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Graphene  2021 

Green’s Functions and DOS for Some 2D Lattices

DOI: 10.4236/graphene.2021.101001, PP. 1-12

Keywords: 2D Lattices

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Abstract:

In this presentation we present the Green’s functions and density of states for the most frequently encountered 2D lattices: square, triangular, honeycomb, kagome, and Lieb lattice. Though the results are well known, we hope that its derivation performed in a uniform way provides some pedagogical value.

References

[1]  Komnik, A. and Heinze, S. (2017) Analytical Results for the Green’s Functions of Lattice Fermions. Physical Review B, 96, Article ID: 155103.
https://doi.org/10.1103/PhysRevB.96.155103
[2]  Varma, V.K. and Monien, H. (2013) Lattice Green’s Functions for Kagome, Diced, and Hyperkagome Lattices. Physical Review E, 87, Article ID: 032109.
https://doi.org/10.1103/PhysRevE.87.032109
[3]  Katsura, S., Morita, T., Inawashiro, S., Horiguchi, T. and Abe, Y. (1971) Lattice Green’s Function. Introduction. Journal of Mathematical Physics, 12, 892-895.
https://doi.org/10.1063/1.1665662
[4]  Economou, E.N. (2006) Green’s Functions in Quantum Physics. 3rd Edition, Springer-Verlag, Berlin.
[5]  Guttmann, A.J. and Prellberg, T. (1993) Staircase Polygons, Elliptic Integrals, Heun Functions, and Lattice Green Functions. Physical Review E, 47, R2233-R2236.
https://doi.org/10.1103/PhysRevE.47.R2233
[6]  Ziff, R.M. (1991) Flux to a Trap. Journal of Statistical Physics, 65, 1217-1233.
https://doi.org/10.1007/BF01049608
[7]  Barber, M.N. and Ninham, B.W. (1970) Random and Restricted Walks. Gordon and Breach, New York.
[8]  Hughes, B.D. (1995) Random Walks and Random Environments. Volume 1: Random Walks. Clarendon, Oxford.
[9]  Cserti, J. (2000) Application of the Lattice Green’s Function for Calculating the Resistance of an Infinite Network of Resistors. American Journal of Physics, 68, 896-906. https://doi.org/10.1119/1.1285881
[10]  Sherafati, M. and Satpathy, S. (2011) RKKY Interaction in Graphene from Lattice Green’s Function. Physical Review B, 83, Article ID: 165425.
https://doi.org/10.1103/PhysRevB.83.165425
[11]  Parhizgar, F., Sherafati, M., Asgari, R. and Satpathy, S. (2013) Ruderman-Kit- tel-Kasuya-Yosida Interaction in Biased Bilayer Graphene. Physical Review B, 87, Article ID: 165429. https://doi.org/10.1103/PhysRevB.87.165429
[12]  Zare, M. (2019) RKKY Plateau in Zero- and One-Dimensional Triangular Kagome Lattice Models.
[13]  Roslyak, O., Gumbs, G., Balassis, A. and Elsayed, H. (2020) Effect of Magnetic Field and Chemical Potential on the RKKY Interaction in the α-T3 Lattice.
[14]  Prudnikov, A.P., Brychkov, Yu.A. and Marichev, O.I. (1986) Integrals and Series, Vol. 2. Gordon and Breach Science Publishers, Amsterdam.
[15]  Henyey, F.S. and Seshadri, V. (1982) On the Number of Distinct Sites Visited in 2D Lattices. The Journal of Chemical Physics, 76, 5530-5534.
https://doi.org/10.1063/1.442908
[16]  Hanisch, Th., Uhrig, G.S. and Muller-Hartmann, E. (1997) Lattice Dependence of Saturated Ferromagnetism in the Hubbard Model. Physical Review B, 56, 13960- 13982. https://doi.org/10.1103/PhysRevB.56.13960
[17]  Moritz, B. and Schwalm, W. (2001) Triangle Lattice Green Functions for Vector Fields. Journal of Physics A: Mathematical and General, 34, 589-602.
https://doi.org/10.1088/0305-4470/34/3/317
[18]  Erdelyi, A. (1985) Higher Transcendental Functions, Vol. II. McGraw-Hill Book Company, Inc., New York.
[19]  Georges, A., Kotliar, G., Krauth, W. and Rozenberg, M. (1996) Dynamical Mean-Field Theory of Strongly Correlated Fermion Systems and the Limit of Infinite Dimensions. Reviews of Modern Physics, 68, 13-125.
https://doi.org/10.1103/RevModPhys.68.13
[20]  Guinea, F., Peres, N.M.R., Novoselov, K.S. and Geim, A.K. (2009) The Electronic Properties of Graphene A. H. Castro Neto. Reviews of Modern Physics, 81, 109-162.
https://doi.org/10.1103/RevModPhys.81.109
[21]  Landau, L.D. and Lifshitz, E.M. (1991) Quantum Mechanics. Pergamon Press, Oxford.
[22]  Ananyev, V.O. and Ovchynnikov, M.I. (2017) On the Density of States of Graphene in the Nearest-Neighbor Approximation. Condensed Matter Physics, 20, Article ID: 43705. https://doi.org/10.5488/CMP.20.43705

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