Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-13T03:00:53.231Z Has data issue: false hasContentIssue false
  • English
  • Français

Lie Group Calculation of the Green Function of Disordered Systems

Published online by Cambridge University Press:  25 February 2011

Christian Brouder
Christian Brouder*
Affiliation:
Laboratoire de Physique du Solide, Université de Nancy 1, B.P.239 F-54506 Nancy, France, and Laboratoire pour l'Utilisation du Rayonnement Electromagnétique, F-91405 Orsay, France
Get access

Abstract

Within the framework of the muffin-tin multiple-scattering theory, the scattering path operators are given by the inverse of a matrix consisting of atomic t-matrices and a structural matrix. The influence of the displacement of an atomic centre on the structural matrix can be described analytically using Lie group techniques. From this analytical expression and the standard perturbation expansion of the Lippmann-Schwinger equation, it is possible to write the Green function of a disordered system as a series of terms whichare averages over configurations. These averages can be calculated analytically from themoments of the interatomic distances. Special terms of this series are then summed up toinfinity using Dyson equation. This formalism is computationally very effective to calculate electronic properties of systems with thermal or structural disorder. In this paper, the theoretical basis of this approach is briefly described and the convergence properties of the expansions are investigated.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 253: Symposium V – Application of Multiple Scattering Theory to Materials Science , 1991 , 411
Copyright
Copyright © Materials Research Society 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1. Hall, B.M., Superlattices Microstruct. 7, 229, (1990).CrossRefGoogle Scholar
2. Rous, P.J., Pendry, J.B., Saldin, D.K., Heinz, K., Müller, K. and Bickel, N., Phys. Rev. Lett. 57, 2951, (1986).Google Scholar
3. Rous, P.J. and Pendry, J.B., Comp. Phys. Commun. 57, 137 (1989).Google Scholar
4. Barton, J.J. and Shirley, D.A., Phys. Rev. A, 32, 1019, (1985).CrossRefGoogle Scholar
5. Danos, M. and Maximon, L.C., J. Math. Phys. 6, 766 (1965).CrossRefGoogle Scholar
6. Brouder, Ch., PhD thesis, University of Nancy, 1987.Google Scholar
7. Brouder, Ch., J. Phys. C, 21, 5075, (1988).Google Scholar
8. Brouder, Ch. and Goulon, J., Physica B, 158, 351, (1989).Google Scholar
9. Gyorffy, B.L. and Stott, M.J., in Band Structure Spectroscopy of Metals and Alloys, edited by Fabian, D.J. and Watson, L.M. (Academic Press, London, 1973) pp.385–403.Google Scholar
10. Fox, R.F., Phys. Rep. 48, 179 (1978).Google Scholar
11. Butler, W.H. and Zhang, X.-G., Phys. Rev. B, 44, 969, (1991).Google Scholar
12. Newton, R.G., Scattering Theory of Waves and Particles, 2nd. ed. (Springer, New York, 1982), p.371.Google Scholar
13. Herman, F. and Skillman, S., Atomic Structure Calculations, (Prentic-Hall, Englewoods Cliffs, N.J., 1963).Google Scholar
14. Weyl, H., Ann. Phys. (Germany) 60, 481 (1919).CrossRefGoogle Scholar
15. Wong, R., Asymptotic Approximations of Integrals, (Academic Press, Boston, 1989), p. 423.Google Scholar
16. Zeller, R., J. Phys. C: Solid State Phys. 20, 2347, (1987).Google Scholar