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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
H. Weyl, Z. Phys. 56, 330 (1929)
H.B. Nielsen, M. Ninomiya, Nucl. Phys. B 193, 173 (1981)
S. Murakami, New J. Phys. 9, 356 (2007)
B.J. Yang, N. Nagaosa, Nat. Commun. 5, 4898 (2014)
H.J. Kim et al., Phys. Rev. Lett. 111, 246603 (2013)
Z.J. Wang, H.M. Weng, Q. Wu, X. Dai, Z. Fang, Phys. Rev. B 88, 125427 (2013)
Z.J. Wang et al., Phys. Rev. B 85, 195320 (2012)
Z.K. Liu et al., Nat. Mater. 13, 677 (2014)
M. Neupane et al., Nat. Commun. 5, 3786 (2014)
S.M. Huang et al., Nat. Commun. 6, 7373 (2015)
H.M. Weng et al., Phys Rev. X 5, 011029 (2015)
S.-Y. Xu et al., Science 349, 613 (2015)
B.Q. Lv et al., Phys. Rev. X 5, 031013 (2015)
A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)
S.M. Young, C.L. Kane, Phys. Rev. Lett. 115, 126803 (2015)
H. Suzuura, T. Ando, Phys. Rev. Lett. 89, 266603 (2002)
S.-Q. Shen, Phys. Rev. B 70, 081311(R) (2004)
G.P. Mikitik, Y.V. Sharlai, Phys. Rev. Lett. 82, 2147 (1999)
K. Wakabayashi, K. Ichi Sasaki, T. Nakanishi, T. Enoki, Sci. Technol. Adv. Mater. 11, 054504 (2010)
S. Ryu, Y. Hatsugai, Phys. Rev. Lett. 89, 077002 (2002)
P. Hosur, X. Qi, C. R. Phys. 14, 857 (2013)
S.Q. Shen, C.A. Li, Q. Niu, 2D Mater. 4, 035014 (2017)
D. Xiao, M.C. Chang, Q. Niu, Rev. Mod. Phys. 82, 1959 (2010)
H.Z. Lu, W.Y. Shan, W. Yao, Q. Niu, S.Q. Shen, Phys. Rev. B 81, 115407 (2010)
H. Li et al., Nat. Commun. 7, 10301 (2016)
Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993)
S.B. Zhang, H.Z. Lu, S.Q. Shen, New J. Phys. 18, 053039 (2016)
S.Q. Shen, M. Ma, X.C. Xie, F.C. Zhang, Phys. Rev. Lett. 92, 256603 (2004)
A. Zee, Quantum Field Theory in a Nutshell (Princeton University Press, Princeton, 2003)
S.L. Adler, Phys. Rev. 177, 2426 (1969)
J.S. Bell, R.W. Jackiw, Nuov. Cim. A 60, 4 (1969)
H.B. Nielsen, M. Ninomiya, Phys. Lett. B 130, 389 (1983)
A. Zee, Quantum Field Theory in a Nutshell (Princeton University Press, Princeton, 2010)
H.Z. Lu, S.Q. Shen, Phys. Rev. B 92, 035203 (2015)
C.L. Zhang et al., Nat. Commun. 7, 10735 (2016)
J. Xiong et al., Science 350, 413 (2015)
Q. Li et al., Nat. Phys. 12, 550 (2016)
K. Fukushima, D.E. Kharzeev, H.J. Warringa, Phys. Rev. D 78, 074033 (2008)
D.T. Son, B.Z. Spivak, Phys. Rev. B 88, 104412 (2013)
T. Liang, Q. Gibson, M.N. Ali, M. Liu, R.J. Cava, N.P. Ong, Nat. Mater. 14, 280 (2015)
c Shekhar et al., Nat. Phys. 11, 645–649 (2015)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-981-10-4606-3_11
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-4605-6
Online ISBN: 978-981-10-4606-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)