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Topological Dirac and Weyl Semimetals

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Topological Insulators

Part of the book series: Springer Series in Solid-State Sciences ((SSSOL,volume 187))

Abstract

A topological Dirac or Weyl semimetal is a topological phase of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Uniaxial rotation symmetries protect the nodes against gap formation. Topological Weyl semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. The chiral anomaly of the Weyl fermions , a pure quantum mechanical phenomenon, can be realized in solids, and is attributed to the exotic magneto-transport properties in Weyl and Dirac semimetals.

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References

  1. H. Weyl, Z. Phys. 56, 330 (1929)

    Article  ADS  Google Scholar 

  2. H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 193, 173 (1981)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. B.J. Yang, N. Nagaosa, Nat. Commun. 5, 4898 (2014)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Z.J. Wang et al., Phys. Rev. B 85, 195320 (2012)

    Article  ADS  Google Scholar 

  8. Z.K. Liu et al., Nat. Mater. 13, 677 (2014)

    Article  ADS  Google Scholar 

  9. M. Neupane et al., Nat. Commun. 5, 3786 (2014)

    Google Scholar 

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

    Article  Google Scholar 

  11. H.M. Weng et al., Phys Rev. X 5, 011029 (2015)

    Google Scholar 

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

    Article  ADS  Google Scholar 

  13. B.Q. Lv et al., Phys. Rev. X 5, 031013 (2015)

    Google Scholar 

  14. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  15. S.M. Young, C.L. Kane, Phys. Rev. Lett. 115, 126803 (2015)

    Article  ADS  Google Scholar 

  16. H. Suzuura, T. Ando, Phys. Rev. Lett. 89, 266603 (2002)

    Article  ADS  Google Scholar 

  17. S.-Q. Shen, Phys. Rev. B 70, 081311(R) (2004)

    Article  ADS  Google Scholar 

  18. G.P. Mikitik, Y.V. Sharlai, Phys. Rev. Lett. 82, 2147 (1999)

    Article  ADS  Google Scholar 

  19. K. Wakabayashi, K. Ichi Sasaki, T. Nakanishi, T. Enoki, Sci. Technol. Adv. Mater. 11, 054504 (2010)

    Article  Google Scholar 

  20. S. Ryu, Y. Hatsugai, Phys. Rev. Lett. 89, 077002 (2002)

    Article  ADS  Google Scholar 

  21. P. Hosur, X. Qi, C. R. Phys. 14, 857 (2013)

    Article  ADS  Google Scholar 

  22. S.Q. Shen, C.A. Li, Q. Niu, 2D Mater. 4, 035014 (2017)

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. H. Li et al., Nat. Commun. 7, 10301 (2016)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. S.Q. Shen, M. Ma, X.C. Xie, F.C. Zhang, Phys. Rev. Lett. 92, 256603 (2004)

    Article  ADS  Google Scholar 

  29. A. Zee, Quantum Field Theory in a Nutshell (Princeton University Press, Princeton, 2003)

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. J.S. Bell, R.W. Jackiw, Nuov. Cim. A 60, 4 (1969)

    Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  33. A. Zee, Quantum Field Theory in a Nutshell (Princeton University Press, Princeton, 2010)

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. J. Xiong et al., Science 350, 413 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  37. Q. Li et al., Nat. Phys. 12, 550 (2016)

    Article  Google Scholar 

  38. K. Fukushima, D.E. Kharzeev, H.J. Warringa, Phys. Rev. D 78, 074033 (2008)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. T. Liang, Q. Gibson, M.N. Ali, M. Liu, R.J. Cava, N.P. Ong, Nat. Mater. 14, 280 (2015)

    Article  ADS  Google Scholar 

  41. c Shekhar et al., Nat. Phys. 11, 645–649 (2015)

    Article  Google Scholar 

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Correspondence to Shun-Qing Shen .

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Shen, SQ. (2017). Topological Dirac and Weyl Semimetals. In: Topological Insulators. Springer Series in Solid-State Sciences, vol 187. Springer, Singapore. https://doi.org/10.1007/978-981-10-4606-3_11

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