Abstract
The Weyl semimetal, due to a non-zero energy difference in the pair of Weyl nodes, shows chiral magnetic effect (CME). This leads to a flow of dissipationless electric current along an applied magnetic field. Such a chiral magnetic effect in Weyl semimetals has been studied using the laws of classical electrodynamics. It has been shown that the CME in such a semimetal changes the properties namely, frequency-dependent skin depth, capacitive transport, plasma frequency, etc., in an unconventional way as compared to the conventional metals. In the low-frequency regime, the properties are controlled by a natural length scale due to CME called the chiral magnetic length. Furthermore, unlike the conventional metals, the plasma frequency in this case is shown to be strongly magnetic field-dependent. Since the plasma frequency lies below the optical frequency, the Weyl semimetals will look transparent. Such new and novel observations might help in exploiting these class of materials in potential applications which would completely change the future technology.
Graphic abstract
Similar content being viewed by others
Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This manuscript is a theoretical one and it contains no experimental data.]
References
C.L. Kane, E.J. Mele, \(Z_2\) Topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005)
C.L. Kane, E.J. Mele, Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005)
B.A. Bernevig, T.L. Hughes, S.-C. Zhang, Quantum spin Hall effect and topological phase transition in \(HgTe\) quantum wells. Science 314, 1757 (2006)
J.E. Moore, L. Balents, Topological invariants of time-reversal invariant band structures. Phys. Rev. B 75, 121306 (2007)
M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.-L. Qi, S.-C. Zhang, Quantum spin Hall insulator state in \(HgTe\) quantum wells. Science 318, 766 (2007)
Y. Xia et al., Observation of a large gap topological insulator class with a single Dirac cone on the surface. Nat. Phys. 5, 398 (2009)
M.Z. Hasan, C.L. Kane, Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010)
Xiao-Liang Qi, Shou -Cheng Zhang, Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011)
X. Wan, A.M. Turner, A. Vishwanath, S.Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011)
N.P. Armitage, E.J. Mele, Ashvin Viswanath, Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018)
Kai-Yu. Yang, Lu Yuan-Ming, Ying Ran, Quantum Hall effect in Weyl semimetal: possible application in pyrochlore iridates. Phys. Rev. B 84, 075129 (2011)
A.A. Burkov, L. Balents, Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011)
G. Xu, H. Weng, Z. Wang, X. Dai, Z. Fang, Chern semimetal and the quantized anomalous Hall effect in \(HgCr_2Se_4\). Phys. Rev. Lett. 107, 186806 (2011)
A.A. Zyuzin, S. Wu, A.A. Burkov, Weyl semimetal with broken time reversal and inversion symmetries. Phys. Rev. B 85, 165110 (2012)
A.A. Zyuzin, A.A. Burkov, Topological response in Weyl semimetals and the chiral anomaly. Phys. Rev. B 86, 115133 (2012)
T. Meng, L. Balents, Weyl superconductors. Phys. Rev. B 86, 054504 (2012)
M. Gong, S. Tewari, C.W. Zhang, BCS-BEC cross-over and topological phase transition in 3D spin-orbit coupled degenerate Fermi gas. Phys. Rev. Lett. 107, 195303 (2011)
J.D. Sau, S. Tewari, Topologically protected surface Majorana arcs and bulk Weyl Fermions in ferromagnetic superconductors. Phys. Rev. B 86, 104509 (2012)
S.-Y. Xu et al., Discovery of a Weyl Fermion semimetal and topological Fermi arcs. Science 349, 613 (2015)
B.Q. Lv et al., Observation of Weyl nodes in \(TaAs\). Nat. Phys. 11, 724 (2015)
B.Q. Lv et al., Experimental discovery of Weyl semimetal \(TaAs\). Phys. Rev. X 5, 031013 (2015)
C. Shekhar et al., Extremely large magnetoresistence and ultra high mobility in the topological Weyl semimetal candidate \(NbP\). Nat. Phys. 11, 645 (2015)
L.X. Yang et al., Weyl semimetal phase in the non-centrosymmetric compound \(TaAs\). Nat. Phys. 11, 728 (2015)
S.-Y. Xu et al., Discovery of a Weyl Fermion state with Fermi arcs in niobium arsenide. Nat. Phys. 11, 748 (2015)
H.B. Nielsen, M. Ninomiya, The Adler-Bell-Jackiw anomaly and Weyl Fermions in a crystal. Phys. Lett. B 130, 389 (1983)
Di Xiao, Yugui Yao, Zhong Fang, Qian Niu, Berry phase effect in anomalous thermoelectric transport. Phys. Rev. Lett. 97, 026603 (2006)
P. Hosur, X.L. Qi, Recent developments in transport phenomena in Weyl semimetals. Comptes Rendus Physique 14, 857 (2013)
A.A. Burkov, Chiral anomaly and transport in Weyl metals. J. Phys. Condens. Matter 27, 113201 (2015)
S. Adler, Axial-vector vertex in spinor electrodynamics. Phys. Rev. 177, 2426 (1969)
J.S. Bell, R. Jackiw, A PCAC puzzle: \(\pi ^0\rightarrow \gamma \gamma \) in the \(\sigma \)- model. Nuovo Cimento A 60, 47 (1969)
D.T. Son, B.Z. Spivak, Chiral anomaly and classical negative magnetoresistence of Weyl metals. Phys. Rev. B 88, 104412 (2013)
Xiaochun Huang et al., Observation of the chiral anomaly induced negative magnetoreistence in 3D Weyl semimetal \(TaAs\). Phys. Rev. X 5, 031023 (2015)
C. Zhang et al., Signature of the Adler-Bell-Jackie chiral anomaly in a Weyl fermion semimetal. Nat. Commun. 7, 10735 (2015)
P. Goswami, S. Tewari, Axionic field theory of (3+1) dimensional Weyl semimetals. Phys. Rev. B 88, 245107 (2013)
M.A. Stephanov, Y. Yin, Chiral kinetic theory. Phys. Rev. Lett. 109, 162001 (2012)
K. Fukushima, D.E. Kharzeev, H.J. Warringa, Chiral magnetic effect. Phys. Rev. D 78, 074033 (2008)
M.M. Vazifeh, M. Franz, Electromagnetic response of Weyl semimetals. Phys. Rev. Lett. 111, 027201 (2013)
Y. Chen, Si Wu, A.A. Burkov, Axion response in Weyl semimetals. Phys. Rev. B 88, 125105 (2013)
Ming-Che Chang, Min-Fong Yang, Chiral magnetic effect in a two-band lattice model of Weyl semimetal. Phys. Rev. B 91, 115203 (2015)
D.J. Griffiths, Introduction to Electrodynamics (PHI Learning Private Limited, New Delhi, 2011)
Due to the axion action mentioned in the introduction, the Gauss’s law and the Ampere’s law can respectively be written as, \({\vec{\nabla }}.{\vec{E}}=4\pi (\rho +\frac{\alpha }{2\pi ^2}{\vec{Q}}.{\vec{B}}) \) and \({\vec{\nabla }}\times {\vec{B}}=\frac{4\pi }{c} [{\vec{J}} +\frac{\alpha }{2\pi ^2}Q_0{\vec{B}}+\frac{\alpha }{2\pi ^2} ({\vec{Q}}\times {\vec{E}})]+\frac{1}{c}\frac{\partial {\vec{E}}}{\partial t}\). Since we are interested here in CME, the terms containing \({\vec{Q}}\) have been neglected and the term related to \(Q_0\) has been absorbed in \(\sigma _{ch}\) as, \(\frac{\alpha }{2\pi ^2}Q_0=\sigma _{ch}\)
The skin depth in a Weyl semimetal might develop an extra frequency dependence through the parameter \(\sigma _{ch}\) in addition to the frequency dependence mentioned in the text which is beyond the scope of the present manuscript
P.E.C. Ashby, J.P. Carbotte, Chiral anomaly and optical absorption in Weyl semimetals. Phys. Rev. B 89, 245121 (2014)
Z. Long et al., Magnetopolariton in Weyl semimetals in a strong magnetic field. Phys. Rev. Lett. 120, 037403 (2018)
P. Goswami, S. Tewari, Chiral magnetic effect of Weyl Fermions and its application to cubic non-centrosymmetric metals. arXiv:1311.1506 [cond-mat.mes-hall] (2013)
S.-Y. Xu et al., Experimental discovery of a topological Weyl semimetal state in TaP. Sci. Adv. 01, 1501092 (2015)
H. Fujita, M. Oshikawa, Universal transport and resonant current from chiral magnetic effect. arXiv:1602.00687v1 [cond-mat.str-e1] (2016)
C.J. Tabert, J.P. Carbotte, E.J. Nicol, Optical and transport properties in 3D Dirac and Weyl semimetals. Phys. Rev. B 93, 085426 (2016). (94, 039901 (2016))
S.Das Sarma, E.H. Hwang, Collective modes of massless Dirac plasma. Phys. Rev. Lett. 102, 206412 (2009)
M. Lv, S.C. Zhang, Dielectric function, Friedel oscillation and plasmons in Weyl semimetals. Int. J. Mod. Phys. B 27, 1350177 (2013)
J. Zhou, Hao-Ran Chang, Di Xiao, Plasmon mode as a detection of chiral anomaly in Weyl semimetals. Phys. Rev. B 91, 035114 (2015)
Ming-Che Chang, Min-Fong Yang, Chiral magnetic effect in the absence of Weyl node. Phys. Rev. B 92, 205201 (2015)
Acknowledgements
The author would like to thank Prof. T. V. Ramakrishnan and Prof. V. S. Subrahmanyam for stimulating discussions and critically reading the manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sa, D. Chiral magnetic effect and Maxwell–Chern–Simons electrodynamics in Weyl semimetals. Eur. Phys. J. B 94, 31 (2021). https://doi.org/10.1140/epjb/s10051-020-00042-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjb/s10051-020-00042-2