winkler GW, Wu Q, Li J, Soluyanov AA 2016. Triple point topological metals. Phys. Rev. X 6:031003
    [Google Scholar]
  35. 35.
    Weng H, Fang C, Fang Z, Dai X 2016. Coexistence of Weyl fermion and massless triply degenerate nodal points. Phys. Rev. B 94:165201
    [Google Scholar]
  36. 36.
    Chang G, Xu S-Y, Huang S-M, Sanchez DS, Hsu C-H et al. 2017. Nexus fermions in topological symmorphic crystalline metals. Sci. Rep. 7:1688
    [Google Scholar]
  37. 37.
    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]
  38. 38.
    Xu S-Y, Liu C, Kushwaha SK, Sankar R, Krizan JW et al. 2015. Observation of Fermi arc surface states in a topological metal. Science 347:294–98
    [Google Scholar]
  39. 39.
    Yang LX, Liu ZK, Sun Y, Peng H, Yang HF et al. 2015. Weyl semimetal phase in the non-centrosymmetric compound TaAs. Nat. Phys. 11:728–32
    [Google Scholar]
  40. 40.
    Bian G, Chang T-R, Sankar R, Xu S-Y, Zheng H et al. 2016. Topological nodal-line fermions in spin-orbit metal PbTaSe2. Nat. Commun. 7:10556
    [Google Scholar]
  41. 41.
    Inoue H, Gyenis A, Wang Z, Li J, Oh SW et al. 2016. Quasiparticle interference of the Fermi arcs and surface-bulk connectivity of a Weyl semimetal. Science 351:1184–87
    [Google Scholar]
  42. 42.
    Batabyal R, Morali N, Avraham N, Sun Y, Schmidt M et al. 2016. Visualizing weakly bound surface Fermi arcs and their correspondence to bulk Weyl fermions. Sci. Adv. 2:e1600709
    [Google Scholar]
  43. 43.
    Potter AC, Kimchi I, Vishwanath A 2014. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5:5161
    [Google Scholar]
  44. 44.
    Moll PJW, Nair NL, Helm T, Potter AC, Kimchi I et al. 2016. Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd3As2. Nature 535:266–70
    [Google Scholar]
  45. 45.
    Liang T, Gibson Q, Ali MN, Liu M, Cava RJ, Ong NP 2015. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2. Nat. Mater. 14:280–84
    [Google Scholar]
  46. 46.
    Shekhar C, Nayak AK, Sun Y, Schmidt M, Nicklas M et al. 2015. Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP. Nat. Phys. 11:645–49
    [Google Scholar]
  47. 47.
    Pippard AB. 1989. Magnetoresistance in Metals Cambridge, UK: Cambridge Univ. Press
  48. 48.
    Ali MN, Xiong J, Flynn S, Tao J, Gibson QD et al. 2014. Large, non-saturating magnetoresistance in WTe2. Nature 514:205–8
    [Google Scholar]
  49. 49.
    Skinner B, Fu L. 2018. Large, nonsaturating thermopower in a quantizing magnetic field. Sci. Adv. 4:eaat2621
    [Google Scholar]
  50. 50.
    Liang T, Gibson Q, Xiong J, Hirschberger M, Koduvayur SP et al. 2013. Evidence for massive bulk Dirac fermions in Pb1−xSnxSe from Nernst and thermopower experiments. Nat. Commun. 4:2696
    [Google Scholar]
  51. 51.
    Stockert U, dos Reis RD, Ajeesh MO, Watzman SJ, Schmidt M et al. 2017. Thermopower and thermal conductivity in the Weyl semimetal NbP. J. Phys. Condens. Matter 29:325701
    [Google Scholar]
  52. 52.
    Jho Y-S, Kim K-S. 2013. Interplay between interaction and chiral anomaly: anisotropy in the electrical resistivity of interacting Weyl metals. Phys. Rev. B 87:205133
    [Google Scholar]
  53. 53.
    Son DT, Spivak BZ. 2013. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Phys. Rev. B 88:104412
    [Google Scholar]
  54. 54.
    Burkov AA. 2014. Anomalous Hall effect in Weyl metals. Phys. Rev. Lett. 113:187202
    [Google Scholar]
  55. 55.
    Karplus R, Luttinger JM. 1954. Hall effect in ferromagnetics. Phys. Rev. 95:1154–60
    [Google Scholar]
  56. 56.
    Haldane FDM. 2004. Berry curvature on the Fermi surface: anomalous Hall effect as a topological Fermi-liquid property. Phys. Rev. Lett. 93:206602
    [Google Scholar]
  57. 57.
    Ikhlas M, Tomita T, Koretsune T, Suzuki M-T, Nishio-Hamane D et al. 2017. Large anomalous Nernst effect at room temperature in a chiral antiferromagnet. Nat. Phys. 13:1085–90
    [Google Scholar]
  58. 58.
    Sakai A, Mizuta YP, Nugroho AA, Sihombing R, Koretsune T et al. 2018. Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal. Nat. Phys. 14:1119–24
    [Google Scholar]
  59. 59.
    Ishizuka H, Hayata T, Ueda M, Nagaosa N 2016. Emergent electromagnetic induction and adiabatic charge pumping in noncentrosymmetric Weyl semimetals. Phys. Rev. Lett. 117:216601
    [Google Scholar]
  60. 60.
    Taguchi K, Imaeda T, Sato M, Tanaka Y 2016. Photovoltaic chiral magnetic effect in Weyl semimetals. Phys. Rev. B 93:201202
    [Google Scholar]
  61. 61.
    Chan C-K, Lindner NH, Refael G, Lee PA 2017. Photocurrents in Weyl semimetals. Phys. Rev. B 95:041104
    [Google Scholar]
  62. 62.
    de Juan F, Grushin AG, Morimoto T, Moore JE 2017. Quantized circular photogalvanic effect in Weyl semimetals. Nat. Commun. 8:15995
    [Google Scholar]
  63. 63.
    Ma Q, Xu S-Y, Chan C-K, Zhang C-L, Chang G et al. 2017. Direct optical detection of Weyl fermion chirality in a topological semimetal. Nat. Phys. 13:842–47
    [Google Scholar]
  64. 64.
    Osterhoudt GB, Diebel LK, Gray MJ, Yang X, Stanco J et al. 2019. Colossal mid-infrared bulk photovoltaic effect in a type-I Weyl semimetal. Nat. Mater 18:471–75
    [Google Scholar]
  65. 65.
    Wu L, Patankar S, Morimoto T, Nair NL, Thewalt E et al. 2016. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13:350–55
    [Google Scholar]
  66. 66.
    Morimoto T, Nagaosa N. 2016. Topological nature of nonlinear optical effects in solids. Sci. Adv. 2:e1501524
    [Google Scholar]
  67. 67.
    Goswami P, Sharma G, Tewari S 2015. Optical activity as a test for dynamic chiral magnetic effect of Weyl semimetals. Phys. Rev. B 92:161110
    [Google Scholar]
  68. 68.
    Ma J, Pesin DA. 2015. Chiral magnetic effect and natural optical activity in metals with or without Weyl points. Phys. Rev. B 92:235205
    [Google Scholar]
  69. 69.
    Zhong S, Moore JE, Souza I 2016. Gyrotropic magnetic effect and the magnetic moment on the Fermi surface. Phys. Rev. Lett. 116:077201
    [Google Scholar]
  70. 70.
    Feng W, Guo G-Y, Zhou J, Yao Y, Niu Q 2015. Large magneto-optical Kerr effect in noncollinear antiferromagnets Mn3X (X = Rh, Ir, Pt). Phys. Rev. B 92:144426
    [Google Scholar]
  71. 71.
    Higo T, Man H, Gopman DB, Wu L, Koretsune T et al. 2018. Large magneto-optical Kerr effect and imaging of magnetic octupole domains in an antiferromagnetic metal. Nat. Photon. 12:73–78
    [Google Scholar]
  72. 72.
    Qian X, Liu J, Fu L, Li J 2014. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346:1344–47
    [Google Scholar]
  73. 73.
    Tang S, Zhang C, Wong D, Pedramrazi Z, Tsai H-Z et al. 2017. Quantum spin Hall state in monolayer 1T′-WTe2. Nat. Phys. 13:683–87
    [Google Scholar]
  74. 74.
    Fei Z, Palomaki T, Wu S, Zhao W, Cai X et al. 2017. Edge conduction in monolayer WTe2. Nat. Phys. 13:677–82
    [Google Scholar]
  75. 75.
    Wu S, Fatemi V, Gibson QD, Watanabe K, Taniguchi T et al. 2018. Observation of the quantum spin Hall effect up to 100 Kelvin in a monolayer crystal. Science 359:76–79
    [Google Scholar]
  76. 76.
    Weng H, Yu R, Hu X, Dai X, Fang Z 2015. Quantum anomalous Hall effect and related topological electronic states. Adv. Phys. 64:227–82
    [Google Scholar]
  77. 77.
    Burkov AA. 2015. Chiral anomaly and transport in Weyl metals. J. Phys. Condens. Matter 27:113201
    [Google Scholar]
  78. 78.
    Chen F, Hongming W, Xi D, Zhong F 2016. Topological nodal line semimetals. Chin. Phys. B 25:117106
    [Google Scholar]
  79. 79.
    Liu C-X, Zhang S-C, Qi X-L 2016. The quantum anomalous Hall effect: theory and experiment. Annu. Rev. Condens. Matter Phys. 7:301–21
    [Google Scholar]
  80. 80.
    Bansil A, Lin H, Das T 2016. Topological band theory. Rev. Mod. Phys. 88:021004
    [Google Scholar]
  81. 81.
    Wang S, Lin B-C, Wang A-Q, Yu D-P, Liao Z-M 2017. Quantum transport in Dirac and Weyl semimetals: a review. Adv. Phys. X 2:518–44
    [Google Scholar]
  82. 82.
    Hasan MZ, Xu S-Y, Belopolski I, Huang S-M 2017. Discovery of Weyl fermion semimetals and topological Fermi arc states. Annu. Rev. Condens. Matter Phys. 8:289–309
    [Google Scholar]
  83. 83.
    Zheng H, Zahid Hasan M 2018. Quasiparticle interference on type-I and type-II Weyl semimetal surfaces: a review. Adv. Phys. X 3:1466661
    [Google Scholar]
  84. 84.
    Nurit A, Jonathan R, Abhay K-N, Noam M, Rajib B et al. 2018. Quasiparticle interference studies of quantum materials. Adv. Mater 30:1707628
    [Google Scholar]
  85. 85.
    Yang S-Y, Yang H, Derunova E, Parkin SSP, Yan B, Ali MN 2018. Symmetry demanded topological nodal-line materials. Adv. Phys. X 3:1414631
    [Google Scholar]
  86. 86.
    Xu S-Y, 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]
  87. 87.
    Xu N, Weng HM, Lv BQ, Matt CE, Park J et al. 2015. Observation of Weyl nodes and Fermi arcs in tantalum phosphide. Nat. Commun. 7:11006
    [Google Scholar]
  88. 88.
    Belopolski I, Xu S-Y, Sanchez DS, Chang G, Guo C et al. 2016. Criteria for directly detecting topological Fermi arcs in Weyl semimetals. Phys. Rev. Lett. 116:066802
    [Google Scholar]
  89. 89.
    Liu ZK, Yang LX, Sun Y, Zhang T, Peng H et al. 2015. Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family. Nat. Mater. 15:27–31
    [Google Scholar]
  90. 90.
    Souma S, Wang Z, Kotaka H, Sato T, Nakayama K et al. 2016. Direct observation of nonequivalent Fermi-arc states of opposite surfaces in the noncentrosymmetric Weyl semimetal NbP. Phys. Rev. B 93:161112
    [Google Scholar]
  91. 91.
    Xu S-Y, Belopolski I, Sanchez DS, Zhang C, Chang G et al. 2015. Experimental discovery of a topological Weyl semimetal state in TaP. Sci. Adv. 1:e1501092
    [Google Scholar]
  92. 92.
    Xu D-F, Du Y-P, Wang Z, Li Y-P, Niu X-H et al. 2015. Observation of Fermi arcs in non-centrosymmetric Weyl semi-metal candidate NbP. Chin. Phys. Lett. 32:107101
    [Google Scholar]
  93. 93.
    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]
  94. 94.
    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]
  95. 95.
    Belopolski I, Sanchez DS, Chang G, Manna K, Ernst B et al. 2017. A three-dimensional magnetic topological phase. arXiv:1712.09992 [cond-mat.mtrl-sci]
  96. 96.
    Chang G, Xu S-Y, Zheng H, Singh B, Hsu C-H 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]
  97. 97.
    Wang Z, Vergniory MG, Kushwaha S, Hirschberger M, Chulkov EV et al. 2016. Time-reversal-breaking Weyl fermions in magnetic Heusler alloys. Phys. Rev. Lett. 117:236401
    [Google Scholar]
  98. 98.
    Ernst B, Sahoo R, Sun Y, Nayak J, Muechler L et al. 2017. Manifestation of the Berry curvature in Co2TiSn Heusler films. arXiv:1710.04393 [cond-mat.mtrl-sci]
  99. 99.
    Kübler J, Felser C. 2016. Weyl points in the ferromagnetic Heusler compound Co2MnAl. Europhys. Lett. 114:47005
    [Google Scholar]
  100. 100.
    Nakatsuji S, Kiyohara N, Higo T 2015. Large anomalous Hall effect in a non-collinear antiferromagnet at room temperature. Nature 527:212–15
    [Google Scholar]
  101. 101.
    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]
  102. 102.
    Hao Y, Yan S, Yang Z, Wu-Jun S, Stuart SPP, Binghai Y 2017. Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn. New J. Phys. 19:015008
    [Google Scholar]
  103. 103.
    Kuroda K, Tomita T, Suzuki MT, Bareille C, Nugroho AA et al. 2017. Evidence for magnetic Weyl fermions in a correlated metal. Nat. Mater. 16:1090–95
    [Google Scholar]
  104. 104.
    Cano J, Bradlyn B, Wang Z, Hirschberger M, Ong NP, Bernevig BA 2017. Chiral anomaly factory: creating Weyl fermions with a magnetic field. Phys. Rev. B 95:161306
    [Google Scholar]
  105. 105.
    Xiong J, Kushwaha SK, Liang T, Krizan JW, Hirschberger M et al. 2015. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350:413–16
    [Google Scholar]
  106. 106.
    Li C-Z, Wang L-X, Liu H, Wang J, Liao Z-M, Yu D-P 2015. Giant negative magnetoresistance induced by the chiral anomaly in individual Cd3As2 nanowires. Nat. Commun. 6:10137
    [Google Scholar]
  107. 107.
    Li Q, Kharzeev DE, Zhang C, Huang Y, Pletikosic I et al. 2016. Chiral magnetic effect in ZrTe5. Nat. Phys. 12:550–54
    [Google Scholar]
  108. 108.
    Nakajima Y, Hu R, Kirshenbaum K, Hughes A, Syers P et al. 2015. Topological RPdBi half-Heusler semimetals: a new family of noncentrosymmetric magnetic superconductors. Sci. Adv. 1:e1500242
    [Google Scholar]
  109. 109.
    Hirschberger M, Kushwaha S, Wang Z, Gibson Q, Liang S et al. 2016. The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi. Nat. Mater 15:1161–65
    [Google Scholar]
  110. 110.
    Shekhar C, Nayak AK, Singh S, Kumar N, Wu S-C et al. 2016. Observation of chiral magneto-transport in RPtBi topological Heusler compounds. arXiv:1604.01641 [cond-mat.mtrl-sci]
  111. 111.
    Wu Y, Mou D, Jo NH, Sun K, Huang L et al. 2016. Observation of Fermi arcs in type-II Weyl semimetal candidate WTe2. Phys. Rev. B 94:121113R)
    [Google Scholar]
  112. 112.
    Wang C, Zhang Y, Huang J, Nie S, Liu G et al. 2016. Observation of Fermi arc and its connection with bulk states in the candidate type-II Weyl semimetal WTe2. Phys. Rev. B 94:241119
    [Google Scholar]
  113. 113.
    Bruno FY, Tamai A, Wu QS, Cucchi I, Barreteau C et al. 2016. Observation of large topologically trivial Fermi arcs in the candidate type-II Weyl WTe2. Phys. Rev. B 94:121112
    [Google Scholar]
  114. 114.
    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]
  115. 115.
    Huang L, McCormick TM, Ochi M, Zhao Z, Suzuki M-T et al. 2016. Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2. Nat. Mater 15:1155–60
    [Google Scholar]
  116. 116.
    Deng K, Wan G, Deng P, Zhang K, Ding S et al. 2016. Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2. Nat. Phys. 12:1105–10
    [Google Scholar]
  117. 117.
    Belopolski I, Sanchez DS, Ishida Y, Pan X, Yu P et al. 2016. Discovery of a new type of topological Weyl fermion semimetal state in MoxW1−xTe2. Nat. Commun. 7:13643
    [Google Scholar]
  118. 118.
    Belopolski I, Xu S-Y, Ishida Y, Pan X, Yu P et al. 2016. Fermi arc electronic structure and Chern numbers in the type-II Weyl semimetal candidate MoxW1−xTe2. Phys. Rev. B 94:085127
    [Google Scholar]
  119. 119.
    Jiang J, Liu ZK, Sun Y, Yang HF, Rajamathi CR et al. 2017. Signature of type-II Weyl semimetal phase in MoTe2. Nat. Commun. 8:13973
    [Google Scholar]
  120. 120.
    Liang A, Huang J, Nie S, Ding Y, Gao Q et al. 2016. Electronic evidence for type II Weyl semimetal state in MoTe2. arXiv:1604.01706 [cond-mat.mtrl-sci]
  121. 121.
    Xu N, Wang ZJ, Weber AP, Magrez A, Bugnon P et al. 2016. Discovery of Weyl semimetal state violating Lorentz invariance in MoTe2. arXiv:1604.02116 [cond-mat.mtrl-sci]
  122. 122.
    Tamai A, Wu QS, Cucchi I, Bruno FY, Riccò S et al. 2016. Fermi arcs and their topological character in the candidate type-ii Weyl semimetal MoTe2. Phys. Rev. X 6:031021
    [Google Scholar]
  123. 123.
    Koepernik K, Kasinathan D, Efremov DV, Khim S, Borisenko S et al. 2016. TaIrTe4: a ternary type-II Weyl semimetal. Phys. Rev. B 93:201101
    [Google Scholar]
  124. 124.
    Belopolski I, Yu P, Sanchez DS, Ishida Y, Chang T-R et al. 2017. Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points. Nat. Commun. 8:942
    [Google Scholar]
  125. 125.
    Autès 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]
  126. 126.
    Liu ZK, Zhou B, Zhang Y, Wang ZJ, Weng HM et al. 2014. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343:864–67
    [Google Scholar]
  127. 127.
    Neupane M, Xu S-Y, Sankar R, Alidoust N, Bian G et al. 2014. Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2. Nat. Commun. 5:3786
    [Google Scholar]
  128. 128.
    Liu ZK, Jiang J, Zhou B, Wang ZJ, Zhang Y et al. 2014. A stable three-dimensional topological Dirac semimetal Cd3As2. Nat. Mater 13:677–81
    [Google Scholar]
  129. 129.
    Borisenko S, Gibson Q, Evtushinsky D, Zabolotnyy V, Büchner B, Cava RJ 2014. Experimental realization of a three-dimensional Dirac semimetal. Phys. Rev. Lett. 113:027603
    [Google Scholar]
  130. 130.
    Yi H, Wang Z, Chen C, Shi Y, Feng Y et al. 2014. Evidence of topological surface state in three-dimensional Dirac semimetal Cd3As2. Sci. Rep. 4:6106
    [Google Scholar]
  131. 131.
    Yang B-J, Nagaosa N. 2014. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nat. Commun. 5:4898
    [Google Scholar]
  132. 132.
    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]
  133. 133.
    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]
  134. 134.
    Wieder BJ, Kane CL. 2016. Spin-orbit semimetals in the layer groups. Phys. Rev. B 94:155108
    [Google Scholar]
  135. 135.
    Young SM, Wieder BJ. 2017. Filling-enforced magnetic Dirac semimetals in two dimensions. Phys. Rev. Lett. 118:186401
    [Google Scholar]
  136. 136.
    Xu S-Y, Xia Y, Wray LA, Jia S, Meier F et al. 2011. Topological phase transition and texture inversion in a tunable topological insulator. Science 332:560–64
    [Google Scholar]
  137. 137.
    Brahlek M, Bansal N, Koirala N, Xu S-Y, Neupane M et al. 2012. Topological-metal to band-insulator transition in thin films. Phys. Rev. Lett. 109:186403
    [Google Scholar]
  138. 138.
    Xu S-Y, Liu C, Alidoust N, Neupane M, Qian D et al. 2012. Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe. Nat. Commun. 3:1192
    [Google Scholar]
  139. 139.
    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]
  140. 140.
    Manzoni G, Gragnaniello L, Autès G, Kuhn T, Sterzi A et al. 2016. Evidence for a strong topological insulator phase in ZrTe5. Phys. Rev. Lett. 117:237601
    [Google Scholar]
  141. 141.
    Park J, Lee G, Wolff-Fabris F, Koh YY, Eom MJ et al. 2011. Anisotropic Dirac fermions in a Bi square net of SrMnBi2. Phys. Rev. Lett. 107:126402
    [Google Scholar]
  142. 142.
    Feng Y, Wang Z, Chen C, Shi Y, Xie Z et al. 2014. Strong anisotropy of Dirac cones in SrMnBi2 and CaMnBi2 revealed by angle-resolved photoemission spectroscopy. Sci. Rep. 4:5385
    [Google Scholar]
  143. 143.
    Liu JY, Hu J, Zhang Q, Graf D, Cao HB et al. 2017. A magnetic topological semimetal Sr1–yMn1−zSb2 (y, z < 0.10). Nat. Mater 16:905–10
    [Google Scholar]
  144. 144.
    Kargarian M, Randeria M, Lu Y-M 2016. Are the surface Fermi arcs in Dirac semimetals topologically protected. ? PNAS 113:8648–52
    [Google Scholar]
  145. 145.
    Bian G, Chang T-R, Zheng H, Velury S, Xu S-Y et al. 2016. Drumhead surface states and topological nodal-line fermions in TlTaSe2. Phys. Rev. B 93:121113
    [Google Scholar]
  146. 146.
    Fang C, Chen Y, Kee H-Y, Fu L 2015. Topological nodal line semimetals with and without spin-orbital coupling. Phys. Rev. B 92:081201
    [Google Scholar]
  147. 147.
    Xie LS, Schoop LM, Seibel EM, Gibson QD, Xie W, Cava RJ 2015. A new form of Ca3P2 with a ring of Dirac nodes. APL Mater 3:083602
    [Google Scholar]
  148. 148.
    Yu R, Weng H, Fang Z, Dai X, Hu X 2015. Topological node-line semimetal and Dirac semimetal state in antiperovskite Cu3PdN. Phys. Rev. Lett. 115:036807
    [Google Scholar]
  149. 149.
    Kim Y, Wieder BJ, Kane CL, Rappe AM 2015. Dirac line nodes in inversion-symmetric crystals. Phys. Rev. Lett. 115:036806
    [Google Scholar]
  150. 150.
    Chiu C-K, Schnyder AP. 2014. Classification of reflection-symmetry-protected topological semimetals and nodal superconductors. Phys. Rev. B 90:205136
    [Google Scholar]
  151. 151.
    Wu Y, Wang L-L, Mun E, Johnson DD, Mou D et al. 2016. Dirac node arcs in PtSn4. Nat. Phys. 12:667–71
    [Google Scholar]
  152. 152.
    Ekahana SA, Shu-Chun W, Juan J, Kenjiro O, Dharmalingam P et al. 2017. Observation of nodal line in non-symmorphic topological semimetal InBi. New J. Phys. 19:065007
    [Google Scholar]
  153. 153.
    Feng X, Yue C, Song Z, Wu Q, Wen B 2018. Topological Dirac nodal-net fermions in AlB2-type TiB2 and ZrB2. Phys. Rev. Mater 2:014202
    [Google Scholar]
  154. 154.
    Schoop LM, Ali MN, Straszer 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]
  155. 155.
    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]
  156. 156.
    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]
  157. 157.
    Takane D, Wang Z, Souma S, Nakayama K, Trang CX et al. 2016. Dirac-node arc in the topological line-node semimetal HfSiS. Phys. Rev. B 94:121108
    [Google Scholar]
  158. 158.
    Chen C, Xu X, Jiang J, Wu SC, Qi YP et al. 2017. Dirac line nodes and effect of spin-orbit coupling in the nonsymmorphic critical semimetals MSiS (M = Hf, Zr). Phys. Rev. B 95:125126
    [Google Scholar]
  159. 159.
    Yamakage A, Yamakawa Y, Tanaka Y, Okamoto Y 2015. Line-node Dirac semimetal and topological insulating phase in noncentrosymmetric pnictides CaAgX (X = P, As). J. Phys. Soc. Jpn. 85:013708
    [Google Scholar]
  160. 160.
    Wang X-B, Ma X-M, Emmanouilidou E, Shen B, Hsu C-H et al. 2017. Topological surface electronic states in candidate nodal-line semimetal CaAgAs. Phys. Rev. B 96:161112
    [Google Scholar]
  161. 161.
    Liang Q-F, Zhou J, Yu R, Wang Z, Weng H 2016. Node-surface and node-line fermions from nonsymmorphic lattice symmetries. Phys. Rev. B 93:085427
    [Google Scholar]
  162. 162.
    Bzdušek T, Wu Q, Rüegg A, Sigrist M, Soluyanov AA 2016. Nodal-chain metals. Nature 538:75–78
    [Google Scholar]
  163. 163.
    Wang S-S, Liu Y, Yu Z-M, Sheng X-L, Yang SA 2017. Hourglass Dirac chain metal in rhenium dioxide. Nat. Commun. 8:1844
    [Google Scholar]
  164. 164.
    Bi R, Yan Z, Lu L, Wang Z 2017. Nodal-knot semimetals. Phys. Rev. B 96:201305
    [Google Scholar]
  165. 165.
    Chen W, Lu H-Z, Hou J-M 2017. Topological semimetals with a double-helix nodal link. Phys. Rev. B 96:041102
    [Google Scholar]
  166. 166.
    Yan Z, Bi R, Shen H, Lu L, Zhang S-C, Wang Z 2017. Nodal-link semimetals. Phys. Rev. B 96:041103
    [Google Scholar]
  167. 167.
    Chang G, Xu S-Y, Zhou X, Huang S-M, Singh B et al. 2017. Topological Hopf and chain link semimetal states and their application to Co2MnGa. Phys. Rev. Lett. 119:156401
    [Google Scholar]
  168. 168.
    Wieder BJ. 2018. Threes company. Nat. Phys. 14:329–30
    [Google Scholar]
  169. 169.
    Lv BQ, 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]
  170. 170.
    Ma JZ, He JB, Xu YF, Lv BQ, Chen D et al. 2018. Three-component fermions with surface Fermi arcs in tungsten carbide. Nat. Phys. 14:349–54
    [Google Scholar]
  171. 171.
    Gao W, Hao N, Zheng F-W, Ning W, Wu M et al. 2017. Extremely large magnetoresistance in a topological semimetal candidate pyrite PtBi2. Phys. Rev. Lett. 118:256601
    [Google Scholar]
  172. 172.
    Narayanan A, Watson MD, Blake SF, Bruyant N, Drigo L et al. 2015. Linear magnetoresistance caused by mobility fluctuations in n-doped Cd3As2. Phys. Rev. Lett. 114:117201
    [Google Scholar]
  173. 173.
    Wang K, Graf D, Lei H, Tozer SW, Petrovic C 2011. Quantum transport of two-dimensional Dirac fermions in SrMnBi2. Phys. Rev. B 84:220401
    [Google Scholar]
  174. 174.
    Novak M, Sasaki S, Segawa K, Ando Y 2015. Large linear magnetoresistance in the Dirac semimetal TlBiSSe. Phys. Rev. B 91:041203
    [Google Scholar]
  175. 175.
    Yi-Yan W, Qiao-He Y, Tian-Long X 2016. Large linear magnetoresistance in a new Dirac material BaMnBi2. Chin. Phys. B 25:107503
    [Google Scholar]
  176. 176.
    Xiong J, Kushwaha S, Krizan J, Liang T, Cava RJ, Ong NP 2016. Anomalous conductivity tensor in the Dirac semimetal Na3Bi. Europhys. Lett. 114:27002
    [Google Scholar]
  177. 177.
    Masuda H, Sakai H, Tokunaga M, Yamasaki Y, Miyake A et al. 2016. Quantum Hall effect in a bulk antiferromagnet EuMnBi2 with magnetically confined two-dimensional Dirac fermions. Sci. Adv. 2:e1501117
    [Google Scholar]
  178. 178.
    He LP, Hong XC, Dong JK, Pan J, Zhang Z et al. 2014. Quantum transport evidence for the three-dimensional Dirac semimetal phase in Cd3As2. Phys. Rev. Lett. 113:246402
    [Google Scholar]
  179. 179.
    Wang Z, Zheng Y, Shen Z, Lu Y, Fang H et al. 2016. Helicity-protected ultrahigh mobility Weyl fermions in NbP. Phys. Rev. B 93:121112
    [Google Scholar]
  180. 180.
    Yang X, Liu Y, Wang Z, Zheng Y, Xu Z-a 2015. Chiral anomaly induced negative magnetoresistance in topological Weyl semimetal NbAs. arXiv:1506.03190 [cond-mat.mtrl-sci]
  181. 181.
    Zhang C, Guo C, Lu H, Zhang X, Yuan Z et al. 2015. Large magnetoresistance over an extended temperature regime in monophosphides of tantalum and niobium. Phys. Rev. B 92:041203(R)
    [Google Scholar]
  182. 182.
    Zhang C-L, Yuan Z, Jiang Q-D, Tong B, Zhang C et al. 2017. Electron scattering in tantalum monoarsenide. Phys. Rev. B 95:085202
    [Google Scholar]
  183. 183.
    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]
  184. 184.
    Wang YL, Thoutam LR, Xiao ZL, Hu J, Das S et al. 2015. Origin of the turn-on temperature behavior in WTe2. Phys. Rev. B 92:180402
    [Google Scholar]
  185. 185.
    Zhao Y, Liu H, Yan J, An W, Liu J et al. 2015. Anisotropic magnetotransport and exotic longitudinal linear magnetoresistance in WTe2 crystals. Phys. Rev. B 92:041104
    [Google Scholar]
  186. 186.
    Zhu Z, Lin X, Liu J, Fauqué B, Tao Q et al. 2015. Quantum oscillations, thermoelectric coefficients, and the Fermi surface of semimetallic WTe2. Phys. Rev. Lett. 114:176601
    [Google Scholar]
  187. 187.
    Wang A, Graf D, Liu Y, Du Q, Zheng J et al. 2017. Large magnetoresistance in the type-II Weyl semimetal WP2. Phys. Rev. B 96:121107
    [Google Scholar]
  188. 188.
    Wang C-L, Zhang Y, Huang J-W, Liu G-D, Liang A-J et al. 2017. Evidence of electron-hole imbalance in WTe2 from high-resolution angle-resolved photoemission spectroscopy. Chin. Phys. Lett. 34:097305
    [Google Scholar]
  189. 189.
    Thirupathaiah S, Jha R, Pal B, Matias JS, Das PK et al. 2017. MoTe2: an uncompensated semimetal with extremely large magnetoresistance. Phys. Rev. B 95:241105
    [Google Scholar]
  190. 190.
    Chamber RG. 1990. Electrons in Metals and Semiconductors New York: Chapman and Hall
  191. 191.
    Luo Y, Ghimire NJ, Wartenbe M, Choi H, Neupane M et al. 2015. Electron-hole compensation effect between topologically trivial electrons and nontrivial holes in NbAs. Phys. Rev. B 92:205134
    [Google Scholar]
  192. 192.
    Hu J, Liu JY, Graf D, Radmanesh SMA, Adams DJ et al. 2016. π Berry phase and Zeeman splitting of Weyl semimetal TaP. Sci. Rep. 6:18674
    [Google Scholar]
  193. 193.
    Du J, Wang H, Mao Q, Khan R, Xu B et al. 2016. Large unsaturated positive and negative magnetoresistance in Weyl semimetal TaP. Sci. China Phys. Mech. Astron. 59:657406
    [Google Scholar]
  194. 194.
    Ghimire NJ, Yongkang L, Neupane M, Williams DJ, Bauer ED, Ronning F 2015. Magnetotransport of single crystalline NbAs. J. Phys. Condens. Matter 27:152201
    [Google Scholar]
  195. 195.
    Abrikosov AA. 1998. Quantum magnetoresistance. Phys. Rev. B 58:2788–94
    [Google Scholar]
  196. 196.
    Datta S. 1995. Electronic Transport in Mesoscopic Systems Cambridge, UK: Cambridge Univ. Press
  197. 197.
    Chen YL, Chu J-H, Analytis JG, Liu ZK, Igarashi K et al. 2010. Massive Dirac fermion on the surface of a magnetically doped topological insulator. Science 329:659–62
    [Google Scholar]
  198. 198.
    Beidenkopf H, Roushan P, Seo J, Gorman L, Drozdov I et al. 2011. Spatial fluctuations of helical Dirac fermions on the surface of topological insulators. Nat. Phys. 7:939–43
    [Google Scholar]
  199. 199.
    Okada Y, Dhital C, Zhou W, Huemiller ED, Lin H et al. 2011. Direct observation of broken time-reversal symmetry on the surface of a magnetically doped topological insulator. Phys. Rev. Lett. 106:206805
    [Google Scholar]
  200. 200.
    Wray LA, Xu S-Y, Xia Y, Hsieh D, Fedorov AV et al. 2011. A topological insulator surface under strong Coulomb, magnetic and disorder perturbations. Nat. Phys. 7:32–37
    [Google Scholar]
  201. 201.
    Liu M, Zhang J, Chang C-Z, Zhang Z, Feng X et al. 2012. Crossover between weak antilocalization and weak localization in a magnetically doped topological insulator. Phys. Rev. Lett. 108:036805
    [Google Scholar]
  202. 202.
    Ando Y. 2013. Topological insulator materials. J. Phys. Soc. Jpn. 82:102001
    [Google Scholar]
  203. 203.
    Shoenberg D. 1984. Magnetic Oscillations in Metals Cambridge, UK: Cambridge Univ. Press
  204. 204.
    Kartsovnik MV. 2004. High magnetic fields: a tool for studying electronic properties of layered organic metals. Chem. Rev. 104:5737–82
    [Google Scholar]
  205. 205.
    McClure JW. 1956. Diamagnetism of graphite. Phys. Rev. 104:666–71
    [Google Scholar]
  206. 206.
    Ando T. 2008. Physics of graphene: zero-mode anomalies and roles of symmetry. Prog. Theor. Phys. Suppl. 176:203–26
    [Google Scholar]
  207. 207.
    Berry MV. 1984. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. A 392:45–57
    [Google Scholar]
  208. 208.
    Xiao D, Chang M-C, Niu Q 2010. Berry phase effects on electronic properties. Rev. Mod. Phys. 82:1959–2007
    [Google Scholar]
  209. 209.
    Mikitik GP, Sharlai YV. 1999. Manifestation of Berry's phase in metal physics. Phys. Rev. Lett. 82:2147–50
    [Google Scholar]
  210. 210.
    Taskin AA, Ando Y. 2011. Berry phase of nonideal Dirac fermions in topological insulators. Phys. Rev. B 84:035301
    [Google Scholar]
  211. 211.
    Lv BQ, Xu N, Weng HM, Ma JZ, Richard P et al. 2015. Observation of Weyl nodes in TaAs. Nat. Phys. 11:724–27
    [Google Scholar]
  212. 212.
    Lifshitz IM, Kosevich AM. 1956. Theory of magnetic susceptibility in metals at low temperatures. Sov. Phys. JETP 2:636–45
    [Google Scholar]
  213. 213.
    Kealhofer R, Jang S, Griffin SM, John C, Benavides KA et al. 2018. Observation of a two-dimensional Fermi surface and Dirac dispersion in YbMnSb2. Phys. Rev. B 97:045109
    [Google Scholar]
  214. 214.
    Shoenberg D. 1984. Magnetization of a two-dimensional electron gas. J. Low Temp. Phys. 56:417–40
    [Google Scholar]
  215. 215.
    Champel T, Mineev VP. 2001. de Haas–van Alphen effect in two- and quasi-two-dimensional metals and superconductors. Philos. Mag. B 81:55–74
    [Google Scholar]
  216. 216.
    Novoselov KS, Geim AK, Morozov SV, Jiang D, Katsnelson MI et al. 2005. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438:197–200
    [Google Scholar]
  217. 217.
    Das Sarma S, Stern F 1985. Single-particle relaxation time versus scattering time in an impure electron gas. Phys. Rev. B 32:8442–44
    [Google Scholar]
  218. 218.
    Hwang EH, Das Sarma S 2008. Single-particle relaxation time versus transport scattering time in a two-dimensional graphene layer. Phys. Rev. B 77:195412
    [Google Scholar]
  219. 219.
    Xiong J, Luo Y, Khoo Y, Jia S, Cava RJ, Ong NP 2012. High-field Shubnikov–de Haas oscillations in the topological insulator Bi2Te2Se. Phys. Rev. B 86:045314
    [Google Scholar]
  220. 220.
    Pariari A, Dutta P, Mandal P 2015. Probing the Fermi surface of three-dimensional Dirac semimetal Cd3As2 through the de Haas–van Alphen technique. Phys. Rev. B 91:155139
    [Google Scholar]
  221. 221.
    Hu J, Tang Z, Liu J, Zhu Y, Wei J, Mao Z 2017. Nearly massless Dirac fermions and strong Zeeman splitting in the nodal-line semimetal ZrSiS probed by de Haas–van Alphen quantum oscillations. Phys. Rev. B 96:045127
    [Google Scholar]
  222. 222.
    Kumar N, Manna K, Qi Y, Wu S-C, Wang L et al. 2017. Unusual magnetotransport from Si-square nets in topological semimetal HfSiS. Phys. Rev. B 95:121109(R)
    [Google Scholar]
  223. 223.
    Jeon S, Zhou BB, Gyenis A, Feldman BE, Kimchi I et al. 2014. Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2. Nat. Mater 13:851–56
    [Google Scholar]
  224. 224.
    Moll PJW, Potter AC, Nair NL, Ramshaw BJ, Modic KA et al. 2016. Magnetic torque anomaly in the quantum limit of Weyl semimetals. Nat. Commun. 7:12492
    [Google Scholar]
  225. 225.
    Arnold F, Shekhar C, Wu S-C, Sun Y, dos Reis RD et al. 2016. Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP. Nat. Commun. 7:11615
    [Google Scholar]
  226. 226.
    Hu J, Zhu YL, Graf D, Tang ZJ, Liu JY, Mao ZQ 2017. Quantum oscillation studies of topological semimetal candidate ZrGeM (M = S, Se, Te). Phys. Rev. B 95:205134
    [Google Scholar]
  227. 227.
    Arnold F, Naumann M, Wu SC, Sun Y, Schmidt M et al. 2016. Chiral Weyl pockets and Fermi surface topology of the Weyl semimetal TaAs. Phys. Rev. Lett. 117:146401
    [Google Scholar]
  228. 228.
    Hu J, Zhu Y, Gui X, Graf D, Tang Z et al. 2018. Quantum oscillation evidence of a topological semimetal phase in ZrSnTe. Phys. Rev. B 97:155101
    [Google Scholar]
  229. 229.
    Zheng W, Schönemann R, Aryal N, Zhou Q, Rhodes D et al. 2018. Detailed study of the Fermi surfaces of the type-II Dirac semimetallic candidates XTe2 (X = Pd, Pt). Phys. Rev. B 97:235154
    [Google Scholar]
  230. 230.
    Zhu Y, Zhang T, Hu J, Kidd J, Graf D et al. 2018. Multiple topologically non-trivial bands in non-centrosymmetric YSn2. Phys. Rev. B 98:035117
    [Google Scholar]
  231. 231.
    Cai PL, Hu J, He LP, Pan J, Hong XC et al. 2015. Drastic pressure effect on the extremely large magnetoresistance in WTe2: quantum oscillation study. Phys. Rev. Lett. 115:057202
    [Google Scholar]
  232. 232.
    Ali MN, Schoop LM, Garg C, Lippmann JM, Lara E et al. 2016. Butterfly magnetoresistance, quasi-2D Dirac Fermi surfaces, and a topological phase transition in ZrSiS. Sci. Adv. 2:e1601742
    [Google Scholar]
  233. 233.
    Singha R, Pariari A, Satpati B, Mandal P 2017. Large nonsaturating magnetoresistance and signature of nondegenerate Dirac nodes in ZrSiS. PNAS 114:2468–73
    [Google Scholar]
  234. 234.
    Wang K, Graf D, Wang L, Lei H, Tozer SW, Petrovic C 2012. Two-dimensional Dirac fermions and quantum magnetoresistance in CaMnBi2. Phys. Rev. B 85:041101
    [Google Scholar]
  235. 235.
    Li L, Wang K, Graf D, Wang L, Wang A, Petrovic C 2016. Electron-hole asymmetry, Dirac fermions, and quantum magnetoresistance in BaMnBi2. Phys. Rev. B 93:115141
    [Google Scholar]
  236. 236.
    Cao J, Liang S, Zhang C, Liu Y, Huang J et al. 2015. Landau level splitting in Cd3As2 under high magnetic fields. Nat. Commun. 6:7779
    [Google Scholar]
  237. 237.
    Zhao Y, Liu H, Zhang C, Wang H, Wang J et al. 2015. Anisotropic Fermi surface and quantum limit transport in high mobility three-dimensional Dirac semimetal Cd3As2. Phys. Rev. X 5:031037
    [Google Scholar]
  238. 238.
    Liu J, Hu J, Cao H, Zhu Y, Chuang A et al. 2016. Nearly massless Dirac fermions hosted by Sb square net in BaMnSb2. Sci. Rep. 6:30525
    [Google Scholar]
  239. 239.
    Huang S, Kim J, Shelton WA, Plummer EW, Jin R 2017. Nontrivial Berry phase in magnetic BaMnSb2 semimetal. PNAS 114:6256–61
    [Google Scholar]
  240. 240.
    Pippard AB. 1965. The Dynamics of Conduction Electrons New York: Gordon and Breach
  241. 241.
    Lv Y-Y, Zhang B-B, Li X, Yao S-H, Chen YB et al. 2016. Extremely large and significantly anisotropic magnetoresistance in ZrSiS single crystals. Appl. Phys. Lett. 108:244101
    [Google Scholar]
  242. 242.
    Wang X, Pan X, Gao M, Yu J, Jiang J et al. 2016. Evidence of both surface and bulk Dirac bands and anisotropic nonsaturating magnetoresistance in ZrSiS. Adv. Electron. Mater 2:1600228
    [Google Scholar]
  243. 243.
    Zhang C-L, Xu S-Y, Belopolski I, Yuan Z, Lin Z et al. 2016. Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal. Nat. Commun. 7:10735
    [Google Scholar]
  244. 244.
    Sankar R, Peramaiyan G, Muthuselvam IP, Butler CJ, Dimitri K et al. 2017. Crystal growth of Dirac semimetal ZrSiS with high magnetoresistance and mobility. Sci. Rep. 7:40603
    [Google Scholar]
  245. 245.
    Pezzini S, van Delft MR, Schoop LM, Lotsch BV, Carrington A et al. 2018. Unconventional mass enhancement around the Dirac nodal loop in ZrSiS. Nat. Phys. 14:178–83
    [Google Scholar]
  246. 246.
    Fête A, Gariglio S, Berthod C, Li D, Stornaiuolo D et al. 2014. Large modulation of the Shubnikov–de Haas oscillations by the Rashba interaction at the LaAlO3/SrTiO3 interface. New J. Phys. 16:112002
    [Google Scholar]
  247. 247.
    Liu JY, Hu J, Graf D, Zou T, Zhu M et al. 2017. Unusual interlayer quantum transport behavior caused by the zeroth Landau level in YbMnBi2. Nat. Commun. 8:646
    [Google Scholar]
  248. 248.
    Fei F, Bo X, Wang R, Wu B, Jiang J et al. 2017. Nontrivial Berry phase and type-II Dirac transport in the layered material PdTe2. Phys. Rev. B 96:041201
    [Google Scholar]
  249. 249.
    Wang Q, Guo P-J, Sun S, Li C, Liu K et al. 2018. Extremely large magnetoresistance and high-density Dirac-like fermions in ZrB2. Phys. Rev. B 97:205105
    [Google Scholar]
  250. 250.
    Ran B, Zili F, Xinqi L, Jingjing N, Jingyue W et al. 2018. Spin zero and large Landé g-factor in WTe2. New J. Phys. 20:063026
    [Google Scholar]
  251. 251.
    Cohen MH, Falicov LM. 1961. Magnetic breakdown in crystals. Phys. Rev. Lett. 7:231–33
    [Google Scholar]
  252. 252.
    Matusiak M, Cooper JR, Kaczorowski D 2017. Thermoelectric quantum oscillations in ZrSiS. Nat. Commun. 8:15219
    [Google Scholar]
  253. 253.
    Klein O. 1929. Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac. Z. Phys. 53:157–65
    [Google Scholar]
  254. 254.
    Ru-Keng S, Siu GG, Xiu C 1993. Barrier penetration and Klein paradox. J. Phys. A Math. Gen. 26:1001
    [Google Scholar]
  255. 255.
    Calogeracos A, Dombey N. 1999. History and physics of the Klein paradox. Contemp. Phys. 40:313–21
    [Google Scholar]
  256. 256.
    Dombey N, Calogeracos A. 1999. Seventy years of the Klein paradox. Phys. Rep. 315:41–58
    [Google Scholar]
  257. 257.
    Katsnelson MI, Novoselov KS, Geim AK 2006. Chiral tunnelling and the Klein paradox in graphene. Nat. Phys. 2:620–25
    [Google Scholar]
  258. 258.
    Young AF, Kim P. 2009. Quantum interference and Klein tunnelling in graphene heterojunctions. Nat. Phys. 5:222–26
    [Google Scholar]
  259. 259.
    O'Brien TE, Diez M, Beenakker CWJ 2016. Magnetic breakdown and Klein tunneling in a type-II Weyl semimetal. Phys. Rev. Lett. 116:236401
    [Google Scholar]
  260. 260.
    Zhang Y, Bulmash D, Hosur P, Potter AC, Vishwanath A 2016. Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals. Sci. Rep. 6:23741
    [Google Scholar]
  261. 261.
    Zhang C, Narayan A, Lu S, Zhang J, Zhang H et al. 2017. Evolution of Weyl orbit and quantum Hall effect in Dirac semimetal Cd3As2. Nat. Commun. 8:1272
    [Google Scholar]
  262. 262.
    Li P, Wen Y, He X, Zhang Q, Xia C et al. 2017. Evidence for topological type-II Weyl semimetal WTe2. Nat. Commun. 8:2150
    [Google Scholar]
  263. 263.
    Zhang Y, Tan Y-W, Stormer HL, Kim P 2005. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438:201–4
    [Google Scholar]
  264. 264.
    Xu Y, Miotkowski I, Liu C, Tian J, Nam H et al. 2014. Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator. Nat. Phys. 10:956–63
    [Google Scholar]
  265. 265.
    Brüne C, Liu CX, Novik EG, Hankiewicz EM, Buhmann H et al. 2011. Quantum Hall effect from the topological surface states of strained bulk HgTe. Phys. Rev. Lett. 106:126803
    [Google Scholar]
  266. 266.
    Büttner B, Liu CX, Tkachov G, Novik EG, Brüne C et al. 2011. Single valley Dirac fermions in zero-gap HgTe quantum wells. Nat. Phys. 7:418–22
    [Google Scholar]
  267. 267.
    Uchida M, Nakazawa Y, Nishihaya S, Akiba K, Kriener M et al. 2017. Quantum Hall states observed in thin films of Dirac semimetal Cd3As2. Nat. Commun. 8:2274
    [Google Scholar]
  268. 268.
    Schumann T, Galletti L, Kealhofer DA, Kim H, Goyal M, Stemmer S 2018. Observation of the quantum Hall effect in confined films of the three-dimensional Dirac semimetal Cd3As2. Phys. Rev. Lett. 120:016801
    [Google Scholar]
  269. 269.
    Borisenko S, Evtushinsky D, Gibson Q, Yaresko A, Kim T et al. 2015. Time-reversal symmetry breaking type-II Weyl state in YbMnBi2. arXiv:1507.04847 [cond-mat.mes-hall]
  270. 270.
    Tajima N, Sugawara S, Kato R, Nishio Y, Kajita K 2009. Effect of the zero-mode Landau level on interlayer magnetoresistance in multilayer massless Dirac fermion systems. Phys. Rev. Lett. 102:176403
    [Google Scholar]
  271. 271.
    Stormer HL, Tsui DC, Gossard AC 1999. The fractional quantum Hall effect. Rev. Mod. Phys. 71:S298–305
    [Google Scholar]
  272. 272.
    Liu Y, Yuan X, Zhang C, Jin Z, Narayan A et al. 2016. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5. Nat. Commun. 7:12516
    [Google Scholar]
  273. 273.
    Zhang C-L, Xu S-Y, Wang CM, Lin Z, Du ZZ et al. 2017. Magnetic-tunnelling-induced Weyl node annihilation in TaP. Nat. Phys. 13:979–86
    [Google Scholar]
  274. 274.
    Wang H, Liu H, Li Y, Liu Y, Wang J et al. 2018. Discovery of log-periodic oscillations in ultra-quantum topological materials. Sci. Adv. 4:eaau5096
    [Google Scholar]
  275. 275.
    Liu H, Jiang H, Wang Z, Joynt R, Xie XC 2018. Discrete scale invariance in topological semimetals. arXiv:1807.02459 [cond-mat.mtrl-sci]
  276. 276.
    Xu R, Husmann A, Rosenbaum TF, Saboungi ML, Enderby JE, Littlewood PB 1997. Large magnetoresistance in non-magnetic silver chalcogenides. Nature 390:57–60
    [Google Scholar]
  277. 277.
    Hu J, Liu TJ, Qian B, Mao ZQ 2013. Coupling of electronic and magnetic properties in Fe1+y(Te1−xSex). Phys. Rev. B 88:094505
    [Google Scholar]
  278. 278.
    Hu J, Rosenbaum TF. 2008. Classical and quantum routes to linear magnetoresistance. Nat. Mater 7:697–700
    [Google Scholar]
  279. 279.
    Kuo H-H, Chu J-H, Riggs SC, Yu L, McMahon PL et al. 2011. Possible origin of the nonmonotonic doping dependence of the in-plane resistivity anisotropy of Ba(Fe1−xTx)2As2 (T = Co, Ni, and Cu). Phys. Rev. B 84:054540
    [Google Scholar]
  280. 280.
    Huynh KK, Tanabe Y, Tanigaki K 2011. Both electron and hole Dirac cone states in Ba(FeAs)2 confirmed by magnetoresistance. Phys. Rev. Lett. 106:217004
    [Google Scholar]
  281. 281.
    Wang K, Petrovic C. 2012. Multiband effects and possible Dirac states in LaAgSb2. Phys. Rev. B 86:155213
    [Google Scholar]
  282. 282.
    Wang K, Graf D, Petrovic C 2013. Quasi-two-dimensional Dirac fermions and quantum magnetoresistance in LaAgBi2. Phys. Rev. B 87:235101
    [Google Scholar]
  283. 283.
    Wang A, Zaliznyak I, Ren W, Wu L, Graf D et al. 2016. Magnetotransport study of Dirac fermions in YbMnBi2 antiferromagnet. Phys. Rev. B 94:165161
    [Google Scholar]
  284. 284.
    Nagaosa N, Sinova J, Onoda S, MacDonald AH, Ong NP 2010. Anomalous Hall effect. Rev. Mod. Phys. 82:1539–92
    [Google Scholar]
  285. 285.
    Smit J. 1955. The spontaneous Hall effect in ferromagnetics. I. Physica 21:877–87
    [Google Scholar]
  286. 286.
    Berger L. 1970. Side-jump mechanism for the Hall effect of ferromagnets. Phys. Rev. B 2:4559–66
    [Google Scholar]
  287. 287.
    Onoda M, Nagaosa N. 2002. Topological nature of anomalous Hall effect in ferromagnets. J. Phys. Soc. Jpn. 71:19–22
    [Google Scholar]
  288. 288.
    Jungwirth T, Niu Q, MacDonald AH 2002. Anomalous Hall effect in ferromagnetic semiconductors. Phys. Rev. Lett. 88:207208
    [Google Scholar]
  289. 289.
    Lee W-L, Watauchi S, Miller VL, Cava RJ, Ong NP 2004. Dissipationless anomalous Hall current in the ferromagnetic spinel CuCr2Se4−xBrx. . Science 303:1647–49
    [Google Scholar]
  290. 290.
    Husmann A, Singh LJ. 2006. Temperature dependence of the anomalous Hall conductivity in the Heusler alloy Co2CrAl. Phys. Rev. B 73:172417
    [Google Scholar]
  291. 291.
    Manyala N, Sidis Y, DiTusa JF, Aeppli G, Young DP, Fisk Z 2004. Large anomalous Hall effect in a silicon-based magnetic semiconductor. Nat. Mater 3:255–62
    [Google Scholar]
  292. 292.
    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]
  293. 293.
    Barth J, Fecher GH, Balke B, Graf T, Shkabko A et al. 2011. Anomalous transport properties of the half-metallic ferromagnets Co2TiSi, Co2TiGe and Co2TiSn. Phil. Trans. R. Soc. A 369:3588–601
    [Google Scholar]
  294. 294.
    Felser C, Hirohata A, eds. 2016. Heusler Alloys: Properties, Growth, Applications Cham, Switz: Springer Int.
  295. 295.
    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]
  296. 296.
    Lin H, Wray LA, Xia Y, Xu S, Jia S et al. 2010. Half-Heusler ternary compounds as new multifunctional experimental platforms for topological quantum phenomena. Nat. Mater 9:546–49
    [Google Scholar]
  297. 297.
    Al-Sawai W, Lin H, Markiewicz RS, Wray LA, Xia Y et al. 2010. Topological electronic structure in half-Heusler topological insulators. Phys. Rev. B 82:125208
    [Google Scholar]
  298. 298.
    Suzuki T, Chisnell R, Devarakonda A, Liu YT, Feng W et al. 2016. Large anomalous Hall effect in a half-Heusler antiferromagnet. Nat. Phys. 12:1119–23
    [Google Scholar]
  299. 299.
    Ye L, Kang M, Liu J, von Cube F, Wicker CR et al. 2018. Massive Dirac fermions in a ferromagnetic kagome metal. Nature 555:638–42
    [Google Scholar]
  300. 300.
    Pal HK, Maslov DL. 2010. Necessary and sufficient condition for longitudinal magnetoresistance. Phys. Rev. B 81:214438
    [Google Scholar]
  301. 301.
    Kim H-J, Kim K-S, Wang JF, Sasaki M, Satoh N et al. 2013. Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena. Phys. Rev. Lett. 111:246603
    [Google Scholar]
  302. 302.
    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]
  303. 303.
    Lv Y-Y, Li X, Zhang B-B, Deng WY, Yao S-H et al. 2017. Experimental observation of anisotropic Adler-Bell-Jackiw anomaly in type-II Weyl semimetal WTe1.98 crystals at the quasiclassical regime. Phys. Rev. Lett. 118:096603
    [Google Scholar]
  304. 304.
    Liang S, Lin J, Kushwaha S, Xing J, Ni N et al. 2018. Experimental tests of the chiral anomaly magnetoresistance in the Dirac-Weyl semimetals Na3Bi and GdPtBi. Phys. Rev. X 8:031002
    [Google Scholar]
  305. 305.
    Reis RDd, Ajeesh MO, Kumar N, Arnold F, Shekhar C et al. 2016. On the search for the chiral anomaly in Weyl semimetals: the negative longitudinal magnetoresistance. New J. Phys. 18:085006
    [Google Scholar]
  306. 306.
    Udagawa M, Bergholtz EJ. 2016. Field-selective anomaly and chiral mode reversal in type-II Weyl materials. Phys. Rev. Lett. 117:086401
    [Google Scholar]
  307. 307.
    Yu Z-M, Yao Y, Yang SA 2016. Predicted unusual magnetoresponse in type-II Weyl semimetals. Phys. Rev. Lett. 117:077202
    [Google Scholar]
  308. 308.
    Sharma G, Goswami P, Tewari S 2017. Chiral anomaly and longitudinal magnetotransport in type-II Weyl semimetals. Phys. Rev. B 96:045112
    [Google Scholar]
  309. 309.
    Burkov AA. 2017. Giant planar Hall effect in topological metals. Phys. Rev. B 96:041110
    [Google Scholar]
  310. 310.
    Nandy S, Sharma G, Taraphder A, Tewari S 2017. Chiral anomaly as the origin of the planar Hall effect in Weyl semimetals. Phys. Rev. Lett. 119:176804
    [Google Scholar]
  311. 311.
    Li P, Zhang CH, Zhang JW, Wen Y, Zhang XX 2018. Giant planar Hall effect in the Dirac semimetal ZrTe5-δ. Phys. Rev. B 98:121108(R)
    [Google Scholar]
  312. 312.
    Li H, Wang H-W, He H, Wang J, Shen S-Q 2018. Giant anisotropic magnetoresistance and planar Hall effect in the Dirac semimetal Cd3As2. Phys. Rev. B 97:201110
    [Google Scholar]
  313. 313.
    Kumar N, Guin SN, Felser C, Shekhar C 2018. Planar Hall effect in the Weyl semimetal GdPtBi. Phys. Rev. B 98:041103
    [Google Scholar]
  314. 314.
    Singha R, Roy S, Pariari A, Satpati B, Mandal P 2018. Planar Hall effect in the type II Dirac semimetal VAl3. Phys. Rev. B 98:081103(R)
    [Google Scholar]
  315. 315.
    Wang YJ, Gong JX, Liang DD, Ge M, Wang JR et al. 2018. Planar Hall effect in type-II Weyl semimetal WTe2. arXiv:1801.05929 [cond-mat.mtrl-sci]
  316. 316.
    West FG. 1963. Rotating‐field technique for galvanomagnetic measurements. J. Appl. Phys. 34:1171–73
    [Google Scholar]
  317. 317.
    Liang T, Lin J, Gibson Q, Kushwaha S, Liu M et al. 2018. Anomalous Hall effect in ZrTe5. Nat. Phys. 14:451–55
    [Google Scholar]
  318. 318.
    Kane CL, Mele EJ. 2005. Z2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95:146802
    [Google Scholar]
  319. 319.
    Fu L, Kane CL, Mele EJ 2007. Topological insulators in three dimensions. Phys. Rev. Lett. 98:106803
    [Google Scholar]
  320. 320.
    Roth A, Brüne C, Buhmann H, Molenkamp LW, Maciejko J et al. 2009. Nonlocal transport in the quantum spin Hall state. Science 325:294–97
    [Google Scholar]
  321. 321.
    Kou X, Fan Y, Wang KL 2017. Review of quantum Hall trio. J. Phys. Chem. Solids press
    [Google Scholar]
  322. 322.
    Xu Q, Song Z, Nie S, Weng H, Fang Z, Dai X 2015. Two-dimensional oxide topological insulator with iron-pnictide superconductor LiFeAs structure. Phys. Rev. B 92:205310
    [Google Scholar]
  323. 323.
    Wang QH, Kalantar-Zadeh K, Kis A, Coleman JN, Strano MS 2012. Electronics and optoelectronics of two-dimensional transition metal dichalcogenides. Nat. Nanotechnol 7:699–712
    [Google Scholar]
  324. 324.
    König M, Wiedmann S, Brüne C, Roth A, Buhmann H et al. 2007. Quantum spin Hall insulator state in HgTe quantum wells. Science 318:766–70
    [Google Scholar]
  325. 325.
    Bradlyn B, Elcoro L, Cano J, Vergniory MG, Wang Z et al. 2017. Topological quantum chemistry. Nature 547:298–305
    [Google Scholar]
  326. 326.
    Eugene JM. 2015. The winding road to topological insulators. Phys. Scr. 2015:014004
    [Google Scholar]
  327. 327.
    Wang C, Hughbanks T. 1995. Main group element size and substitution effects on the structural dimensionality of zirconium tellurides of the ZrSiS type. Inorg. Chem. 34:5524–29
    [Google Scholar]
  328. 328.
    Qi X-L, Hughes TL, Zhang S-C 2010. Chiral topological superconductor from the quantum Hall state. Phys. Rev. B 82:184516
    [Google Scholar]
  329. 329.
    Liu X, Wang Z, Xie XC, Yu Y 2011. Abelian and non-Abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect. Phys. Rev. B 83:125105
    [Google Scholar]
  330. 330.
    Chang C-Z, Zhang J, Feng X, Shen J, Zhang Z et al. 2013. Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator. Science 340:167–70
    [Google Scholar]
  331. 331.
    Checkelsky JG, Yoshimi R, Tsukazaki A, Takahashi KS, Kozuka Y et al. 2014. Trajectory of the anomalous Hall effect towards the quantized state in a ferromagnetic topological insulator. Nat. Phys. 10:731–36
    [Google Scholar]
  332. 332.
    He QL, Pan L, Stern AL, Burks EC, Che X et al. 2017. Chiral Majorana fermion modes in a quantum anomalous Hall insulator–superconductor structure. Science 357:294–99
    [Google Scholar]
  333. 333.
    Po HC, Vishwanath A, Watanabe H 2017. Symmetry-based indicators of band topology in the 230 space groups. Nat. Commun. 8:50
    [Google Scholar]
  334. 334.
    Tang F, Po HC, Vishwanath A, Wan X2019. Comprehensive search for topological materials using symmetry indicators. Nature 566:486–89
  335. 335.
    Vergniory MG, Elcoro L, Felser CRegnault N, Bernevig BA, Wang Z. 2019. A complete catalogue of high-quality topological materials. Nature 566:480–85
  336. 336.
    Zhang T, Jiang Y, Song Z, Huang H, He Y et al.2019. Catalogue of topological electronic materials. Nature 566:475–79
  337. 336a.
    Kruthoff J, de Boer J, Wezel J, Kane CL, Slager R 2017. Topological classification of crystalline insulators through band structure combinatorics. Phys. Rev. X 7:041069
    [Google Scholar]
  338. 337.
    Zhou Q, Rhodes D, Zhang QR, Tang S, Schönemann R, Balicas L 2016. Hall effect within the colossal magnetoresistive semimetallic state of MoTe2. Phys. Rev. B 94:121101
    [Google Scholar]
  339. 338.
    Rhodes D, Schönemann R, Aryal N, Zhou Q, Zhang QR et al. 2017. Bulk Fermi surface of the Weyl type-II semimetallic candidate g-MoTe2. Phys. Rev. B 96:165134
    [Google Scholar]
  340. 339.
    Qi Y, Naumov PG, Ali MN, Rajamathi CR, Schnelle W et al. 2016. Superconductivity in Weyl semimetal candidate MoTe2. Nat. Commun. 7:11038
    [Google Scholar]
  341. 340.
    Chen FC, Lv HY, Luo X, Lu WJ, Pei QL et al. 2016. Extremely large magnetoresistance in the type-II Weyl semimetal MoTe2. Phys. Rev. B 94:235154
    [Google Scholar]
  342. 341.
    Mun E, Ko H, Miller GJ, Samolyuk GD, Bud'ko SL, Canfield PC 2012. Magnetic field effects on transport properties of PtSn4. Phys. Rev. B 85:035135
    [Google Scholar]
  343. 342.
    Wang YJ, Liang DD, Ge M, Yang J, Gong JX et al. 2018. Topological nature of the node-arc semimetal PtSn4 probed by de Haas–van Alphen quantum oscillations. J. Phys. Condens. Matter 30:155701
    [Google Scholar]
  344. 343.
    Fu C, Scaffidi T, Waissman J, Sun Y, Saha R et al. 2018. Thermoelectric signatures of the electron-phonon fluid in PtSn4. arXiv:1802.09468 [cond-mat.mtrl-sci]
  345. 344.
    Liang S, Lin J, Kushwaha S, Xing J, Ni N et al. 2018. Experimental tests of the chiral anomaly magnetoresistance in the Dirac-Weyl semimetals Na3Bi and GdPtBi. Phys. Rev. X 8:031002
    [Google Scholar]
  346. 345.
    He JB, Wang DM, Chen GF 2012. Giant magnetoresistance in layered manganese pnictide CaMnBi2. Appl. Phys. Lett. 100:112405
    [Google Scholar]
  347. 346.
    He JB, Fu Y, Zhao LX, Liang H, Chen D et al. 2017. Quasi-two-dimensional massless Dirac fermions in CaMnSb2. Phys. Rev. B 95:045128
    [Google Scholar]
  348. 347.
    Singha R, Pariari A, Satpati B, Mandal P 2017. Magnetotransport properties and evidence of a topological insulating state in LaSbTe. Phys. Rev. B 96245138
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