1932

Abstract

Weyl metal is the first example of a conducting material with a nontrivial electronic structure topology, making it distinct from an ordinary metal. Unlike in insulators, the nontrivial topology is not related to invariants associated with completely filled bands but with ones associated with the Fermi surface. The Fermi surface of a topological metal consists of disconnected sheets, each enclosing a Weyl node, which is a point of contact between two nondegenerate bands. Such a point contact acts as a source of Berry curvature or a magnetic monopole in momentum space. Its charge, or the flux of the Berry curvature through the enclosing Fermi surface sheet, is a topological invariant. We review the current state of this rapidly growing field with a focus on bulk transport phenomena in topological metals.

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/content/journals/10.1146/annurev-conmatphys-033117-054129
2018-03-10
2024-04-19
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Literature Cited

  1. Haldane FDM. 1.  1988. Phys. Rev. Lett. 61:2015–18
  2. Hasan MZ, Kane CL. 2.  2010. Rev. Mod. Phys. 82:3045–67
  3. Qi XL, Zhang SC. 3.  2011. Rev. Mod. Phys. 83:1057–110
  4. Volovik G. 4.  2003. The Universe in a Helium Droplet Oxford, UK: Clarendon
  5. Haldane FDM. 5.  2004. Phys. Rev. Lett. 93:206602
  6. Volovik GE. 6.  2007. Quantum Analogues: From Phase Transitions to Black Holes and Cosmology W Unruh, R Schtzhold , vol. 718 Lecture Notes in Physics 31–73 Berlin/Heidelberg: Springer
  7. Murakami S. 7.  2007. New J. Phys. 9:356
  8. Wan X, Turner AM, Vishwanath A, Savrasov SY. 8.  2011. Phys. Rev. B 83:205101
  9. Yang KY, Lu YM, Ran Y. 9.  2011. Phys. Rev. B 84:075129
  10. Burkov AA, Balents L. 10.  2011. Phys. Rev. Lett. 107:127205
  11. Burkov AA, Hook MD, Balents L. 11.  2011. Phys. Rev. B 84:235126
  12. Xu G, Weng H, Wang Z, Dai X, Fang Z. 12.  2011. Phys. Rev. Lett. 107:186806
  13. Young SM, Zaheer S, Teo JCY, Kane CL, Mele EJ, Rappe AM. 13.  2012. Phys. Rev. Lett. 108:140405
  14. Wang Z, Sun Y, Chen XQ, Franchini C, Xu G. 14.  et al. 2012. Phys. Rev. B 85:195320
  15. Wang Z, Weng H, Wu Q, Dai X, Fang Z. 15.  2013. Phys. Rev. B 88:125427
  16. Xu SY, Belopolski I, Alidoust N, Neupane M, Bian G. 16.  et al. 2015. Science 349:613–17
  17. Neupane M, Xu SY, Sankar R, Alidoust N, Bian G. 17.  et al. 2014. Nat. Commun. 5:3786
  18. Lv BQ, Xu N, Weng HM, Ma JZ, Richard P. 18.  et al. 2015. Nat. Phys. 11:724–27
  19. Lv BQ, Weng HM, Fu BB, Wang XP, Miao H. 19.  et al. 2015. Phys. Rev. X 5:031013
  20. Lu L, Wang Z, Ye D, Ran L, Fu L. 20.  et al. 2015. Science 349:622–24
  21. Yan B, Felser C. 21.  2017. Annu. Rev. Condens. Matter Phys. 8:337–54
  22. Hasan MZ, Xu SY, Belopolski I, Huang SM. 22.  2017. Annu. Rev. Condens. Matter Phys. 8:289–309
  23. Kohmoto M, Halperin BI, Wu YS. 23.  1992. Phys. Rev. B 45:13488–93
  24. Chang CZ, Zhang J, Feng X, Shen J, Zhang Z. 24.  et al. 2013. Science 340:167–70
  25. Liu C-X, Zhang S-C, Qi X-L. 25.  2016. Annu. Rev. Condens. Matter Phys. 7:301–21
  26. Redlich AN. 26.  1984. Phys. Rev. Lett. 52:18–21
  27. Ludwig AWW, Fisher MPA, Shankar R, Grinstein G. 27.  1994. Phys. Rev. B 50:7526–52
  28. Fu L, Kane CL. 28.  2007. Phys. Rev. B 76:045302
  29. Halász GB, Balents L. 29.  2012. Phys. Rev. B 85:035103
  30. Adler SL. 30.  1969. Phys. Rev. 177:2426–38
  31. Bell JS, Jackiw R. 31.  1969. Nuovo Cim. A 60:4
  32. Alekseev AY, Cheianov VV, Fröhlich J. 32.  1998. Phys. Rev. Lett. 81:3503–6
  33. Zyuzin AA, Wu S, Burkov AA. 33.  2012. Phys. Rev. B 85:165110
  34. Vazifeh MM, Franz M. 34.  2013. Phys. Rev. Lett. 111:027201
  35. Zhang SC, Hu J. 35.  2001. Science 294:823–28
  36. Chen Y, Wu S, Burkov AA. 36.  2013. Phys. Rev. B 88:125105
  37. Burkov AA. 37.  2014. Phys. Rev. Lett. 113:247203
  38. Burkov AA. 38.  2015. Phys. Rev. B 91:245157
  39. Fukushima K, Kharzeev DE, Warringa HJ. 39.  2008. Phys. Rev. D 78:074033
  40. Son DT, Yamamoto N. 40.  2012. Phys. Rev. Lett. 109:181602
  41. Altland A, Bagrets D. 41.  2016. Phys. Rev. B 93:075113
  42. Son DT, Spivak BZ. 42.  2013. Phys. Rev. B 88:104412
  43. Lundgren R, Laurell P, Fiete GA. 43.  2014. Phys. Rev. B 90:165115
  44. Hirschberger M, Kushwaha S, Wang Z, Gibson Q, Liang S. 44.  et al. 2016. Nat. Mater. 15:1161–65
  45. Spivak BZ, Andreev AV. 45.  2016. Phys. Rev. B 93:085107
  46. Lucas A, Davison RA, Sachdev S. 46.  2016. PNAS 113:9463–68
  47. Burkov AA, Kim YB. 47.  2016. Phys. Rev. Lett. 117:136602
  48. Xiong J, Kushwaha SK, Liang T, Krizan JW, Hirschberger M. 48.  et al. 2015. Science 350:413–16
  49. Li Q, Kharzeev DE, Zhang C, Huang Y, Pletikosic I. 49.  et al. 2016. Nat. Phys. 12:550–54
  50. Parameswaran SA, Grover T, Abanin DA, Pesin DA, Vishwanath A. 50.  2014. Phys. Rev. X 4:031035
  51. Abanin DA, Morozov SV, Ponomarenko LA, Gorbachev RV, Mayorov AS. 51.  et al. 2011. Science 332:328–30
  52. Moll PJW, Nair NL, Helm T, Potter AC, Kimchi I. 52.  et al. 2016. Nature 535:266–70
  53. Baum Y, Berg E, Parameswaran SA, Stern A. 53.  2015. Phys. Rev. X 5:041046
  54. Baireuther P, Hutasoit JA, Tworzyd J, Beenakker CWJ. 54.  2016. New J. Phys. 18:045009
  55. Jian-Hui Z, Hua J, Qian N, Jun-Ren S. 55.  2013. Chin. Phys. Lett. 30:027101
  56. Cortijo A, Ferreirós Y, Landsteiner K, Vozmediano MAH. 56.  2015. Phys. Rev. Lett. 115:177202
  57. Pikulin DI, Chen A, Franz M. 57.  2016. Phys. Rev. X 6:041021
  58. Grushin AG, Venderbos JWF, Vishwanath A, Ilan R. 58.  2016. Phys. Rev. X 6:041046
  59. Soluyanov AA, Gresch D, Wang Z, Wu Q, Troyer M. 59.  et al. 2015. Nature 527:495–98
  60. Lee PA, Ramakrishnan TV. 60.  1985. Rev. Mod. Phys. 57:287–337
  61. Moll PJW, Potter AC, Nair NL, Ramshaw BJ, Modic KA. 61.  et al. 2016. Nat. Commun. 7:12492
  62. Liu CX, Ye P, Qi XL. 62.  2013. Phys. Rev. B 87:235306
  63. Panfilov I, Burkov AA, Pesin DA. 63.  2014. Phys. Rev. B 89:245103
  64. Zhou J, Chang HR, Xiao D. 64.  2015. Phys. Rev. B 91:035114
  65. Araki Y, Nomura K. 65.  2016. Phys. Rev. B 93:094438
  66. Zhang XX, Nagaosa N. 66.  2017. Phys. Rev. B 95:205143
  67. Morimoto T, Nagaosa N. 67.  2016. Sci. Rep. 6:19853
  68. Meng T, Grushin AG, Shtengel K, Bardarson JH. 68.  2017. Phys. Rev. B 94:155136
  69. Meng T, Balents L. 69.  2012. Phys. Rev. B 86:054504
  70. Cho GY, Bardarson JH, Lu YM, Moore JE. 70.  2012. Phys. Rev. B 86:214514
  71. Wei H, Chao SP, Aji V. 71.  2014. Phys. Rev. B 89:014506
  72. Lu B, Yada K, Sato M, Tanaka Y. 72.  2015. Phys. Rev. Lett. 114:096804
  73. Bednik G, Zyuzin AA, Burkov AA. 73.  2015. Phys. Rev. B 92:035153
  74. Li Y, Haldane FDM. 74.  2015. arXiv:1510.01730
  75. Bednik G, Zyuzin AA, Burkov AA. 75.  2016. New J. Phys. 18:085002
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