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Annual Review of Condensed Matter Physics

Volume 8, 2017

Topological Materials: Weyl Semimetals

Abstract

Topological insulators and topological semimetals are both new classes of quantum materials, which are characterized by surface states induced by the topology of the bulk band structure. Topological Dirac or Weyl semimetals show linear dispersion around nodes, termed the Dirac or Weyl points, as the three-dimensional analog of graphene. We review the basic concepts and compare these topological states of matter from the materials perspective with a special focus on Weyl semimetals. The TaAs family is the ideal materials class to introduce the signatures of Weyl points in a pedagogical way, from Fermi arcs to the chiral magnetotransport properties, followed by hunting for the type-II Weyl semimetals in WTe, MoTe, and related compounds. Many materials are members of big families, and topological properties can be tuned. As one example, we introduce the multifunctional topological materials, Heusler compounds, in which both topological insulators and magnetic Weyl semimetals can be found. Instead of a comprehensive review, this article is expected to serve as a helpful introduction and summary by taking a snapshot of the quickly expanding field.

Keyword(s): anomalous Hall effect, Berry phase, chiral anomaly, Fermi arcs, Heusler compound, magnetoresistance, monopole, spin Hall effect, surface states, transition-metal dichalcogenide, transition-metal pnictide
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2017-03-31
2024-07-03
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Literature Cited

  1. Qi XL, Zhang SC. 1.  2011. Rev. Mod. Phys. 83:1057 [Google Scholar]
  2. Hasan MZ, Kane CL. 2.  2010. Rev. Mod. Phys. 82:3045–67 [Google Scholar]
  3. Maciejko J, Hughes TL, Zhang SC. 3.  2011. Annu. Rev. Condens. Matter Phys. 2:31–53 [Google Scholar]
  4. Hasan MZ, Moore JE. 4.  2011. Annu. Rev. Condens. Matter Phys. 2:55–78 [Google Scholar]
  5. Yan B, Zhang SC. 5.  2012. Rep. Prog. Phys. 75:096501 [Google Scholar]
  6. Ando Y. 6.  2013. J. Phys. Soc. Jpn. 82:102001 [Google Scholar]
  7. Bernevig BA, Hughes TL, Zhang SC. 7.  2006. Science 314:1757 [Google Scholar]
  8. König M, Wiedmann S, Brüne C, Roth A, Buhmann H. 8.  et al. 2007. Science 318:766–70 [Google Scholar]
  9. Zhang H, Liu CX, Qi XL, Dai X, Fang Z, Zhang SC. 9.  2009. Nat. Phys. 5:438–42 [Google Scholar]
  10. Xia Y, Qian D, Hsieh D, Wray L, Pal A. 10.  et al. 2009. Nat. Phys. 5:398–402 [Google Scholar]
  11. Wan XG, Turner AM, Vishwanath A, Savrasov SY. 11.  2011. Phys. Rev. B 83:205101 [Google Scholar]
  12. Volovik GE. 12.  2003. The Universe in a Helium Droplet Oxford: Clarendon Press [Google Scholar]
  13. Balents L. 13.  2011. Physics 4:36 [Google Scholar]
  14. Burkov AA, Hook MD, Balents L. 14.  2011. Phys. Rev. B 84:235126 [Google Scholar]
  15. Hosur P, Qi XL. 15.  2013. C. R. Phys. 14:857–70 [Google Scholar]
  16. Vafek O, Vishwanath A. 16.  2014. Annu. Rev. Condens. Matter Phys. 5:83–112 [Google Scholar]
  17. Witczak-Krempa W, Chen G, Kim YB, Balents L. 17.  2014. Annu. Rev. Condens. Matter Phys. 5:57–82 [Google Scholar]
  18. Weyl H. 18.  1929. PNAS 15:323–34 [Google Scholar]
  19. Weng H, Fang C, Fang Z, Bernevig BA, Dai X. 19.  2015. Phys. Rev. X 5:011029 [Google Scholar]
  20. Huang SM, Xu SY, Belopolski I, Lee CC, Chang G. 20.  et al. 2015. Nat. Commun. 6:8373 [Google Scholar]
  21. Xu SY, Belopolski I, Alidoust N, Neupane M, Bian G. 21.  et al. 2015. Science 349:613 [Google Scholar]
  22. Lv BQ, Weng HM, Fu BB, Wang XP, Miao H. 22.  et al. 2015. Phys. Rev. X 5:031013 [Google Scholar]
  23. Yang LX, Liu ZK, Sun Y, Peng H, Yang HF. 23.  et al. 2015. Nat. Phys. 11:728–32 [Google Scholar]
  24. Murakami S. 24.  2008. New J. Phys. 10:029802 [Google Scholar]
  25. Nielsen HB, Ninomiya M. 25.  1981. Nucl. Phys. B 185:20–40 [Google Scholar]
  26. Nielsen HB, Ninomiya M. 26.  1981. Nucl. Phys. B 193:173–94 [Google Scholar]
  27. Young SM, Zaheer S, Teo JCY, Kane CL, Mele EJ, Rappe AM. 27.  2012. Phys. Rev. Lett. 108:140405 [Google Scholar]
  28. Wang Z, Sun Y, Chen XQ, Franchini C, Xu G. 28.  et al. 2012. Phys. Rev. B 85:195320 [Google Scholar]
  29. Wang Z, Weng H, Wu Q, Dai X, Fang Z. 29.  2013. Phys. Rev. B 88:125427 [Google Scholar]
  30. Xu G, Weng H, Wang Z, Dai X, Fang Z. 30.  2011. Phys. Rev. Lett. 107:186806 [Google Scholar]
  31. Yang KY, Lu YM, Ran Y. 31.  2011. Phys. Rev. B 84:075129 [Google Scholar]
  32. Burkov AA, Balents L. 32.  2011. Phys. Rev. Lett. 107:127205 [Google Scholar]
  33. Grushin AG. 33.  2012. Phys. Rev. D 86:045001 [Google Scholar]
  34. Sun Y, Zhang Y, Felser C, Yan B. 34.  2016. Phys. Rev. Lett. 117:146403 [Google Scholar]
  35. Adler SL. 35.  1969. Phys. Rev. 177:2426–38 [Google Scholar]
  36. Bell JS, Jackiw R. 36.  1969. Nuovo Cim. A 60:47–61 [Google Scholar]
  37. Nielsen HB, Ninomiya M. 37.  1983. Phys. Lett. B 130:389–96 [Google Scholar]
  38. Son DT, Spivak BZ. 38.  2013. Phys. Rev. B 88:104412 [Google Scholar]
  39. Parameswaran SA, Grover T, Abanin DA, Pesin DA, Vishwanath A. 39.  2014. Phys. Rev. X 4:031035 [Google Scholar]
  40. Potter AC, Kimchi I, Vishwanath A. 40.  2014. Nat. Commun. 5:5161 [Google Scholar]
  41. Baum Y, Berg E, Parameswaran SA, Stern A. 41.  2015. Phys. Rev. X 5:041046 [Google Scholar]
  42. Bulmash D, Liu CX, Qi XL. 42.  2014. Phys. Rev. B 89:081106(R) [Google Scholar]
  43. Lu L, Wang Z, Ye D, Ran L, Fu L. 43.  et al. 2015. Science 349:622–24 [Google Scholar]
  44. Huang X, Zhao L, Long Y, Wang P, Chen D. 44.  et al. 2015. Phys. Rev. X 5:031023 [Google Scholar]
  45. Zhang CL, Xu SY, Belopolski I, Yuan Z, Lin Z. 45.  et al. 2016. Nat. Commun. 7:10735 [Google Scholar]
  46. Shekhar C, Nayak AK, Sun Y, Schmidt M, Nicklas M. 46.  et al. 2015. Nat. Phys. 11:645 [Google Scholar]
  47. Arnold F, Shekhar C, Wu SC, Sun Y, dos Reis RD. 47.  et al. 2016. Nat. Commun. 7:11615 [Google Scholar]
  48. Liu ZK, Zhou B, Zhang Y, Wang ZJ, Weng HM. 48.  et al. 2014. Science 343:864–67 [Google Scholar]
  49. Liu ZK, Jiang J, Zhou B, Wang ZJ, Zhang Y. 49.  et al. 2014. Nat. Mater. 13:677–81 [Google Scholar]
  50. Neupane M, Xu SY, Sankar R, Alidoust N, Bian G. 50.  et al. 2014. Nat. Commun. 5:3786 [Google Scholar]
  51. Borisenko S, Gibson Q, Evtushinsky D, Zabolotnyy V, Büchner B, Cava RJ. 51.  2014. Phys. Rev. Lett. 113:027603 [Google Scholar]
  52. Soluyanov AA, Gresch D, Wang Z, Wu Q, Troyer M. 52.  et al. 2015. Nature 527:495–98 [Google Scholar]
  53. Sun Y, Wu SC, Ali MN, Felser C, Yan B. 53.  2015. Phys. Rev. B 92:161107(R) [Google Scholar]
  54. Liu ZK, Yang LX, Sun Y, Zhang T, Peng H. 54.  et al. 2016. Nat. Mater. 15:27–31 [Google Scholar]
  55. Sun Y, Wu SC, Yan B. 55.  2015. Phys. Rev. B 92:115428 [Google Scholar]
  56. Lv BQ, Xu N, Weng HM, Ma JZ, Richard P. 56.  et al. 2015. Nat. Phys. 11:724–27 [Google Scholar]
  57. Xiao D, Chang MC, Niu Q. 57.  2010. Rev. Mod. Phys. 82:1959–2007 [Google Scholar]
  58. Moll PJW, Nair NL, Helm T, Potter AC, Kimchi I. 58.  et al. 2016. Nature 535:266–70 [Google Scholar]
  59. Xu SY, Alidoust N, Belopolski I, Yuan Z, Bian G. 59.  et al. 2015. Nat. Phys. 11:748 [Google Scholar]
  60. Belopolski I, Xu SY, Sanchez DS, Chang G, Guo C. 60.  et al. 2016. Phys. Rev. Lett. 116:066802 [Google Scholar]
  61. Xu N, Weng HM, Lv BQ, Matt CE, Park J. 61.  et al. 2016. Nat. Commun. 7:11006 [Google Scholar]
  62. Souma S, Wang Z, Kotaka H, Sato T, Nakayama K. 62.  et al. 2016. Phys. Rev. B 93:161112 [Google Scholar]
  63. Lv BQ, Muff S, Qian T, Song ZD, Nie SM. 63.  et al. 2015. Phys. Rev. Lett. 115:217601 [Google Scholar]
  64. Xu SY, Belopolski I, Sanchez DS, Neupane M, Chang G. 64.  et al. 2016. Phys. Rev. Lett. 116:096801 [Google Scholar]
  65. Inoue H, Gyenis A, Wang Z, Li J, Oh SW. 65.  et al. 2016. Science 351:1184–87 [Google Scholar]
  66. Batabyal R, Morali N, Avraham N, Sun Y, Schmidt M. 66.  et al. 2016. Sci. Adv. 2:e1600709 [Google Scholar]
  67. Kourtis S, Li J, Wang Z, Yazdani A, Bernevig BA. 67.  2016. Phys. Rev. B 93:041109 [Google Scholar]
  68. Kim HJ, Kim KS, Wang JF, Sasaki M, Satoh N. 68.  et al. 2013. Phys. Rev. Lett. 111:246603 [Google Scholar]
  69. Li Q, Kharzeev DE, Zhang C, Huang Y, Pletikosic I. 69.  et al. 2016. Nat. Phys. 12:550–54 [Google Scholar]
  70. Xiong J, Kushwaha SK, Liang T, Krizan JW, Hirschberger M. 70.  et al. 2015. Science 350:413–16 [Google Scholar]
  71. Li H, He H, Lu HZ, Zhang H, Liu H. 71.  et al. 2016. Nat. Commun. 7:10301 [Google Scholar]
  72. Wang Z, Zheng Y, Shen Z, Zhou Y, Yang X. 72.  et al. 2016. Phys. Rev. B 93:121112 [Google Scholar]
  73. Yoshida K. 73.  1976. J. Phys. Soc. Jpn. 40:1027 [Google Scholar]
  74. Goswami P, Pixley JH, Das Sarma S. 74.  2015. Phys. Rev. B 92:075205 [Google Scholar]
  75. Chang MC, Yang MF. 75.  2015. Phys. Rev. B 92:205201 [Google Scholar]
  76. Ma J, Pesin D. 76.  2015. Phys. Rev. B 92:235205 [Google Scholar]
  77. Zhong S, Moore JE, Souza I. 77.  2016. Phys. Rev. Lett. 116:077201 [Google Scholar]
  78. Arnold F, Naumann M, Wu SC, Sun Y, Schmidt M. 78.  et al. 2016. Phys. Rev. Lett. 117:146401 [Google Scholar]
  79. Klotz J, Wu SC, Shekhar C, Sun Y, Schmidt M. 79.  et al. 2016. Phys. Rev. B 93:121105 [Google Scholar]
  80. Luo Y, Ghimire NJ, Bauer ED, Thompson JD, Ronning F. 80.  2016. J. Phys. Condens. Matter 28:055502 [Google Scholar]
  81. dos Reis RD, Wu SC, Sun Y, Ajeesh MO, Shekhar C. 81.  et al. 2016. Phys. Rev. B 93:205102 [Google Scholar]
  82. Liang T, Gibson Q, Ali MN, Liu M, Cava RJ, Ong NP. 82.  2014. Nat. Mater. 14:280–84 [Google Scholar]
  83. Narayanan A, Watson MD, Blake SF, Bruyant N. 83.  2015. Phys. Rev. Lett. 114:117201 [Google Scholar]
  84. Parkin S, Jiang X, Kaiser C, Panchula A, Roche K, Samant M. 84.  2003. Proc. IEEE 91:661–80 [Google Scholar]
  85. Singleton J. 85.  2001. Band Theory and Electronic Properties of Solids Oxford, UK: Oxford Univ. Press [Google Scholar]
  86. Ghimire NJ, Luo Y, Neupane M, Williams DJ, Bauer ED, Ronning F. 86.  2015. J. Phys. Condens. Matter 27:152201 [Google Scholar]
  87. Luo Y, Ghimire NJ, Wartenbe M, Choi H, Neupane M. 87.  et al. 2015. Phys. Rev. B 92:205134 [Google Scholar]
  88. Moll PJW, Potter AC, Ramshaw B, Modic K, Riggs S. 88.  et al. 2016. Nat. Commun. 7:12492 [Google Scholar]
  89. Chang TR, Chang G, Lee CC, Huang SM, Wang B. 89.  et al. 2016. Nat. Commun. 7:1–9 [Google Scholar]
  90. Wang Z, Gresch D, Soluyanov AA, Xie W, Kushwaha S. 90.  et al. 2016. Phys. Rev. Lett. 117:056805 [Google Scholar]
  91. Huang L, McCormick TM, Ochi M, Zhao Z, Suzuki M-T. 91.  et al. 2016. Nat. Mater. 15:1155–60 [Google Scholar]
  92. Deng K, Wan G, Deng P, Zhang K, Ding S. 92.  et al. 2016. Nat. Phys. 121105–10 [Google Scholar]
  93. Jiang J, Liu ZK, Sun Y, Yang HF, Rajamathi R. 93.  et al. 2016. arXiv:1604.00139
  94. Liang A, Huang J, Nie S, Ding Y, Gao Q. 94.  et al. 2016. arXiv:1604.01706
  95. Bruno FY, Tamai A, Wu QS, Cucchi I, Barreteau C. 95.  et al. 2016. Phys. Rev. B 94:121112(R) [Google Scholar]
  96. Wang C, Zhang Y, Huang J, Nie S, Liu G. 96.  et al. 2016. arXiv:1604.04218
  97. Wu Y, Jo NH, Mou D, Huang L, Bud'ko SL. 97.  et al. 2016. Phys. Rev. B 94:121113 [Google Scholar]
  98. Ali MN, Xiong J, Flynn S, Tao J, Gibson QD. 98.  et al. 2014. Nature 514:205–8 [Google Scholar]
  99. Muechler L, Alexandradinata A, Neupert T, Car R. 99.  2016. arXiv:1604.01398
  100. Keum DH, Cho S, Kim JH, Choe DH, Sung HJ. 100.  et al. 2015. Nat. Phys. 11:482–86 [Google Scholar]
  101. Qi Y, Naumov PG, Ali MN, Rajamathi CR, Schnelle W. 101.  et al. 2016. Nat. Commun. 7:11038 [Google Scholar]
  102. Kang D, Zhou Y, Yi W, Yang C, Guo J. 102.  et al. 2015. Nat. Commun. 6:7804 [Google Scholar]
  103. Pan XC, Chen X, Liu H, Feng Y, Wei Z. 103.  et al. 2015. Nat. Commun. 6:7805 [Google Scholar]
  104. Graf T, Felser C, Parkin SSP. 104.  2011. Prog. Solid State Chem. 39:1–50 [Google Scholar]
  105. Yan B, de Visser A. 105.  2014. MRS Bull. 39:859–66 [Google Scholar]
  106. Canfield PC, Thompson JD, Beyermann WP, Lacerda A, Hundley MF. 106.  et al. 1991. J. Appl. Phys. 70:5800 [Google Scholar]
  107. Butch NP, Syers P, Kirshenbaum K, Hope AP, Paglione J. 107.  2011. Phys. Rev. B 84:220504 [Google Scholar]
  108. Tafti F, Fujii T, Juneau-Fecteau A, de Cotret SR, Doiron-Leyraud N. 108.  et al. 2013. Phys. Rev. B 87:184504 [Google Scholar]
  109. Pan Y, Nikitin AM, Bay TV, Huang YK, Paulsen C. 109.  et al. 2013. Europhys. Lett. 104:27001 [Google Scholar]
  110. Nakajima Y, Hu R, Kirshenbaum K. 110.  2015. Sci. Adv. 1:e1500242 [Google Scholar]
  111. Kim H, Wang K, Nakajima Y, Hu R, Ziemak S. 111.  et al. 2016. arXiv:1603.03375
  112. Fisk Z, Canfield PC, Beyermann WP, Thompson JD, Hundley MF. 112.  et al. 1991. Phys. Rev. Lett. 67:3310–13 [Google Scholar]
  113. Fu L, Kane CL. 113.  2008. Phys. Rev. Lett. 100:096407 [Google Scholar]
  114. Chadov S, Qi XL, Kübler J, Fecher GH, Felser C, Zhang SC. 114.  2010. Nat. Mater. 9:541 [Google Scholar]
  115. Xiao D, Yao Y, Feng W, Wen J, Zhu W. 115.  et al. 2010. Phys. Rev. Lett. 105:096404 [Google Scholar]
  116. Lin H, Wray LA, Xia Y, Xu S, Jia S. 116.  et al. 2010. Nat. Mater. 9:546–49 [Google Scholar]
  117. Liu C, Lee Y, Kondo T, Mun ED, Caudle M. 117.  et al. 2011. Phys. Rev. B 83:205133 [Google Scholar]
  118. Wang W, Du Y, Xu G, Zhang X, Liu E. 118.  et al. 2013. Sci. Rep. 3:2181 [Google Scholar]
  119. Shekhar C, Kampert E, Foerster T, Yan B, Nayak AK. 119.  et al. 2015. arXiv:1502.00604
  120. Liu Z, Yang L, Wu SC, Shekhar C, Jiang J. 120.  et al. 2016. Nat. Commun. 7:12924 [Google Scholar]
  121. Logan JA, Patel SJ, Harrington SD, Polley CM, Schultz BD. 121.  et al. 2016. Nat. Commun. 7:11993 [Google Scholar]
  122. Chu RL, Shan WY, Lu J, Shen SQ. 122.  2011. Phys. Rev. B 83:075110 [Google Scholar]
  123. Bruene C, Liu CX, Novik EG, Hankiewicz EM, Buhmann H. 123.  et al. 2011. Phys. Rev. Lett. 106:126803 [Google Scholar]
  124. Wu SC, Yan B, Felser C. 124.  2014. Europhys. Lett. 107:57006 [Google Scholar]
  125. Shekhar C, Nayak AK, Singh S, Kumar N, Wu SC. 125.  et al. 2016. arXiv1604.01641
  126. Kreyssig A, Kim MG, Kim JW, Pratt DK, Sauerbrei SM. 126.  et al. 2011. Phys. Rev. B 84:220408 [Google Scholar]
  127. Müller RA, Lee-Hone NR, Lapointe L, Ryan DH, Pereg-Barnea T. 127.  et al. 2014. Phys. Rev. B 90:041109 [Google Scholar]
  128. Müller RA, Desilets-Benoit A, Gauthier N, Lapointe L, Bianchi AD. 128.  et al. 2015. Phys. Rev. B 92:184432 [Google Scholar]
  129. Hirschberger M, Kushwaha S, Wang Z, Gibson Q, Liang S. 129.  et al. 2016. Nat. Mater. 15:1161–65 [Google Scholar]
  130. Wang Z, Vergniory MG, Kushwaha S, Hirschberger M, Chulkov EV. 130.  et al. 2016. arXiv:1603.00479
  131. Ruan J, Jian SK, Yao H, Zhang H, Zhang SC, Xing D. 131.  2016. Nat. Commun. 7:11136 [Google Scholar]
  132. Yan B, Müchler L, Felser C. 132.  2012. Phys. Rev. Lett. 109:116406 [Google Scholar]
  133. Wang Z, Alexandradinata A, Cava RJ, Bernevig BA. 133.  2016. Nature 532:189–94 [Google Scholar]
  134. Tang P, Zhou Q, Xu G, Zhang SC. 134.  2016. Nat. Phys. 121100–4 [Google Scholar]
  135. Nakatsuji S, Kiyohara N, Higo T. 135.  2015. Nature 527:212–15 [Google Scholar]
  136. Nayak AK, Fischer JE, Sun Y, Yan B, Karel J. 136.  et al. 2016. Sci. Adv. 2:e1501870 [Google Scholar]
  137. Yang H, Sun Y, Zhang Y, Shi W-J, Parkin SSP, Yan B. 137.  2016. arXiv:1608.03404
  138. Schoop LM, Ali MN, Straßer C, Topp A, Varykhalov A. 138.  et al. 2016. Nat. Commun. 7:11696 [Google Scholar]
  139. Xu SY, Alidoust N, Chang G, Lu H, Singh B. 139.  et al. 2016. arXiv:1603.07318
  140. Sinova J, Valenzuela SO, Wunderlich J, Back C, Jungwirth T. 140.  2015. Rev. Mod. Phys. 87:1213 [Google Scholar]
  141. Müchler L, Zhang H, Chadov S, Yan B, Casper F. 141.  et al. 2012. Angew. Chem. 124:7333–37 [Google Scholar]
  142. Kong D, Cui Y. 142.  2011. Nat. Chem 3:845–49 [Google Scholar]
  143. Chen H, Zhu W, Xiao D, Zhang Z. 143.  2011. Phys. Rev. Lett. 107056804 [Google Scholar]
  144. Xiao J, Kou L, Yam CY, Frauenheim T, Yan B. 144.  2015. ACS Catal. 5:7063–67 [Google Scholar]
  145. Yan B, Stadtmüller B, Haag N, Jakobs S, Seidel J. 145.  et al. 2015. Nat. Commun. 6:10167 [Google Scholar]
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Topological Materials: Weyl Semimetals
Annual Review of Condensed Matter Physics 8, 337 (2017); https://doi.org/10.1146/annurev-conmatphys-031016-025458
/content/journals/10.1146/annurev-conmatphys-031016-025458
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