Propriedades Eletrônicas do Grafeno investigada pelo modelo Tight Binding

Pablo Ribeiro Alves de Oliveira; Sandra Cristina Ramos; Jorge Anderson Paiva Ramos

doi:10.22481/exon.v11i2.20585

Authors

Pablo Ribeiro Alves de Oliveira Southwest Bahia State University
Sandra Cristina Ramos Southwest Bahia State University
Jorge Anderson Paiva Ramos Southwest Bahia State University

DOI:

https://doi.org/10.22481/exon.v11i2.20585

Keywords:

Dirac Cone, Dispersion Relation, Graphene-Like Structure, Tight Binding Model

Abstract

Some theorical studies have been developed in order to solve Schrodinger equation. By Bloch's theorem has been possible to make some approach in the Hamiltonian, such as regard electrons in a specific potential, or in a spherical symmetric potential, thar a lead an energy bands structure study. However, there is no theorical formalism that leads to investigate electronic properties of that structure. This paper brings the development of analytical formalism that allows to study any materials, in one (1D) and two-dimensional (2D), by using Tight Binding Model (TB). In this way, it was used the Bloch's theorem and wavevector reciprocal lattice of desire in the First Brillouin Zone. The solution of time independent Schrodinger equation was applied to graphene structure to examine its electronic properties. The TB approach has presented results, as the six points of Dirac, which has provided greater emphasis to that region than another research.

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References

Novoselov, K.; Geim, A.; Neto, A.H.C; Guinea, F. The electronical properties of graphene. Reviews of Modern Physics, v.81,2009.

Dalpian, G.; Fazzio, A.; Pontes, R.B. Barrier-free substitutional doping of graphene sheets with boron atoms: Ab initio calculations. Physical Review B, v.79 ,2009.

Papaconstantopoulos, D.A.; Mehl, J.A. The Slater–Koster tight-binding method: a computationally efficient and accurate approach. journal of physics: condendensed matter. USA. v.15, 3 Mar.2003.

Liu, J; Zhang,Z.H; Deng,X.Q; Fan,Z.Q; Tang,G.P. Electronic structure and transport properties of armchair Graphene nanoribbons by ordered doping. Organic Electronics, 2015.

Fuchs, J.N.; Goebirg, M.O. Introduction to the Physical properties of Graphene-Lectures Notes. 2008. Available in: http://web.physics.ucsb.edu/~phys123B/w2015/pdf_CoursGraphene2008.pdf Access in: Mar 14 of 2018.

Novoselov, K.S, Geim, A.K et al. Electric field effect in atomically thin carbon films. Science, 306(5696):666–669, 2004.

Asano, K.; Hotta, C.; Designing Dirac points in two-dimensional lattices. Condensed Matter Review, v.2, 2011.

Chen, Y.; Fan, Z.; Two-Dimensional Metal Nanomaterials: Synthesis, Properties, and Applications. Chemical Reviews, 2018 [9]Uchoa, B.; Neto, A.H.C. Superconducting states of Pure and doped Graphene. Condensed Matter, v.3, Abril de 2007.

Zarneia,A.M; Chaves,A; Farias,G,A; Peeters,F.M. Energy levels of triangular and hexagonal graphene quantum dots: A comparative study between the tight-binding and Dirac equation approach, Physical Review B,v.89,2011.

Jung, J.; Macdonald, A.H. Tight-binding model for graphene π-bands from maximally localized Wannier functions. Physical Review B, v.87, 2013

Hove, V.L. The Occurrence of Singularities in the Elastic Fretluency Distribution of a Crystal. Physical Review, v.89, 1953.

Yang, Q.; Jieyang, W.; vertically-oriented graphene nanowalls: Growth and application in Li-ion batteries. Diamond And Releated Materials, v.6, 2018.

Ashcroft, N.W.; Mermin, N.D. Solid State Physics. Cenage Learning, 2011.

Pise, P. J., 1982, Laterally loaded piles in a two-layer soil system., J. Geotech. Engrg. Div., 108(9), 1177–1181.

Hao, J.; Huang, C.; A promising way to open an energy gap in Bilayer graphene. Nanoscale, v.7, 2015.

Ramos, S.C., Lobo, A., Antunes, E., Corat, E.; Influence of polar groups on the wetting properties of vertically aligned multiwalled carbon nanotube surfaces. Theoretical Chemistry Accounts, v.130, 2011.

Asano, K; Hotta, C. Designing Dirac points in two-dimensional lattices. Journal of Condensed matter , vol.2 , 2015

L. D. Landau, and L. M. Lifshitz, Quantum Mechanics Non-Relativistic Theory, Butterworth-Heinemann, 3rd edition, (1981) Section 79.

Kuhl, U.; Barkhofen, S. Dirac point and edge states in a microwave realization of tightbinding graphene-like structures. Physical Review B , v.82, 2010.