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Transmission of Dirac Electrons Through Graphene Multilayers with Gaussian Profile

  • J. A. Aguilar-Hernández (a1), J. Madrigal-Melchor (a1), J. C. Martínez-Orozco (a1) and I. Rodríguez-Vargas (a1)


In this work, we use the T-matrix method to study the tunneling of Dirac electrons through graphene multilayers. A graphene sheet is deposited on top of slabs of SiO2-SiC substrates, of which we applied a Gaussian distribution in the size width of the SiC substrate. We calculate the transmittance as a function of energy for different incident angles and different number of layers of the Gaussian distribution. We obtain different stop-band regions. These regions are wider when the width of the barrier is increased. Furthermore, it is possible to tune the width and the position of stop-band with the angle of incidence, the σ value of the Gaussian distribution, and the difference between the maximum-minimum sizes of the barrier.



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[1] Novoselov, K. S., et al. ., “Electric Field Effect in Atomically Thin Carbon Films,” Science, vol. 306, pp. 666669, 2004.
[2] Novoselov, K. S., et al. ., “Two-dimensional gas of massless Dirac fermions in graphene,” Nature, vol. 438, pp. 197200, 2005.
[3] Zhang, Y., et al. ., “Experimental observation of the quantum Hall effect and Berry’s phase in grapheneNature, vol. 438, pp. 201204, 2005.
[4] Katsnelson, M. I., et al. ., “Chiral tunnelling and the Klein paradox in graphene,” Nat. Phys., vol. 2, pp. 620625, 2006.
[5] Schedin, F., et al. ., “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater., vol. 6, pp. 652655, 2007.
[6] Geim, A. K. and Novoselov, K. S., “The rise of graphene,” Nat. Mater., vol. 6, pp. 183191, 2007.
[7] Wallace, P. R., “The Band Theory of Graphite,” Physical Review, vol. 71, pp. 622634, 1947.
[8] Giovannetti, P. A. K. G., Brocks, G., Kelly, P. J., and van den Brink, J., “Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations,” Phys. Rev. B, vol. 76, p. 073103, 2007.
[9] Zhou, S. Y., et al. ., “Substrate-induced band gap opening in epitaxial graphene,” Nat. Mater., vol. 6, pp. 770774, 2007.
[10] Arriaga, J. and Saldanña, X. I., “Band structure and reflectivity of omnidirectional Si-based mirrors with a Gaussian profile refractive index,” Journal of Applied Physics, vol. 100, p. 044911, 2006.
[11] Madrigal Melchor, J., et al. ., “Transmittance of a layered system with a gaussian modulation of the refractive index and inserted metamaterial,” Superficies y Vacío, vol. 23(S), pp. 5760, 2010.
[12] González-Castañón, J. G., et al. ., “Gaussian superlattice as an electron energy filter,” in Some current topics in condensed matter physics, Workshops on Condensed Matter and Molec- ular Physics, UAEM, México, 2010, pp. 6976.
[13] Tung, H.-H. and Lee, C.-P., “An Energy Band-Pass Filter Using Superlattice Structures,” IEEE Journal of Quantum Electronics, vol. 32, pp. 507-512, march 1996 1996.
[14] Yeh, P., Optical waves in layered media vol. 95: Wiley New York, 1988.
[15] Chen, X. and Wang, L.-G., “Propagation of Electron Waves in Monolayer Graphene and Optical Simulations with Negative-Zero-Positive Index Metamaterials,” in Physics and Applications of Graphene - Theory, Mikhailov, S., Ed.: InTech, 2011, pp. 433458.
[16] Carvalho, C. A. A. d., et al. ., “Plasmon polariton and ⃞n⃞ = 0 non-Bragg gaps in superlattices with metamaterials,” Phys. Rev. B, vol. 83, p. 081408(R), 2011.
[17]. Gomes, J. V. and Peres, N. M. R., “Tunneling of Dirac electrons through spatial regions of finite mass,” Journal of Physics: Condensed Matter, vol. 20, p. 325221, 2008.
[18] Masir, M. R., et al. ., “Graphene in inhomogeneous magnetic fields: bound, quasi-bound and scattering states,” Journal of Physics: Condensed Matter, vol. 23, p. 315301, 2011.

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Transmission of Dirac Electrons Through Graphene Multilayers with Gaussian Profile

  • J. A. Aguilar-Hernández (a1), J. Madrigal-Melchor (a1), J. C. Martínez-Orozco (a1) and I. Rodríguez-Vargas (a1)


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