Abstract
The role of the chiral magnetic effect (CME) in Weyl semimetals is considered within the framework of classical electrodynamics. The dispersion relation of electromagnetic waves is studied using their helical polarization. It has been shown that the refractive index in this class of materials becomes negative in the frequency range below the plasma frequency. The CME (a signature of chiral anomaly/ axial anomaly) which is due to the application of parallel electric and magnetic fields in Weyl semimetals thus opens up a new way of realizing negative refractive index (NRI). The relevance of the present work to negative refraction through chiral route where cross polarization (magnetization) induced by magnetic fields (electric fields) occurs in chiral materials is discussed. This novel phenomenon of negative refraction in Weyl semimetals might help in exploiting this class of materials in potential applications.
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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 \({{ }_{ch}}\) as, \(\frac{\alpha }{2\pi ^2}Q_0 = {{ }_{ch}}\)
From the continuity equation (equation (5) in the text), \((\rho _{+}-\rho _{-})\) can be calculated as, \((\rho _{+}-\rho _{-})=\frac{2e^3}{4\pi ^2} E B \tau _{ch}\) for B parallel to E, where \(\tau _{ch}\) is the chirality changing scattering time. Thus, \({{ }_{ch}}\) becomes, \({{ }_{ch}}=\frac{e^2}{4\pi ^2}\frac{2e^3}{4\pi ^2}\frac{1}{e g_B} E B\tau _{ch}\). The CME conductivity \({{ }_{CME}}\) which is experimentally measured, is related to the chiral conductivity \({{ }_{ch}}\) as, \({{ }_{ch}}= {{ }_{CME}}\frac{E}{B}\)
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Acknowledgements
The author would like to thank Prof. T. V. Ramakrishnan and Prof. V. S. Subrahmanyam for stimulating discussions and critically reading the manuscript.
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Sa, D. Chiral magnetic effect in Weyl semimetals and negative refraction. Eur. Phys. J. B 95, 11 (2022). https://doi.org/10.1140/epjb/s10051-021-00274-w
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DOI: https://doi.org/10.1140/epjb/s10051-021-00274-w