Abstract
An expression for the Green's function (GF) of diamond lattice is evaluated analytically and numerically for a single impurity interacting with the first nearest-neighboring host atoms. The density of states (DOS), phase shift and scattering cross-section are expressed in terms of complete elliptic integrals of the first kind.
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References
Bateman Manuscript Project (1963). In: Higher Transcendental Functions, A. Erdelyi et al. (Eds.), McGraw-Hill, New York, Vol. I.
Doniach, S. and Sondheimer, E. H. (1974). Green's Functions for Solid State Physicists, Benjamin, Reading, MA.
Economou, E. N. (1983). Green Function in Quantum Physics, 2nd edn., Springer-Verlag, Berlin.
Gradshteyn, I. S. and Ryzhik, I. M. (1965). Tables of Integrals, Series, and Products, Academic Press, New York.
Guttmann, A. J. and Prellberg, T. (1993). Staircase polygons, elliptic integrals, heun functions and lattice green functions. Physical Review E 47, R2233.
Hijjawi, R. S., Asad, J. H., Sakaji, A., and Khalifeh, J. M. (2004). Lattice Green's function for the face centered cubic lattice. Journal of Theoretical Physics 43, 1388.
Hijjawi, R. S. and Khalifeh, J. M. (2002). Remarks on the lattice Green's function, the general glasser case. Journal of Theoretical Physics 41, 1769.
Inoue, M. (1974). Lattice Green's function for the face centered cubic lattice. Journal of Mathematical Physics 15, 704.
Ishioka, S. and Koiwa, M. (1978). Random walks on diamond and hexagonal close packed lattices. Philosophical Magazine A 37, 517.
Joyce, G. S. (1973). On the simple cubic lattice Green's function. Transactions of the Royal Society 273(A1236), 583–610.
Katsura, S., Morita, T., Inawashiro, S., Horiguci, T., and Abe, Y. (1971). Lattice Green's function introduction. Journal of Mathematical Physics 12, 892.
Koiwa, M. and Ishioka, S. (1979). Random walks on three-dimensional lattices with the coordination number four. Philosophical Magazine A 40, 625.
Morita, T. and Horiguci, T. (1971). Lattice Green's function for cubic lattices in terms of complete elliptic integral. Journal of Mathematical Physics 12, 981.
Sakaji, A., Hijjawi, R. S., Shawagfeh, N., and Khalifeh, J. M. (2002a). Lattice Green's function for the body-centered cubic lattice. Journal of Theoretical Physics 41, 973.
Sakaji, A., Hijjawi, R. S., Shawagfeh, N., and Khalifeh, J. M. (2002b). Remarks on the lattice Green's function, the glasser case. Journal of Mathematical Physics 43, 1.
Slater, L. J. (1966). Generalized Hypergeometric Functions, Cambridge University Press.
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Hijjawi, R.S. Lattice Green's Function for the Diamond Lattice. Int J Theor Phys 45, 129–140 (2006). https://doi.org/10.1007/s10773-005-9012-0
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DOI: https://doi.org/10.1007/s10773-005-9012-0