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Weyl Semimetals

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Topology in Magnetism

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 192))

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Abstract

Currently, the topological behavior in condensed matter system is a hot topic. As a new class of topological quantum material, Weyl semimetals (WSM) have attracted extensive interest. In this Book chapter, we review the basic concepts of WSM: the semimetallic states are topologically protected, with corresponding Fermi arcs surface states. We also summarize the unique transport properties and the recent progress in this field.

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References

  1. M.Z. Hasan, C.L. Kane, Rev. Mod. Phys. 82, 3045 (2010)

    Article  ADS  Google Scholar 

  2. X.L. Qi, S.C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)

    Article  ADS  Google Scholar 

  3. Y. Ando, J. Phys. Soc. Jpn. 82, 102001 (2013)

    Article  ADS  Google Scholar 

  4. X. Wan, A.M. Turner, A. Vishwanath, S.Y. Savrasov, Phys. Rev. B 83, 205101 (2011)

    Article  ADS  Google Scholar 

  5. H. Weyl, Zeitshrift fur Physik 56, 330 (1929)

    Article  ADS  Google Scholar 

  6. L. Balents, Physics 4, 36 (2011)

    Article  Google Scholar 

  7. T.O. Wehling, A.M. Black-Schaffer, A.V. Balatsky, Adv. Phys. 63, 1 (2014)

    Article  ADS  Google Scholar 

  8. N.P. Armitage, E.J. Mele, A. Vishwanath, arXiv:1705.01111 (2017)

  9. N. Taria, M. Wakeshima, Y. Hinatsu, J. Phys. Condens. Matter 13, 5527 (2001)

    Article  ADS  Google Scholar 

  10. K. Matsuhira et al., J. Phys. Soc. Jpn. 76, 043706 (2007)

    Article  ADS  Google Scholar 

  11. S. Nakatsuj, Phys. Rev. Lett. 96, 087204 (2006). Y. Machida et al., Nature 463, 210 (2011)

    Google Scholar 

  12. K. Matsuhira et al., J. Phys. Soc. Jpn. 80, 094701 (2011)

    Article  ADS  Google Scholar 

  13. S.M. Disseler, Phys. Rev. B 89, 140413 (2014). H. Liu et al., Solid State Commum. 179, 1 (2014)

    Google Scholar 

  14. J.J. Ishikawa, E.C.T. O’Farrell, S. Nakatsuji, Phys. Rev. B 85, 245109 (2012)

    Article  ADS  Google Scholar 

  15. E.Y. Ma et al., Science 350, 538 (2015)

    Article  ADS  Google Scholar 

  16. D.A. Pesin, L. Balents, Nature Phys. 6, 376 (2010)

    Article  ADS  Google Scholar 

  17. G. Kotliar, S.Y. Savrasov, K. Haule, V.S. Oudovenko, O. Parcollet, C.A. Marianetti, Rev. Mod. Phys. 78, 865 (2006)

    Article  ADS  Google Scholar 

  18. D. Lurie, Particles and Fields (Wiley, New York, 1968)

    Google Scholar 

  19. A.M. Turner, A. Vishwanath, arXiv:1301.0330 (2013)

  20. S.M. Young, S. Zaheer, J.C.Y. Teo, C.L. Kane, E.J. Mele, A.M. Rappe, Phys. Rev. Lett. 108, 140405 (2012)

    Article  ADS  Google Scholar 

  21. Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, Z. Fang, Phys. Rev. B 85, 195320 (2012)

    Article  ADS  Google Scholar 

  22. Z. Wang, H. Weng, Q. Wu, X. Dai, Z. Fang, Phys. Rev. B 88, 125427 (2013)

    Article  ADS  Google Scholar 

  23. Y. Du, B. Wan, D. Wang, L. Sheng, C.-G. Duan, X. Wan, Sci. Rep. 5, 14423 (2015)

    Article  ADS  Google Scholar 

  24. D. Xiao, M.-C. Chang, Q. Niu, Rev. Mod. Phys. 82, 1959 (2010)

    Article  ADS  Google Scholar 

  25. R. Arita, J. Kuneš, A.V. Kozhevnikov, A.G. Eguiluz, M. Imada, Phys. Rev. Lett. 108, 086403 (2012)

    Article  ADS  Google Scholar 

  26. K.-Y. Yang, Y.-M. Lu, Y. Ran, Phys. Rev. B 84, 075129 (2011)

    Article  ADS  Google Scholar 

  27. H.-Z. Lu, S.- B. Zhang, S.-Q. Shen, Phys. Rev. B 92, 045203 (2015)

    Google Scholar 

  28. G.E. Volovik, The Universe in a Helium Droplet (Clarendon Press, 2003)

    Google Scholar 

  29. Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  30. H.-Z. Lu, W.-Y. Shan, W. Yao, Q. Niu, S.-Q. Shen, Phys. Rev. B 81, 115407 (2010)

    Article  ADS  Google Scholar 

  31. D.T. Son, B.Z. Spivak, Phys. Rev. B 88, 104412 (2013)

    Article  ADS  Google Scholar 

  32. D.E. Kharzeev, H.U. Yee, Phys. Rev. B 88, 115119 (2013)

    Article  ADS  Google Scholar 

  33. A.A. Burkov, Phys. Rev. Lett. 113, 247203 (2014)

    Article  ADS  Google Scholar 

  34. D.T. Son, N. Yamamoto, Phys. Rev. Lett. 109, 181602 (2012)

    Article  ADS  Google Scholar 

  35. M.A. Stephanov, Y. Yin, Phys. Rev. Lett. 109, 162001 (2012)

    Article  ADS  Google Scholar 

  36. K. Landsteiner, E. Megías, F. Pena-Benitez, Phys. Rev. Lett. 107, 021601 (2011)

    Article  ADS  Google Scholar 

  37. M.-C. Chang, M.-F. Yang, Phys. Rev. B 91, 115203 (2015)

    Article  ADS  Google Scholar 

  38. S.L. Adler, Phys. Rev. 177, 2426 (1969)

    Article  ADS  Google Scholar 

  39. J.S. Bell, R. Jackiw, Il Nuovo Cimento A 60, 47 (1969)

    Article  ADS  Google Scholar 

  40. H.B. Nielsen, M. Ninomiya, Phys. Lett. B 130, 389 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  41. H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 185, 20 (1981)

    Article  ADS  Google Scholar 

  42. H.J. Kim et al., Phys. Rev. Lett. 111, 246603 (2013)

    Article  ADS  Google Scholar 

  43. K.S. Kim, H.J. Kim, M. Sasaki, Phys. Rev. B 89, 195137 (2014)

    Article  ADS  Google Scholar 

  44. X.C. Huang et al., Phys. Rev. X 5, 031023 (2015)

    Google Scholar 

  45. C.L. Zhang et al., Nat. Commun. 7, 10735 (2016)

    Article  ADS  Google Scholar 

  46. C. Zhang et al., Phys. Rev. B 92, 041203 (2015)

    Article  ADS  Google Scholar 

  47. F. Arnold et al., Nat. Commun. 7, 11615 (2016)

    Article  ADS  Google Scholar 

  48. C.-L. Zhang et al., Nat. Phys. 13, 979 (2017)

    Article  Google Scholar 

  49. E.V. Gorbar, V.A. Miransky, I.A. Shovkovy, Phys. Rev. B 89, 085126 (2014)

    Article  ADS  Google Scholar 

  50. S. Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, 1997)

    Google Scholar 

  51. V. Aji, Phys. Rev. B 85, 241101 (2012)

    Article  ADS  Google Scholar 

  52. P. Goswami, J.H. Pixley, S.D. Sarma, Phys. Rev. B 92, 075205 (2015)

    Google Scholar 

  53. M.-C. Chang, Q. Niu, Phys. Rev. Lett. 75, 1348 (1995)

    Article  ADS  Google Scholar 

  54. J.-H. Zhou, H. Jiang, Q. Niu, J.-R. Shi, Chin. Phys. Lett. 30, 027101 (2013)

    Article  ADS  Google Scholar 

  55. A.A. Burkov, Phys. Rev. B 91, 245157 (2015)

    Article  ADS  Google Scholar 

  56. P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)

    Article  ADS  Google Scholar 

  57. H.-Z. Lu, S.-Q. Shen, Phys. Rev. B 92, 035203 (2015)

    Article  ADS  Google Scholar 

  58. G.D. Mahan, Many-Particle Physics (Plenum Press, 1990)

    Google Scholar 

  59. S. Murakami, New J. Phys. 9, 356 (2007)

    Article  ADS  Google Scholar 

  60. G. Xu, H. Weng, Z. Wang, X. Dai, Z. Fang, Phys. Rev. Lett. 107, 186806 (2011)

    Article  ADS  Google Scholar 

  61. P.K. Baltzer, H.W. Lehmann, M. Robbins, Phys. Rev. Lett. 15, 493 (1965)

    Article  ADS  Google Scholar 

  62. P.K. Baltzer, P.J. Wojtowicz, M. Robbins, E. Lopatin, Phys. Rev. 151, 367 (1966)

    Article  ADS  Google Scholar 

  63. T. Guan, C. Lin, C. Yang, Y. Shi, C. Ren, Y. Li, H. Weng, X. Dai, Z. Fang, S. Yan, P. Xiong, Phys. Rev. Lett. 115, 087002 (2015)

    Article  ADS  Google Scholar 

  64. A.A. Burkov, L. Balents, Phys. Rev. Lett. 107, 127205 (2011)

    Article  ADS  Google Scholar 

  65. X. Wan, A. Vishwanath, S.Y. Savrasov, Phys. Rev. Lett. 108, 146601 (2012)

    Article  ADS  Google Scholar 

  66. D. Bulmash, C.-X. Liu, X.-L. Qi, Phys. Rev. B 89, 081106 (2014)

    Article  ADS  Google Scholar 

  67. H. Weng, C. Fang, Z. Fang, B.A. Bernevig, X. Dai, Phys. Rev. X 5, 011029 (2015)

    Google Scholar 

  68. S.-M. Huang et al., Nat. Commun. 6, 7373 (2015)

    Article  Google Scholar 

  69. G. Bian et al., Nat. Commun. 7, 10556 (2015)

    Article  ADS  Google Scholar 

  70. A.M. Turner, Y. Zhang, R.S.K. Mong, A. Vishwanath, Phys. Rev. B 85, 165120 (2012)

    Article  ADS  Google Scholar 

  71. T.L. Hughes, E. Prodan, B.A. Bernevig, Phys. Rev. B 83, 245132 (2011)

    Article  ADS  Google Scholar 

  72. T. Fukui, Y. Hatsugai, H. Suzuki, J. Phys. Soc. Jpn. 74, 6 (2005)

    Article  Google Scholar 

  73. M. Taillefumier, V.K. Dugaev, B. Canals, C. Lacroix, P. Bruno, Phys. Rev. B 78, 155330 (2008)

    Article  ADS  Google Scholar 

  74. B.Q. Lv et al., Phy. Rev. X 5, 031013 (2015)

    Google Scholar 

  75. B.Q. Lv et al., Nat. Phys. 11, 724 (2015)

    Article  Google Scholar 

  76. S.-Y. Xu et al., Science 349, 613 (2015)

    Article  ADS  Google Scholar 

  77. L.X. Yang et al., Nat. Phys. 11, 728 (2015)

    Article  Google Scholar 

  78. S.-Y. Xu et al., Nat. Phys. 11, 748 (2015)

    Article  Google Scholar 

  79. N. Xu et al., Nat. Commun. 7, 11006 (2016)

    Article  ADS  Google Scholar 

  80. S.-Y. Xu et al., Sci. Adv. 1, 1501092 (2015)

    Article  ADS  Google Scholar 

  81. D.F. Xu et al., Chin. Phys. Lett. 32, 107101 (2015)

    Article  ADS  Google Scholar 

  82. S.-B. Zhang, H.-Z. Lu, S.-Q. Shen, New J. Phys. 18, 053039 (2016)

    Article  ADS  Google Scholar 

  83. S.-K. Jian, Y.-F. Jiang, H. Yao, Phys. Rev. Lett. 114, 237001 (2015)

    Article  ADS  Google Scholar 

  84. P. Hosur, X. Qi, CR Phys. 14, 857 (2013)

    Article  ADS  Google Scholar 

  85. J. Ruan, S.-K. Jian, D. Zhang, H. Yao, H. Zhang, S.-C. Zhang, D. Xing, Phys. Rev. Lett. 116, 226801 (2016)

    Article  ADS  Google Scholar 

  86. J. Ruan, S.-K. Jian, H. Yao, H. Zhang, S.-C. Zhang, D. Xing, Nat. Commun. 7, 11136 (2016)

    Article  ADS  Google Scholar 

  87. C.-K. Chan, P.A. Lee, K.S. Burch, J.H. Han, Y. Ran, Phys. Rev. Lett. 116, 026805 (2016)

    Article  ADS  Google Scholar 

  88. C.-K. Chan, N.H. Lindner, G. Refael, P.A. Lee, Phys. Rev. B 95, 041104 (2017)

    Article  ADS  Google Scholar 

  89. G.B. Halasz, L. Balents, Phys. Rev. B 85, 035103 (2012)

    Article  ADS  Google Scholar 

  90. M. Hirayama, R. Okugawa, S. Ishibashi, S. Murakami, T. Miyake, Phys. Rev. Lett. 114, 206401 (2015)

    Article  ADS  Google Scholar 

  91. J. Liu, D. Vanderbilt, Phys. Rev. B 90, 155316 (2014)

    Article  ADS  Google Scholar 

  92. A.A. Soluyanov et al., Nature 527, 495 (2015)

    Article  ADS  Google Scholar 

  93. Y. Xu, F. Zhang, C. Zhang, Phys. Rev. Lett. 115, 265304 (2015)

    Article  ADS  Google Scholar 

  94. M.N. Ali et al., Nature 514, 205 (2014)

    Article  ADS  Google Scholar 

  95. J. Jiang et al., Phys. Rev. Lett. 115, 166601 (2015)

    Article  ADS  Google Scholar 

  96. X.-C. Pan et al., Nat. Commun. 6, 7805 (2015)

    Article  Google Scholar 

  97. D. Kang et al., Nat. Commun. 6, 7804 (2015)

    Article  Google Scholar 

  98. Z.-M. Yu, Y. Yao, S.A. Yang, Phys. Rev. Lett. 117, 077202 (2016)

    Article  ADS  Google Scholar 

  99. A.A. Zyuzin, R.P. Tiwari, JETP Lett. 103, 717 (2016)

    Article  ADS  Google Scholar 

  100. M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nat. Phys. 2, 620 (2006)

    Article  Google Scholar 

  101. T.E. O’Brien, M. Diez, C.W.J. Beenakker, Phys. Rev. Lett. 116, 236401 (2016)

    Article  ADS  Google Scholar 

  102. Y. Wang et al., Nat. Commun. 7, 13142 (2016)

    Article  ADS  Google Scholar 

  103. E. Zhang et al., Nano Lett. 17, 878 (2017)

    Article  ADS  Google Scholar 

  104. Y.-Y. Lv et al., Phys. Rev. Lett. 118, 096603 (2017)

    Article  ADS  Google Scholar 

  105. I. Pletikosić, Mazhar N. Ali, A.V. Fedorov, R.J. Cava, T. Valla, Phys. Rev. Lett. 113, 216601 (2014)

    Article  ADS  Google Scholar 

  106. P.L. Cai et al., Phys. Rev. Lett. 115, 057202 (2015)

    Article  ADS  Google Scholar 

  107. Z. Zhu et al., Phys. Rev. Lett. 114, 176601 (2015)

    Article  ADS  Google Scholar 

  108. C. Wang et al., Phys. Rev. B 94, 241119 (2016)

    Article  ADS  Google Scholar 

  109. Y. Sun, S.-C. Wu, M.N. Ali, C. Felser, B. Yan, Phys. Rev. B 92, 161107 (2015)

    Article  ADS  Google Scholar 

  110. Z. Wang et al., Phys. Rev. Lett. 117, 056805 (2016)

    Article  ADS  Google Scholar 

  111. T.-R. Chang et al., Nat. Commun. 7, 10639 (2016)

    Article  ADS  Google Scholar 

  112. I. Belopolski et al., Nat. Commun. 7, 13643 (2016)

    Article  ADS  Google Scholar 

  113. M. Udagawa, E.J. Bergholtz, Phys. Rev. Lett. 117, 086401 (2016)

    Article  ADS  Google Scholar 

  114. G. Autes, D. Gresch, M. Troyer, A.A. Soluyanov, O.V. Yazyev, Phys. Rev. Lett. 117, 066402 (2016)

    Article  ADS  Google Scholar 

  115. G. Chang et al., Sci. Adv. 2, e1600295 (2016)

    Article  ADS  Google Scholar 

  116. K. Koepernik et al., Phys. Rev. B 93, 201101 (2016)

    Article  ADS  Google Scholar 

  117. S.A. Parameswaran, T. Grover, D.A. Abanin, D.A. Pesin, A. Vishwanath, Phys. Rev. X 4, 031035 (2014)

    Google Scholar 

  118. A.C. Potter, I. Kimchi, A. Vishwanath, Nat. Commun. 5, 5161 (2014)

    Article  ADS  Google Scholar 

  119. P. Hosur, X. Dai, Z. Fang, X.-L. Qi, Phys. Rev. B 90, 045130 (2014)

    Article  ADS  Google Scholar 

  120. G. Bednik, A.A. Zyuzin, A.A. Burkov, Phys. Rev. B. 92, 035153 (2015)

    Article  ADS  Google Scholar 

  121. Y. Li, F.D.M. Haldane, arXiv:1510.01730 (2015)

  122. L. Lu, L. Fu, J.D. Joannopoulos, M. Soljacic, Nat. Photon. 7, 294 (2013)

    Article  ADS  Google Scholar 

  123. L. Lu et al., Science 349, 622 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  124. F.-Y. Li, Y.-D. Li, Y.B. Kim, L. Balents, Y. Yu, G. Chen, Nat. Commun. 7, 12691 (2016)

    Article  ADS  Google Scholar 

  125. Z. Yang, B. Zhang, Phys. Rev. Lett. 117, 224301 (2016)

    Article  ADS  Google Scholar 

  126. F. Tang, X. Luo, Y. Du, Y. Yu and X. Wan, arXiv:1612.05938 (2016)

  127. B. Bradlyn, J. Cano, Z. Wang, M.G. Vergniory, C. Felser, R.J. Cava, B.A. Bernevig, Science 353, 6299 (2016)

    Article  Google Scholar 

  128. B.Q. Lv et al., Nature 546, 627 (2017)

    Article  ADS  Google Scholar 

  129. H. Weng, C. Fang, Z. Fang, X. Dai, Phys. Rev. B 94, 165201 (2016)

    Article  ADS  Google Scholar 

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Acknowledgements

This work was supported by NSFC (Grants No. 11525417, No. 51721001, and No. 11574127), Guangdong Innovative and Entrepreneurial Research Team Program (Grant No. 2016ZT06D348), the National Key R & D Program (Grant No. 2016YFA0301700), and the Science, Technology and Innovation Commission of Shenzhen Municipality (Grant No. ZDSYS20170303165926217).

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Authors and Affiliations

  1. National Laboratory of Solid State Microstructures, School of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China

    Bo Wan & Xiangang Wan

  2. Institute for Quantum Science and Engineering and Department of Physics, South University of Science and Technology of China, Shenzhen, 518055, China

    Bo Wan & Hai-Zhou Lu

  3. Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, 51805, China

    Hai-Zhou Lu

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  1. Bo Wan
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  2. Hai-Zhou Lu
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  3. Xiangang Wan
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Correspondence to Xiangang Wan .

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Editors and Affiliations

  1. University of New Hampshire, Durham, NH, USA

    Jiadong Zang

  2. Unité Mixte de Physique CNRS/Thales, Palaiseau, France

    Vincent Cros

  3. Materials Science Division, Argonne National Laboratory, Lemont, IL, USA

    Axel Hoffmann

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Wan, B., Lu, HZ., Wan, X. (2018). Weyl Semimetals. In: Zang, J., Cros, V., Hoffmann, A. (eds) Topology in Magnetism. Springer Series in Solid-State Sciences, vol 192. Springer, Cham. https://doi.org/10.1007/978-3-319-97334-0_8

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