1932

Abstract

Weyl semimetals are conductors whose low-energy bulk excitations are Weyl fermions, whereas their surfaces possess metallic Fermi arc surface states. These Fermi arc surface states are protected by a topological invariant associated with the bulk electronic wave functions of the material. Recently, it has been shown that the TaAs and NbAs classes of materials harbor such a state of topological matter. We review the basic phenomena and experimental history of the discovery of the first Weyl semimetals, starting with the observation of topological Fermi arcs and Weyl nodes in TaAs and NbAs by angle and spin-resolved surface and bulk sensitive photoemission spectroscopy and continuing through magnetotransport measurements reporting the Adler–Bell–Jackiw chiral anomaly. We hope that this article provides a useful introduction to the theory of Weyl semimetals, a summary of recent experimental discoveries, and a guideline to future directions.

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2017-03-31
2024-04-16
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Literature Cited

  1. Wilczek F. 1.  1998. Phys. Today 51:11–13
  2. Anderson PW. 2.  1984. Basic Notions of Condensed Matter Physics Reading, Mass.: Addison Wesley
  3. Geim AK, Novoselov KS. 3.  2007. Nat. Mater. 6:183–91
  4. Hasan MZ, Kane CL. 4.  2010. Rev. Mod. Phys. 82:3045–67
  5. Hasan MZ, Moore JE. 5.  2011. Annu. Rev. Condens. Matter Phys. 2:55–78
  6. Qi X-L, Zhang S-C. 6.  2011. Rev. Mod. Phys. 83:1057–110
  7. Volovik GE. 7.  2009. The Universe in a Helium Droplet Oxford, UK: Clarendon
  8. Turner AM, Vishwanath A. 8.  2013. Beyond band insulators: topology and semi-metals and interacting phases. arXiv:1301.0330 [Google Scholar]
  9. Hasan MZ, Xu S-Y, Neupane M. 9.  2015. Topological Insulators, Fundamentals and Perspectives F Ortmann, S Roche, SO Valenzuela 55–100 San Francisco: John Wiley & Sons
  10. Vafek O, Vishwanath A. 10.  2014. Annu. Rev. Condens. Matter Phys. 5:83–112
  11. Hasan MZ, Xu S-Y, Bian G. 11.  2015. Phys. Scr. T164:014001
  12. Weyl H. 12.  1929. Z. Phys. 56:330–52
  13. Herring C. 13.  1937. Phys. Rev. 52:365–73
  14. Abrikosov AA, Beneslavskii SD. 14.  1971. J. Low Temp. Phys. 5:141–54
  15. Nielsen HB, Ninomiya M. 15.  1983. Phys. Lett. B 130:389–96
  16. Murakami S. 16.  2007. New J. Phys. 9:356
  17. Wan X, Turner AM, Vishwanath A, Savrasov SY. 17.  2011. Phys. Rev. B 83:205101
  18. Yang K-Y, Lu Y-M, Ran Y. 18.  2011. Phys. Rev. B 84:075129
  19. Burkov AA, Balents L. 19.  2011. Phys. Rev. Lett. 107:127205
  20. Burkov AA, Hook MD, Balents L. 20.  2011. Phys. Rev. B 84:235126
  21. Xu G, Weng H, Wang Z, Dai X, Fang Z. 21.  2011. Phys. Rev. Lett. 107:186806
  22. Singh B, Sharma A, Lin H, Hasan MZ, Prasad R, Bansil A. 22.  2012. Phys. Rev. B 86:115208
  23. Xu S-Y, Xia Y, Wray LA, Jia S, Meier F. 23.  et al. 2011. Science 332:560–64
  24. Balents L. 24.  2011. Physics 4:36
  25. Vishwanath A. 25.  2015. Physics 8:84
  26. Huang SM, Xu S-Y, Belopolski I, Lee CC, Chang G. 26.  et al. 2015. Nat. Commun. 6:7373
  27. Weng H, Fang C, Fang Z, Bernevig BA, Dai X. 27.  2015. Phys. Rev. X 5:011029
  28. Xu S-Y, Belopolski I, Alidoust N, Neupane M, Bian G. 28.  et al. 2015. Science 349:613–17
  29. Xu S-Y, Liu C, Kushwaha SK, Sankar R, Krizan JW. 29.  et al. 2015. Science 347:294–98
  30. Xu S-Y, Alidoust N, Belopolski I, Zhang C, Bian G. 30.  et al. 2015. Nat. Phys. 11:748–54
  31. Xu S-Y, Belopolski I, Sanchez DS, Guo C, Chang G. 31.  et al. 2015. Sci. Adv. 13e1501092
  32. Lv BQ, Weng HM, Fu BB, Wang XP, Miao H. 32.  et al. 2015. Phys. Rev. X 5:031013
  33. Lv BQ, Xu N, Weng HM, Ma JZ, Richard P. 33.  et al. 2015. Nat. Phys. 11:724–27
  34. Lu L, Wang Z, Ye D, Ran L, Fu L. 34.  et al. 2015. Science 349:622–24
  35. Belopolski I, Xu S-Y, Sanchez DS, Chang G, Guo C. 35.  et al. 2016. Phys. Rev. Lett. 116:066802
  36. Meng T, Balents L. 36.  2012. Phys. Rev. B 86:1054504
  37. Bednik G, Zyuzin AA, Burkov AA. 37.  2015. Phys. Rev. B 92:035153
  38. Li Y, Haldane FDM. 38.  2015. Topological nodal Cooper pairing in doped Weyl metals. arXiv:1510.01730 [Google Scholar]
  39. Taft FF, Ishikawa JJ, McCollam A, Nakatsuji S, Julian SR. 39.  2012. Phys. Rev. B 85:205104
  40. Ueda K, Fujioka J, Takahashi Y, Suzuki T, Ishiwata S. 40.  et al. 2012. Phys. Rev. Lett. 109:136402
  41. Shapiro MC, Riggs SC, Stone MB. Cruz CR, Chi S. 41. , de la et al. 2012. Phys. Rev. B 85:214434
  42. Liu H, Tong W, Ling L, Zhang S, Zhang R. 42.  et al. 2012. Solid State Commun. 179:1
  43. Sushkov AB, Hofmann JB, Jenkins GS, Ishikawa J, Nakatsuji S. 43.  et al. 2015. Phys. Rev. B 92:241108
  44. Bulmash D, Liu C-X, Qi X-L. 44.  2015. Phys. Rev. Lett. 115:087002
  45. Liu ZK, Zhou B, Zhang Y, Wang ZJ, Weng HM. 45.  et al. 2014. Science 343:864
  46. Xu S-Y, Liu C, Belopolski I, Kushwaha SK, Sankar R. 46.  et al. 2015. Phys. Rev. B 92:075115
  47. Neupane M, Xu S-Y, Sankar R, Alidoust N, Bian G. 47.  et al. 2014. Nat. Commun. 5:3786
  48. Liu ZK, Jian J, Zhou B, Wang ZJ, Zhang Y. 48.  et al. 2014. Nat. Mat. 13:677
  49. Borisenko S, Gibson Q, Evtushinsky D, Zabolotnyy V, Büchner G. 49.  et al. 2014. Phys. Rev. Lett. 113:027603
  50. Guan T, Lin C, Yang C, Shi Y, Ren C. 50.  et al. 2015. Phys. Rev. Lett. 115:087002
  51. Halász GB, Balents L. 51.  2012. Phys. Rev. B 85:035103
  52. Liu J, Vanderbilt D. 52.  2014. Phys. Rev. B 90:155316
  53. Shekhar C, Nayak AK, Sun Y, Schmidt M, Nicklas M. 53.  et al. 2015. Nat. Phys. 11:645–49
  54. Wang Z, Zheng Y, Shen Z, Lu Y, Fang H. 54.  et al. 2015. Phys. Rev. B 93:121112(R)
  55. Huang S-M, Xu S-Y, Belopolski I, Lee C-C, Chang G. 55.  et al. 2016. PNAS 113:1180–85
  56. Xu S-Y, Alidoust N, Change G, Lu H, Singh B. 56.  et al. 2016. Discovery of Lorentz-violating Weyl fermion semimetal state in LaAlGe materials. arXiv:1603.07318 [Google Scholar]
  57. Chang G, Singh B, Xu S-Y, Bian G, Huang S-M. 57.  et al. 2016. Theoretical prediction of magnetic and noncentrosymmetric Weyl fermion semimetal states in the R-Al-X family of compounds (R = rare earth, Al = aluminium, X = Si, Ge). arXiv:1604.02124 [Google Scholar]
  58. Soluyanov AA, Gresh D, Wang Z, Wu QS, Troyer M. 58.  et al. 2015. Nature 527:495–98
  59. Chang T-R, Xu S-Y, Chang G, Lee C-C, Huang S-M. 59.  et al. 2016. Nat. Commun. 7:10639
  60. Sun Y, Wu S-C, Ali MN, Felser C, Yan G. 60.  2015. Phys. Rev. B 92:161107(R)
  61. Chang G, Xu S-Y, Sanchez DS, Huang S-M, Lee C-C. 61.  et al. 2015. Sci. Adv. 2:e1600295
  62. Koepernik K, Kasinathan D, Efremov DV, Khim S, Borisenko S. 62.  et al. 2016. Phys. Rev. B 93:201101(R)
  63. Autés G, Gresh D, Troyer M, Soluyanov AA, Yazyev OV. 63.  2016. Phys. Rev. Lett. 117:066402
  64. Liu C-C, Zhou J-J, Yao Y, Zhang F. 64.  2016. Phys. Rev. Lett. 116:066801
  65. Hosur P, Qi X. 65.  2013. C. R. Phys. 14:857–70
  66. Grushin AG. 66.  2012. Phys. Rev. D 86:045001
  67. Bergholtz EJ, Liu Z, Trescher M, Moessner R, Udagawa M. 67.  2015. Phys. Rev. Lett. 114:016806
  68. Trescher M, Sbierski B, Brouwer PW, Bergholtz EJ. 68.  2015. Phys. Rev. B 91:115135
  69. Beenakker C. 69.  2015. Journal Club for Condensed Matter Physics commentary posted in August
  70. Zyuzin AA, Tiwari RP. 70.  2016. J. Exp. Theoret. Phys. 103:717–22
  71. Isobe H, Nagaosa N. 71.  2016. Phys. Rev. Lett. 116:116803
  72. Yang LX, Liu ZK, Sun Y, Peng H, Yang HF. 72.  et al. 2015. Nat. Phys. 11:728–32
  73. Xu N, Weng HM, Lv BQ, Matt CE, Park J. 73.  et al. 2016. Nat. Commun. 7:11006
  74. Liu Z, Yang LX, Sun Y, Zhang T, Peng H. 74.  et al. 2016. Nat. Mat. 15:27–31
  75. Xu DF, Du Y-P, Wang Z, Li Y-P, Niu X-H. 75.  et al. 2015. Chin. Phys. Lett. 32:107101
  76. Souma S, Wang Z, Kotaka H, Sato T, Nakayama K. 76.  et al. 2016. Phys. Rev. B. 93:161112
  77. Lv BQ, Muss S, Qian T, Song ZD, Nie SM. 77.  et al. 2015. Phys. Rev. Lett. 115:217601
  78. Xu S-Y, Belopolski I, Sanchez DS, Neupane M, Chang G. 78.  et al. 2016. Phys. Rev. Lett. 116:096801
  79. Bertlmann RA. 79.  2001. Anomalies in Quantum Field Theory International Series of Monographs on Physics. 91 Oxford, UK: Oxford Univ. Press. Rev. Ed. [Google Scholar]
  80. Adler S. 80.  1969. Phys. Rev. 177:2426–38
  81. Bell JS, Jackiw R. 81.  1969. Il Nuovo Cim. A 60:47
  82. Duval C, Horvath Z, Horvathy PA, Martina L, Stichel PC. 82.  2006. Mod. Phys. Lett. B 20:373–78
  83. Fukushima K, Kharzeev DE, Warringa HJ. 83.  2008. Phys. Rev. D 78:074033
  84. Son DT, Spivak BZ. 84.  2013. Phys. Rev. B 88:104412
  85. Burkov AA. 85.  2014. Phys. Rev. Lett. 113:247203
  86. Suzuki T, Chisnell R, Devarakonda A, Liu Y-T, Feng W. 85a.  et al. 2016. Nat. Phys. 12:1119–23
  87. Xiong J, Kushwaha SK, Liang T, Krizan JW, Wang W. 86.  et al. 2015. Evidence for the chiral anomaly in the Dirac semimetal Na3 Bi. Presented at 2015 Am. Phys. Soc. March Meet., San Antonio, TX arXiv:1503.08179
  88. Zhang C, Zhang E, Liu Y, Chen Z-G, Liang S. 87.  et al. 2015. Detection of chiral anomaly and valley transport in Dirac semimetals. arxiv:1504.07698 [Google Scholar]
  89. Kim H-J, Kim K-S, Wang J-F, Sasaki M, Satoh N. 88.  et al. 2013. Phys. Rev. Lett. 111:246603
  90. Ritchie L, Xiao G, Ji Y, Chen TY, Chien CL, Zhang M. 89.  et al. 2003. Phys. Rev. B 68:104430
  91. Pippard AB. 90.  1989. Magnetoresistance in Metals Cambridge, UK: Cambridge University Press
  92. Hu J, Rosenbaum TF, Betts JB. 91.  2005. Phys. Rev. Lett. 95:186603
  93. Argyres PN, Adams EN. 92.  1956. Phys. Rev. 104:900
  94. Sugihara K, Tokumoto M, Yamanouchi C, Yoshihiro K. 93.  1976. J. Phys. Soc. Jpn. 41:109–15
  95. Kikugawa Goswami P, Kiswandhi A, Choi ES, Graf D. 94.  et al. 2016. Nat. Commun. 7:10903
  96. Goswami P, Pixley JH, Das Sarma S. 95.  2015. Phys. Rev. B 92:075205
  97. Huang X, Zhao L, Long Y, Wang P, Chen D. 96.  et al. 2015. Phys. Rev. X 5:031023
  98. Zhang C-L, Xu S-Y, Belopolski I, Yuan Z, Lin Z. 97.  et al. 2016. Nat. Commun. 7:10735
  99. Ghimire NJ, Luo Y, Neupane M, Williams DJ, Bauer ED, Ronning F. 98.  2015. J. Phys.: Condens. Matter 27:152201
  100. Luo Y, Ghimire NJ, Wartenbe M, Choi H, Neupane M. 99.  et al. 2015. Phys. Rev. B 92:205134
  101. Moll PJW, Potter AC, Ramshaw B, Modic K, Riggs S. 100.  et al. 2016. Nat. Commun. 7:12492
  102. Yang X, Liu Y, Wang Z, Zheng Y, Xu Z-A. 101.  et al. 2015. Chiral anomaly induced negative magneoresistance in topological Weyl semimetal NbAs. arxiv:1506.03190 [Google Scholar]
  103. Zhang C, Guo C, Lu H, Zhang X, Yuan Z. 102.  et al. 2015. Phys. Rev. B 92:041203(R)
  104. Zhang C, Lin Z, Guo C, Xu S-Y, Lee C-C. 103.  et al. 2015. Quantum phase transitions in Weyl semimetal tantalum monophosphide. arxiv:1507.06301 [Google Scholar]
  105. Du J, Wang H, Chen Q, Mao Q, Khan R. 104.  et al. 2016. Sci. China Phys. Mech. Astron. 59:657406
  106. Arnold F, Shekhir C, Wu S-C, Sun Y, Donizeth dos Reis R. 105.  et al. 2016. Nat. Commun. 7:11615
  107. Jia S, Xu S-Y, Hasan MZ. 106.  2016. Weyl semimetals, Fermi arcs and chiral anomalies (a short review). arXiv:1612.00416
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