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Influence of the Magnetic Field on the Graphene Conductivity

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DOI: 10.4236/jmp.2012.39129    4,922 Downloads   8,619 Views   Citations

ABSTRACT

The transversal conductivity of the gap-modification of the graphene was studied in the cases of weak nonquatizing and quantizing magnetic field. In the case of nonquantizing magnetic field the expression of the current density was derived from the Boltzmann equation. The dependence of conductivity and Hall conductivity on the magnetic field intensity was investigated. In the case of quantizing magnetic field the expression for the graphene transversal magnetoconductivity taking into account the scattering on the acoustic phonons was derived in the Born approximation. The graphene conductivity dependence on the magnetic field intensity was investigated. The graphene conductivity was shown to have the oscillations when the magnetic field intensity changes. The features of the Shubnikov-de Haas oscillations in graphene superlattice are discussed.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

S. Kryuchkov and E. Kukhar, "Influence of the Magnetic Field on the Graphene Conductivity," Journal of Modern Physics, Vol. 3 No. 9, 2012, pp. 994-1001. doi: 10.4236/jmp.2012.39129.

References

[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films,” Science, Vol. 306, No. 5696, 2004, pp. 666-669. doi:10.1126/science.1102896
[2] J. Milton Pereira Jr., P. Vasilopoulos and F. M. Peeters, “Graphene-Based Resonant-Tunneling Structures,” Applied Physics Letters, Vol. 90, No. 13, 2007, pp. 132122- 132125. doi:10.1063/1.2717092
[3] Z. Chen, Y.-M. Lin, M. J. Rooks and P. Avouris, “Graphene Nano-Ribbon Electronics,” Physica E, Vol. 40, No. 2, 2007, pp. 228-234. doi:10.1016/j.physe.2007.06.020
[4] Y. Q. Wu, P. D. Ye, M. A. Capano, Y. Xuan, Y. Sui, M. Qi, J. A. Cooper, T. Shen, D. Pandey, G. Prakash and R. Reifenberger, “Top-Gated Graphene Field-Effect-Transistors Formed by Decomposition of SiC,” Applied Physics Letters, Vol. 92, No. 9, 2008, Article ID: 092102. doi:10.1063/1.2889959
[5] A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov and A. K. Geim, “The Electronic Properties of Graphene,” Reviews of Modern Physics, Vol. 81, No. 1, 2009, pp. 109-162. doi:10.1103/RevModPhys.81.109
[6] S. Reich, J. Maultzsch, C. Thomsen and P. Ordejon, “Tight-Binding Description of Graphene,” Physical Review B, Vol. 66, No. 3, 2002, pp. 035412-035417.
[7] P. R. Wallace, “The Band Theory of Graphite,” Physical Review, Vol. 71, No. 9, 1947, pp. 622-634. doi:10.1103/PhysRev.71.622
[8] S. A. Mikhailov, “Nonlinear Cyclotron Resonance of a Massless Quasiparticle in Graphene,” Physical Review B, Vol. 79, No. 24, 2009, pp. 241309-241313. doi:10.1103/PhysRevB.79.241309
[9] D. V. Zav’yalov, S. V. Kryuchkov and E. V. Marchuk, “On the Possibility of Transverse Current Rectification in Graphene,” Technical Physics Letters, Vol. 34, No. 11, 2008, pp. 915-917. doi:10.1134/S1063785008110047
[10] D. V. ZAV’YALOV, V. I. KONCHENKOV AND S. V. KRYUCHKOV, “MUTUAL RECTIFICATION OF ALTERNATING CURRENTS INDUCED BY ELECTROMAGNETIC WAVES IN GRAPHENE,” PHYSICS OF THE SOLID STATE, VOL. 51, NO. 10, 2009, PP. 2157-2160. DOI:10.1134/S1063783409100278
[11] D. V. ZAV’YALOV, V. I. KONCHENKOV AND S. V. KRYUCHKOV, “INFLUENCE OF A MAGNETIC FIELD ON THE MUTUAL RECTIFICATION OF ALTERNATING CURRENTS INDUCED BY ELECTROMAGNETIC WAVES IN GRAPHENE,” PHYSICS OF THE SOLID STATE, VOL. 52, NO. 4, 2010, PP. 800-804. DOI:10.1134/S1063783410040219
[12] L. A. CHERNOZATONSKII, P. B. SOROKIN, E. E. BELOVA, I. BRYUNING AND A. S. FEDOROV, “METAL-SEMICONDUCTOR (SEMI-METAL) SUPERLATTICES ON A GRAPHITE SHEET WITH VACANCIES,” JETP LETTERS, VOL. 84, NO. 3, 2006, PP. 115-118. DOI:10.1134/S0021364006150033
[13] L. A. CHERNOZATONSKII, P. B. SOROKIN, E. E. BELOVA, I. BRYUNING AND A. S. FEDOROV, “SUPERLATTICES CONSISTING OF ‘LINES’ OF ADSORBED HYDROGEN ATOM PAIRS ON GRAPHENE,” JETP LETTERS, VOL. 85, NO. 1, 2007, PP. 77-81. DOI:10.1134/S002136400701016X
[14] F. Guinea, M. I. Katsnelson and M. A. H. Vozmediano, “Midgap States and Charge Inhomogeneities in Corrugated Graphene,” Physical Review, Vol. 77, No. 7, 2008, pp. 075422-075429. doi:10.1103/PhysRevB.77.075422
[15] H. Sevincli, M. Topsakal and S. Ciraci, “Superlattice Structures of Graphene-Based Armchair Nanoribbons,” Physical Review, Vol. 78, No. 24, 2008, pp. 245402-245409. doi:10.1103/PhysRevB.78.245402
[16] M. R. Masir, P. Vasilopulos and F. M. Peeters, “Tunneling, Conductance, and Wavevector Filtering through Magnetic Barriers in Bilayer Graphene,” Physical Review, Vol. 79, No. 3, 2009, Article ID: 035409. doi:10.1103/PhysRevB.79.035409
[17] M. Tahir and K. Sabeeh, “Quantum Transport of Dirac Electrons in Graphene in the Presence of a Spatially Modulated Magnetic Field,” Physical Review B, Vol. 77, No. 19, 2008, pp. 195421-195426. doi:10.1103/PhysRevB.77.195421
[18] X.-Z. Yan and C. S. Ting, “Magnetoconductivity of Dirac Fermions in Graphene under Charged Impurity Scatterings,” New Journal of Physics, Vol. 11, No. 9, 2009, Article ID 093026. doi:10.1088/1367-2630/11/9/093026
[19] T. Shen, Y. Q. Wu, M. A. Capano, L. P. Rokhinson, L. W. Engel and P. D. Ye, “Magnetoconductance Oscillations in Graphene Antidot Arrays,” Applied Physics Letters, Vol. 93, No. 12, 2008, pp. 122102-122110. doi:10.1063/1.2988725
[20] J. Jobst, D. Waldmann, F. Speck, R. Hirner, D. K. Maude, T. Seyller and H. B. Weber, “Quantum Oscillations and Quantum Hall Effect in Epitaxial Graphene,” Physical Review B, Vol. 81, 2010, pp. 195434-195440. doi:10.1103/PhysRevB.81.195434
[21] S. G. Sharapov and V. P. Gusynin, “Magnetic Oscillations in Planar Systems with the Dirac-Like Spectrum of Quasiparticle Excitations II: Transport Properties,” Physical Review B, Vol. 71, No. 12, 2005, pp. 125124-125132.
[22] K. Y. Bliokh, “Weak Antilocalization of Ultrarelativistic Fermions,” Physics Letters A, Vol. 344, No. 2-4, 2005, pp. 127-130. doi:10.1016/j.physleta.2005.06.062
[23] V. P. Gusynin, S. G. Sharapov and J. P. Carbotte, “Dirac Quasiparticles in the Magneto-Optical Response of Graphene,” Journal of Physics: Condensed Matter, Vol. 19, 2007, Article ID: 026222. doi:10.1088/0953-8984/19/2/026222
[24] N. M. R. Peres, F. Guinea and A. H. C. Neto, “Electronic Properties of Disordered Two-Dimensional Carbon,” Physical Review B, Vol. 73, 2006, pp. 125411-125434.
[25] V. P. Gusynin and S. G. Sharapov, “Transport of Dirac Quasiparticles in Graphene: Hall and Optical Conductivities,” Physical Review B, Vol. 73, No. 24, 2006, pp. 245411-245429. doi:10.1103/PhysRevB.73.245411
[26] S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. C. Neto and A. Lanzara, “Substrate-Induced Band Gap Opening in Epi- taxial Graphene,” Nature Materials, Vol. 6, No. 10, 2007, pp. 770-775. doi:10.1038/nmat2003
[27] A. Mattausch and O. Pankratov, “Ab Initio Study of Graphene on SiC,” Physical Review Letters, Vol. 99, No. 7, 2007, Article ID: 076802. doi:10.1103/PhysRevLett.99.076802
[28] P. V. RATNIKOV, “SUPERLATTICE BASED ON GRAPHENE ON A STRIP SUBSTRATE,” JETP LETTERS, VOL. 90, NO. 6, 2009, PP. 469-474. DOI:10.1134/S0021364009180143
[29] S. V. Kryuchkov, E. I. Kuhar and V. A. Yakovenko, “Effect of the Mutual Rectification of Two Electromagnetic Waves with Perpendicular Polarization Planes in a Superlattice Based on Graphene,” Bulletin of the Russian Academy of Sciences: Physics, Vol. 74, No. 12, 2010, pp. 1679-1681. doi:10.3103/S1062873810120129
[30] E. Adams and T. Holstein, “Quantum Theory of Transversal Galvanic-Magnetic Phenomena,” Journal of Physics and Chemistry of Solids, Vol. 10, No. 4, 1959, pp. 254-297. doi:10.1016/0022-3697(59)90002-2
[31] E. H. Hwang and S. D. Sarma, “Dielectric Function, Screening, and Plasmons in Two-Dimensional Graphene,” Physical Review B, Vol. 75, No. 20, 2007, pp. 205418-205424.
[32] L. D. Landau and E. M. Lifshits, “Physical Kinetics,” Physical and Mathematical Literature, Moscow, 2001, pp. 462-466.
[33] A. G. Zhylich, “The Energy Spectrum of Electrons and Optical Properties of the Superlattice in a Magnetic Field,” Physics of the Solid State, Vol. 36, No. 3, 1994, pp. 792-804.

  
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