General Scattering Mechanism and Transport in Graphene

Affiliation(s)

University for Development Studies, Faculty of Applied Science, Department of Applied Physics, Navrongo, Ghana.

Center for Laser and Fiber Optics, Physics Department, University of Cape Coast, Cape Coast, Ghana.

University for Development Studies, Faculty of Applied Science, Department of Applied Physics, Navrongo, Ghana.

Center for Laser and Fiber Optics, Physics Department, University of Cape Coast, Cape Coast, Ghana.

ABSTRACT

Using quasi time dependent semiclassical transport theory, within relaxation time approximation, we obtained coupled electronic current equations in the presence of time varying field, and based on general scattering mechanism,. In the vicinity of Dirac points, we find that a characteristic exponent corresponds to acoustic phonon scattering, long range Coulomb scattering mechanism and is short range (delta or contact potential) scattering in which the conductivity is constant of temperature. The case is the ballistic regime. In the low energy dynamics of Dirac electrons in graphene, the effect of the time dependent electric field is to alter just the electron charge by making electronic conductivity nonlinear. The effect of constant magnetic field at finite temperature is also considered.

Using quasi time dependent semiclassical transport theory, within relaxation time approximation, we obtained coupled electronic current equations in the presence of time varying field, and based on general scattering mechanism,. In the vicinity of Dirac points, we find that a characteristic exponent corresponds to acoustic phonon scattering, long range Coulomb scattering mechanism and is short range (delta or contact potential) scattering in which the conductivity is constant of temperature. The case is the ballistic regime. In the low energy dynamics of Dirac electrons in graphene, the effect of the time dependent electric field is to alter just the electron charge by making electronic conductivity nonlinear. The effect of constant magnetic field at finite temperature is also considered.

Cite this paper

M. Rabiu, S. Mensah and S. Abukari, "General Scattering Mechanism and Transport in Graphene,"*Graphene*, Vol. 2 No. 1, 2013, pp. 49-54. doi: 10.4236/graphene.2013.21007.

M. Rabiu, S. Mensah and S. Abukari, "General Scattering Mechanism and Transport in Graphene,"

References

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[1] A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novo- selov 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

[2] M. I. Katsenelson and K. S. Novoselov, “Graphene: New Bridge between Condensed Matter Physics and Quantum Electrodynamics,” Solid State Communications, Vol. 143, No. 1-2, 2007, pp. 3-13. doi:10.1016/j.ssc.2007.02.043

[3] F. Guinea, A. H. C. Neto and N. M. R. Peres, “Electronic States and Landau Levels in Graphene Stacks,” Physical Review B, Vol. 73, No. 24, 2006, Article ID: 245426.

doi:10.1103/PhysRevB.73.245426

[4] S. Shivaraman, R. A. Barton, X. Yu, J. Alden, L. Her- man, M. V. S. Chandrashekhar, J. Park, P. L. McEuen, J. M. Parpia, H. G. Craighead and M. G. Spencer, “Free- Standing Epitaxial Graphene,” Nano Letters, Vol. 9, No. 9, 2009, pp. 3100-3105. doi:10.1021/nl900479g

[5] B. Uchoa and A. H. C. Neto, “Superconducting States in Pure and Doped Grapheme,” Physical Review Letters, Vol. 98, 2007, Article ID: 146801. doi:10.1103/PhysRevLett.98.146801

[6] S. Adam, E. H. Hwang, V. M Galitski and S. Dar Sarma, “A Self-Consistent Theory for Graphene Transport,” Pro- ceedings of the National Academy of Sciences, Vol. 104, No. 47, 2007, pp. 18392-18397. doi:10.1073/pnas.0704772104

[7] S. Adam, E. H. Hwang and S. Das Sarma, “Scattering Mechanisms and Boltzmann Transport in Graphene,” Physica E-Low-Dimensional Systems & Nanostructures, Vol. 40, No. 5, 2008, pp. 1022-1025.

[8] A. K. Geim and K. S. Novoselov, “The Rise of Gra- phene,” Progress Article, Nature Materials, Vol. 6, 2007, pp. 183-191. doi:10.1038/nmat1849

[9] N. M. R. Peres, J. M. B. L. dos Santos and T. Stauber, “Phenomenological Study of the Electronic Transport Co- efficients of Graphene,” Physical Review B, Vol. 76, No. 7, 2007, Article ID: 073412.

[10] T. Stauber, N. M. R. peres and F. Guinea, “Electronic Transport in Graphene: A Semiclassical Approach In- cluding Midgap States,” Physical Review B, Vol. 76, No. 20, 2007, Article ID: 205423.

[11] J. Nilsson, A. H. C. Neto, F. Guinea and N. M. R. Peres, “Electronic Properties of Graphene Multilayers,” Physical Review Letters, Vol. 97, No. 26, 2006, Article ID: 266801.

[12] J. M. Ziman and F. R. S. Melville, “Principles of the The- ory of Solids,” 2nd Edition, Cambridge University Press, Cambridge, 1972.

[13] S. Y. Mensah, F. K. A. Allotey, N. G. Mensah and G. Nkrumah, “Differential Thermopower of a CNT Chiral Carbon Nanotube,” Journal of Physics: Condensed Mat- ter, Vol. 13, No. 24, 2001, pp. 5653-5662. doi:10.1088/0953-8984/13/24/310

[14] O. Madelung, “Introduction to Solid State Theory,” Springer-Verlag, Berlin, 1978. doi:10.1007/978-3-642-61885-7

[15] T. Ando and T. Nakanishi, “Impurity Scattering in Car- bon Nanotubes-Absence of Back Scattering,” Journal of the Physical Society of Japan, Vol. 67, 1998, pp. 1704- 1713. doi:10.1143/JPSJ.67.1704

[16] J.-H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Wil- liams and M. Ishigami, “Charged-Impurity Scattering in Graphene,” Nature Physics, Vol. 4, 2008, pp. 377-381. doi:10.1038/nphys935

[17] S. V. Kryuchkov and E. I. Kukhar, “Influence of the Magnetic Field onthe Graphene Conductivity,” Journal of Modern Physics: Scientific Research, Vol. 3, No. 9, 2012, pp. 994-1001.

[18] K. Namura and A. H McDonald, “Quantum Hall Ferro- magnetism in Graphene,” Physical Review Letters, Vol. 96, No. 25, 2006, Article ID: 256602.