Geodesic
Study of temperature Green's functions of graphene-like systems in a half-space
Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 3, pp. 426-439 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the formalism of temperature Green's functions to study the electronic properties of a semi-infinite two-dimensional graphene lattice at a given temperature. Under most general assumptions about the graphene boundary structure, we calculate the propagator in the corresponding diagram technique. The obtained propagator survives limit transitions between physically different states of the system boundary, i.e., a zig-zag edge and a boundary condition in the "infinite mass" approximation, and also correctly describes the problem where the electron–hole symmetry is violated because of the presence of an external potential applied to the graphene boundary. We illustrate the use of the propagator, its analytic properties, and specific features of calculating with it in the example of determining the dependence of the electron density on the distance to the system boundary.
Keywords: temperature Green's function, quantum field perturbation theory, boundary condition.
Mots-clés : graphene 
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     author = {I. A. D'yakonov and M. V. Komarova and M. Yu. Nalimov},
     title = {Study of temperature {Green's} functions of graphene-like systems in a~half-space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     year = {2017},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2017_190_3_a4/}
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I. A. D'yakonov; M. V. Komarova; M. Yu. Nalimov. Study of temperature Green's functions of graphene-like systems in a half-space. Teoretičeskaâ i matematičeskaâ fizika, Tome 190 (2017) no. 3, pp. 426-439. http://geodesic.mathdoc.fr/item/TMF_2017_190_3_a4/

[1] P. R. Wallace, “The band theory of graphite”, Phys. Rev., 71:9 (1947), 622–634 | DOI | Zbl

[2] C. Oshima, A. Nagashima, “Ultra-thin epitaxial films of graphite and hexagonal boron nitride on solid surfaces”, J. Phys., 9:1 (1997), 1–20 | DOI | MR

[3] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, “Electric field effect in atomically thin carbon films”, Science, 306:5696 (2004), 666–669 | DOI

[4] M. I. Katsnelson, Graphene. Carbon in Two Dimensions, Cambridge Univ. Press, Cambridge, 2012

[5] C. G. Beneventano, I. Fialkovsky, E. M. Santangelo, D. V. Vassilevich, “Charge density and conductivity of disordered Berry–Mondragon graphene nanoribbons”, Eur. Phys. J. B, 87:3 (2014), 50, 9 pp. | DOI | MR

[6] C. G. Beneventano, E. M. Santangelo, “Boundary conditions in the Dirac approach to graphene devices”, Internat. J. Modern Phys. Conf. Ser., 14 (2012), 240–249 | DOI

[7] A. R. Akhmerov, C. W. J. Beenakker, “Boundary conditions for Dirac fermions on a terminated honeycomb lattice”, Phys. Rev. B, 77:8 (2008), 085423, 10 pp. | DOI

[8] A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinskii, Metody kvantovoi teorii polya v statisticheskoi fizike, Dobrosvet, M., 2006 | MR | Zbl

[9] A. N. Vasilev, Funktsionalnye metody v kvantovoi teorii polya i statistike, LGU, L., 1976

[10] A. Nieto, “Evaluating sums over the Matsubara frequencies”, Comput. Phys. Commun., 92:1 (1995), 54–64 | DOI