Electronic Transmission Wave Function of Disordered Graphene by Direct Method and Green's Function Method
الموضوعات : فصلنامه نانوساختارهای اپتوالکترونیکی
1 - Department of physics, Faculty of science, Imam Khomeini International University, Qazvin, Iran
الکلمات المفتاحية: Finite difference method, Graphene, Disordered graphene, Green's function,
ملخص المقالة :
We describe how to obtain electronic transport properties of disordered graphene, including the tight binding model and nearest neighbor hopping. We present a new method for computing, electronic transport wave function and Greens function of the disordered Graphene. In this method, based on the small rectangular approximation, break up the potential barriers in to small parts. Then using the finite difference method, the Dirac equations of disordered graphene, reduce to the discrete matrix equation. The discrete matrix equation is solved by direct and Green’s function methods. In this method, geometry of disorder plays an important role. This method allows for an amenable inclusion of several disorder mechanisms at the microscopic level. The effect of impurity on the transmission probability and conductivity are obtained, using the electronic transport wave function. The results show that, for the conductance, geometry plays an important role. In addition, by transmission probability and using Landau formula, the Fano factor is investigated.
[1] M. I. Katsnelson, K. S. Novoselov and A. K. Geim, Chiral tunnelling and the Klein paradox in graphene, Nature Physics, 2 (2006) 620 - 625.
[2] N. M. R. Peres, Colloquium: The transport properties of graphene: An introduction, Rev. Mod. Phys. 82 (2010) 2673.
[3] M. I. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge University Press, 2012).
[4] J. H. Chen, C. Jang, S. Adam, M. S. Fuhrer, E. D. Williams, M. Ishigami ,Charged-impurity scattering in graphene,Nature Physics, 4 (2008) 377 - 381.
[5] B. Huard, J. A. Sulpizio, N. Stander, K. Todd, B. Yang, and D. Goldhaber-Gordon,Transport Measurements Across a Tunable Potential Barrier in Graphene ,Phys. Rev. Lett. 98 (2007) 236803 .
[6] E. R. Mucciolo, C. H. Lewenkopf., disorder and electronic transport in graphene, J. Phys. Condens. Matter 22 (2010) 273201
[7] C. H. Lewenkopf, E. R. Mucciolo, The recursive Greens function method for graphene, Journal of Computational Electronics, 12 (2013) 203-231.
[8] D. Gunlycke and C. T. White, Specular graphene transport barrier, Phys. Rev. B 90 (2014) 035452 .
[9] K. Sasaki, K. Wakabayashi, and T. Enoki, Electron Wave Function in Armchair Graphene Nanoribbons,J. Phys. Soc. Jpn. 80 (2011) 044710.
[10] J. A. Lawlora, M. S. Ferreir, Green functions of graphene: An analytic approach, Physica B: Condensed Matter, 463 (2015) 4853.
[11] D. Klpfer, A. D. Martino, D. U. Matrasulov, R. Egger, Scattering theory and ground-state energy of Dirac fermions in graphene with two Coulomb impurities, Eu. Phys. J. B 87 (2014) 187.
[12] E. V. Gorbar, V. P. Gusynin and O. O. Sobol, Supercritical electric dipole and migration of electron wave function in gapped graphene, EPL (Europhysics Letters), 111 (2015) 3.
[13] B R K Nanda, M Sherafati, Z S Popovi and S Satpathy, Electronic structure of the substitu-tional vacancy in graphene: density-functional and Green's function studies, New J. of Phys., 14 (2012) .
[14] E. H. Hwang, S. Adam, and S. D. Sarma ,Carrier Transport in Two-Dimensional Graphene layers, Phys. Rev. Lett. 98, 186806 (2007) 1-4.
[15] Z. Rashidian, F. M. Mojarabian, P. Bayati, G. Rashedi, A. Ueda and T. Yokoyama, Conductance and Fano factor in normal/ferromagnetic/normal bilayer graphene junction, J. Phys: Condens. Matter 26 (2014) 25530211
[16] Y.-W. Tan, Y. Zhang, K. Bolotin, Y. Zhao, S. Adam, E. H. Hwang, S. D Sarma, H. L. Stormer, and P. Kim, Measurement of Scattering Rate and Minimum Conductivity in Graphene , Phys. Rev. Lett. 99 (2007) 246803.
[17] M. I. Katsnelson, Zitterbewegung, chirality and minimal conductivity in graphene, The Eu-ropean Physical Journal B Condensed Matter and Complex Systems 51 (2006) 157-160.
[18] K. Ziegler, Minimal conductivity of graphene: Nonuniversal values from the Kubo formula, Phys. Rev. B 75 (2007) 233407.
[19] X. Du, I. Skachko, A. Barker, E. Y. Andrei, Approaching ballistic transport in suspended graphene, Nature Nanotechnology, 3 (2008) 491 - 495 .
[20] A. R. Mitchell, D. F. Griffiths, The finite difference method in partial differential equations, New York: John Wiley (1980).
[21] R. landaure, spatial variation of currents and fields due to localized scatters in metallic conduction, IBM J. RES. Develop. 32 (1988) 306.