Graphene as a Strictly 2D Sheet or as a Film of Small but Finite Thickness

Bo E. Sernelius

Division of Theory and Modeling, Department of Physics, Chemistry, and Biology, Link?ping University, Link?ping, Sweden.

DOI: 10.4236/graphene.2012.12003                

Abstract

We study an interface between two media separated by a strictly 2D sheet. We show how the amplitude reflection coef- ficient can be modeled by that for an interface where the 2D sheet has been replaced by a film of small but finite thick- ness. We give the relationship between the 3D dielectric function of the thin film and the 2D dielectric function of the sheet. We apply this to graphene and show how the van der Waals interaction between two graphene sheets is modified when going from the 2D sheet description to the thin film description. We also show the wrong result from keeping the 2D dielectric function to represent the film medium.

Keywords

Graphene; 2D Sheet; Thin Film; Casimir; Van Der Waals

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	T. Ando, A. B. Fowler and F. Stern, “Electronic Proper- ties of Two-Dimensional Systems,” Reviews of Modern Physics, Vol. 54, No. 2, 1982, pp. 437-672. doi:10.1103/RevModPhys.54.437
[2]	F. Stern, “Polarizability of a Two-Dimensional Electron Gas,” Physical Review Letters, Vol. 18, No. 14, 1967, pp. 546-548. doi:10.1103/PhysRevLett.18.546
[3]	J. Gonzáles, F. Guinea and M. A. H. Vozmediano, “Non-Fermi Liquid Behavior of Electrons in the Half- Filled Honeycomb Lattice (A Renormalization Group Approach),” Nuclear Physics B, Vol. 424, No. 3, 1994, pp. 595-618.
[4]	B. Wunsch, T. Stauber, F. Sols and F. Guinea, “Dynami- cal Polarization of Graphene at Finite Doping,” New Journal of Physics, Vol. 8, 2006, p. 318. doi:10.1088/1367-2630/8/12/318
[5]	E. H. Hwang, and S. Das Sarma, “Dielectric Function, Screening, and Plasmons in Two-Dimensional Gra- phene,” Physical Review B, Vol. 75, No. 20, 2007, p. 205418. doi:10.1103/PhysRevB.75.205418
[6]	B. E. Sernelius, “Retarded Interactions in Graphene Sys- tems,” Physical Review B, Vol. 85, No. 19, 2012, p. 195427. doi:10.1016/0550-3213(94)90410-3
[7]	B. E. Semelius, “Casimir Interactions in Graphene Sys- tems” Europhysics Letters, Vol. 5, No. 5, 2011, p. 57003. doi:10.1209/0295-5075/95/57003
[8]	L. A. Falkovsty and S. S. Pershoguba, “Optical Far-In- frared Properties of a Graphene Monolayer and Multi- layer,” Physical Review B, Vol. 76, No. 15, 2007, p. 153410. doi:10.1103/PhysRevB.76.153410
[9]	T. Stauber, N. M. R. Peres and A. K. Geim, “Optical Conductivity of Graphene in the Visible Region of the Spectrum,” Physical Review B, Vol. 78, No. 8, 2008, p. 085432. doi:10.1103/PhysRevB.78.085432
[10]	B. E. Sernelius, “Surface Modes in Physics,” Wiley-VCH, Berlin, 2001.
[11]	B. E. Sernelius, “Effects of Spatial Dispersion on Electromagnetic Surface Modes and on Modes Associated with a Gap between Two Half Spaces,” Physical Review B, Vol. 71, No. 23, 2005, p. 235114. doi:10.1103/PhysRevB.71.235114
[12]	R. Esquivel and V. B. Svetovoy “Correction to the Casimir Force Due to the Anomalous Skin Effect,” Physical Review A, Vol. 69, No. 6, 2004, p. 062102. doi:10.1103/PhysRevA.69.062102
[13]	B. E. Sernelius and P. Bj?rk, “Interaction Energy for a Pair of Quantum Wells,” Physical Review B, Vol. 57, No. 11, 1998, p. 6592. doi:10.1103/PhysRevB.57.6592
[14]	M. Bostr?m and Bo E. Sernelius, “Fractional van der Waals Interaction between Thin Metallic Films,” Physical Review B, Vol. 61, No. 3, 2000, p. 2204. doi:10.1103/PhysRevB.61.2204
[15]	J. F. Dobson, A. White and A. Rubio, “Asymptotics of the Dispersion Interaction: Analytic Benchmarks for van der Waals Energy Functionals,” Physical Review Letters, Vol. 96, No. 7, 2006, p. 073201. doi:10.1103/PhysRevLett.96.073201
[16]	Bo E. Sernelius, “Casimir Effects in Graphene Sys- tems: Unexpected Power Laws,” International Journal of Modern Physics: Conference Series, Vol. 14, 2012, p. 531. doi:10.1142/S2010194512007660
[17]	J. Mahanty and B. W. Ninham, “Dispersion Forces,” Academic Press, London, 1976.
[18]	G. Gómez-Santos, “Thermal van der Waals Interac- tion between Graphene Layers,” Physical Review B, Vol. 80, 2009, p. 245424. doi:10.1103/PhysRevB.80.245424
[19]	V. Svetovoy, Z. Moktadir, M. Elwenspoek, and H. Mizuta, “Tailoring the Thermal Casimir Force with Gra- phene,” Europhysics Letters, Vol. 96, No. 1, 2011, p. 14006. doi:10.1209/0295-5075/96/14006
[20]	Jalal Sarabadani, Ali Naji, Reza Asgari, and Rudolf Podgornik, “Many-Body Effects in the van der Waals- Casimir Interaction between Graphene Layers,” Physical Review B, Vol. 84, No. 15, 2011, p. 155407. doi:10.1103/PhysRevB.84.155407