Chiral Current in a Graphene Battery

DOI: 10.4236/jemaa.2012.410059   PDF   HTML     5,687 Downloads   8,637 Views   Citations


We review the formulation of graphene’s massless Dirac equation, under the chiral electromagnetism approach, hopefully demystifying the material’s unusual chiral, relativistic, effective theory. In Dirac’s theory, many authors replace the speed of light by the Fermi velocity, in this paper we deduce that in graphene the Fermi velocity is obtained from the connection between the electromagnetic chirality and the fine structure constant when the electric wave E is quasi parallel to the magnetic wave H. With this approach we can consider the properties of electric circuits involving graphene or Weyl semimetals. The existence of the induced chiral magnetic current in a graphene subjected to magnetic field causes an interesting and unusual behavior of such circuits. We discuss an explicit example of a circuit involving the current generation in a “chiral battery”. The special properties of this circuit may be utilized for creating “chiral electronic” devices.

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H. Torres-Silva and D. Cabezas, "Chiral Current in a Graphene Battery," Journal of Electromagnetic Analysis and Applications, Vol. 4 No. 10, 2012, pp. 426-431. doi: 10.4236/jemaa.2012.410059.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] X. Wan et al., “Topological Semimetal and Fermi-Arc Surface States in the Electronic Structure of Pyrochlore Iridates,” Phys-ical Review B, Vol. 83, No. 20, 2011, Article ID: 205101.
[2] A. K. Geim and K. S. Novoselov, “The Rise of Graphene,” Nature Materials, Vol. 6, 2007, pp. 183-191.
[3] C. L. Kane and E. J. Mele, “Z2 Topological Order and the Quantum Spin Hall Effect,” Physical Review Letters, Vol. 95, No. 14, 2005, Article ID: 146802.
[4] A. A. Burkov and L. Balents, “Weyl Semimetal in a Topological Insulator Multilayer,” Physical Review Letters, Vol. 107, No. 12, 2011, pp. 127205-127209.
[5] A. A. Zyuzin, S. Wu and A. A. Burkov, “Weyl Semimetal with Broken Time Reversal and Inversion Symmetries,” Physical Review B, Vol. 85, No. 16, 2012, pp. 165110165119.
[6] D. Kharzeev and H. Warringa, “Chiral Magnetic Conductivity”, Physical Review D, Vol. 80, No. 3, 2009, pp. 34028-34038
[7] D. Kharzeev and A. Zhitnitsky, “Charge Separation Induced by P-Odd Bubbles in QCD Matter,” Nuclear Physical A, Vol. 797, No. 1-2, 2007, pp. 67-79.
[8] D. E. Kharzeev and D. Son, “Testing the Chiral Magnetic and Chiral Vortical Effects in Heavy Ion Collisions,” Physical Review Letters, Vol. 106, No. 6, 2011, pp. 062301-062305. doi:10.1103/PhysRevLett.106.062301
[9] K. Fukushima, D. E. Kharzeev and H. J. Warringa, “The Chiral Magnetic Effect,” Physical Review D, Vol. 78, No. 7, 2008, p. 074033. doi:10.1103/PhysRevD.78.074033
[10] D. E. Kharzeev, “Topologically Induced Local P and CP Violation in QCD x QED,” Annals Physics, Vol. 325, 2010, pp. 205-229.
[11] B. I. Abelev, et al., “Azimuthal Charged-Particle Correlations and Possible Local Strong Parity Violation,” Physical Review Letters, Vol. 103, 2009, pp. 251601251605.
[12] A. Vilenkin, “Holographic Multiverse and the Measure Problem,” JCAP, Vol. 6, No. 6, 2011, p. 32.
[13] G. M. Eliashberg, “Electrical Current and Magnetic Fields in Conductors with Mirror-Isomeric Structure,” JETP Letters, Vol. 38, No. 4, 1983, pp. 220-223.
[14] L. S. Levitov, Yu. V. Nazarov and G. M. Eliashberg, “Electron Spin Susceptibility of Superconductors,” JETP Letters, Vol. 41, No. 5, 1985, pp. 228-231.
[15] M. Giovannini and M. E. Shaposhnikov, “Primordial Magnetic Fields, Anomalous Isocurvature Fluctuations and Big Bang Nucleosynthesis,” Physical Review Letters, Vol. 80, 1998, pp. 22-25.
[16] A. Yu. Alekseev, V. V. Cheianov and J. Frolich, “Universality of Transport Properties in Equilibrium, the Goldstone Theorem, and Chiral Anomaly,” Physical Review Letters, Vol. 81, 1998, pp. 3503-3506.
[17] H. B., Nielsen and M. Ninomiya, “Physical Derivation of Chiral Anomaly by Using Dirac Sea,” Physical Review Letters, Vol. 130, 1983, pp. 389-393.
[18] I. Zahed, “Anomalous Chiral Fermi Surface,” Physical Review Letters, Vol. 109, No. 9, 2012, pp. 091603-091607.
[19] D. T. Son and B. Z. Spivak, “Chiral Anomaly and Classical Negative Magnetoresistance of Weyl Metals,” 2012.
[20] A. A. Zyuzin and A. A. Burkov, “Topo-logical Response in Weyl Semimetals and the Chiral Anomaly,” Physical Review B, Vol. 6, No. 11, 2012, pp. 115-133.
[21] K. S. Novoselov, et al., “Two-Dimensional Gas of Massless Dirac Fermions in Graphene,” Nature, Vol. 438, 2005, pp. 197-200.
[22] M. I. Katsnelson, et al., “Chiral Tunnelling and the Klein Paradox in Graphene,” Nature Physics, Vol. 2, No. , 2006, pp. 620-624.
[23] R. A. Shelby, et al., “Experimental Verification of a Negative Index of Refraction,” Science, Vol. 292, No. 6, 2001, pp. 77-79. doi:10.1126/science.1058847
[24] V. G. Veselago, “The Electrodynamics of Substances with Simultaneously Negative Values of and ,” Soviet Physics Uspekhi, Vol. 10, No. 4, 1968, pp. 509514. doi:10.1070/PU1968v010n04ABEH003699
[25] D. R. Smith et al., “Composite Medium with Simultaneously Negative Permeability and Permittivity,” Physical Review Letters, Vol. 84, No. 18, 2000, pp. 4184-4187. doi:10.1103/PhysRevLett.84.4184
[26] C. Monzon and D. W. Forester, “Negative Refraction and Focusing of Circularly Polarized Waves in Optically Active Media,” Physical Review Letters, Vol. 95, 2005, pp. 123904-123907.
[27] H. Torres-Silva et al., “Chiral Waves in a Metamaterial Medium”, International Journal of Pure and Applied Sciences and Tech-nology , Vol. 2, No. 2, 2011, pp. 54-65.
[28] E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukolis and N. I. Zheledev, “Metamaterial with Negative Index due to Chirality,” Physical Review B, Vol. 79, No. 3, 2009, pp. 0354071-0354076. doi:10.1103/PhysRevB.79.035407
[29] J. Zhou, J. Dong, B. Wang, T. Koschny, M. Kafesaki and C. Soukoulis, “Negative Refractive Index due to Chirality,” Physical Review B, Vol. 79, 2009, pp. 121104-121107.
[30] H. Torres-Silva, “The Close Relation between the Maxwell System and the Dirac Equation when the Electric Field is Parallel to the Magnetic Field,” Inge-niare, Vol. 16, No. 1, 2008, pp. 43-47.
[31] H. Torres-Silva, “Dirac Matrices in Chiral Representation and the Connection with the Electric Field Parallel to the Magnetic Field,” Ingeniare, Vol. 16, No. 1, 2008, pp. 4852.
[32] H. Torres-Silva, “Chiral Transverse Electromagnetic Standing Waves with E II H in the Dirac Equation and the Spectra of the Hydrogen Atom,” In: A. Akdagli, Ed., Behavior of Electromagnetic Waves in Different Media and Structures, Intech, Croatia, 2011, pp. 301-324.

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