Next-Nearest-Neighbor Tight-Binding Model of Plasmons in Graphene

Vladimir Kadirko, Klaus Ziegler, Eugene Kogan

Department of Physics, Bar-Ilan University, Ramat Gan, Israel.
Institut für Physik, Universitat Augsburg, Augsburg, Germany.

DOI: 10.4236/graphene.2013.23014                

Abstract

In this paper we investigate the influence of the next-nearest-neighbor coupling on the spectrum of plasmon excitations in graphene. The nearest-neighbor tight-binding model was previously considered to calculate the plasmon spectrum in graphene [1]. We extend these results to the next-nearest-neighbor tight-binding model. As in the calculation of the nearest-neighbor model, our approach is based on the numerical calculation of the dielectric function and the loss function. We compare the plasmon spectrum of the two models and discuss the differences in the dispersion.

Keywords

Graphene; Plasmon; Tight-Binding Model

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. Hill, S. A. Mikhailov and K. Ziegler, “Dielectric Function and Plasmons in Graphene,” EPL (Europhysics Let ters), Vol. 87, No. 2, 2009, Article ID: 27005.
[2]	A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov and A. K. Geim, “The Electronic Properties of Grapheme,” Reviews of Modern Physics, Vol. 81, No. 1, 2009, pp. 109-162. doi:10.1103/RevModPhys.81.109
[3]	D. S. L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler and T. Chakraborty, “Properties of Graphene: A Theoretical Perspective,” Advances in Physics, Vol. 59, No. 4, 2010, pp. 261-482. doi:10.1080/00018732.2010.487978
[4]	B. Wunsch, T. Stauber, F. Sols and F. Guinea, “Dynami- cal Polarization of Graphene at Finite Doping,” New Journal of Physics, Vol. 8, No. 12, 2006, p. 318.
[5]	E. H. Hwang and S. Das Sarma, “Dielectric Function, Screening, and Plasmons in Two-Dimensional Graphene,” Physical Review B, Vol. 75, No. 20, 2007, Article ID: 205418. doi:10.1103/PhysRevB.75.205418
[6]	M. Polini, R. Asgari, G. Borghi, Y. Barlas, T. PeregBarnea and A. H. MacDonald, “Plasmons and the Spectral Function of Grapheme,” Physical Review B, Vol. 77, No. 8, 2008, Article ID: 081411(R).
[7]	S. J. Yuan, R. Roldan and M. I. Katsnelson, “Excitation Spectrum and High Energy Plasmons in Single-Layer and Multilayer Grapheme,” Physical Review B, Vol. 84, No. 3, 2011, Article ID: 035439.
[8]	G. Mahan, “Many Particle Physics,” Plenum Pr., New York, 1990. doi:10.1007/978-1-4613-1469-1
[9]	H. Ehrenreich and M. H. Cohen, “Self-Consistent Field Approach to the Many-Electron Problem,” Physical Re- view, Vol. 115, No. 4, 1959, pp. 786-790. doi:10.1103/PhysRev.115.786
[10]	M. Dressel and G. Gruner, “Electrodynamics of Solids: Optical Properties of Electrons in Matter,” Cambridge University Press, Cambridge, 2002. doi:10.1017/CBO9780511606168
[11]	P. R. Wallace, “The Band Theory of Graphite,” Physical Review, Vol. 71, No. 9, 1947, pp. 622-634. doi:10.1103/PhysRev.71.622