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Prog. Theor. Phys. Vol. 31 No. 3 (1964) pp. 357-377

A Note on Electronic State of Random Lattice

Fumiko Yonezawa

Department of Physics, Kyoto University, Kyoto

(Received September 16, 1963)

Abstract:

The modification of the density of electron energy levels and conductivity due to random impurities in solids is investigated. The diagram perturbation method developed by Matsubara and Toyozawa for semi-conductor (referred to as M-T method) is employed in actual calculation. In order to estimate the accuracy of the M-T method, we compare it with other methods. Detailed discussions on the nature of various approximations are given and perfect correspondence between the M-T method and those by Edwards and by Klauder is established. It is concluded that the M-T method is the tractable best approximation. Numerical calculation for simplified model of three dimensional system is performed and some results are shown.

URL : http://ptp.ipap.jp/link?PTP/31/357/
DOI : 10.1143/PTP.31.357

[ Full Text PDF : FREE ACCESS (1018K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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References:

1. There exist a number of reference papers on this problem.
   Here only some of them are listed:
   H. M. James and A. S. Ginzbarg, J. Phys. Chem. 57 (1953), 840[CrossRef].
   E. H. Kerner, Phys. Rev. 95 (1954), 687[APS].
   P. Aigrain, Physica 20 (1954), 978[CrossRef].
   M. Lax and J. C. Phillips, Phys. Rev. 110 (1958), 41[APS].
   H. L. Frisch and S. P. Lloyd, Phys. Rev. 120 (1960), 1175[APS].
   H. Matsuda, Prog. Theor. Phys. 27 (1962), 811[PTP].
2. S. F. Edwards, Phil. Mag. 3 (1958), 1020.
3. R. Klauder, Ann. of Phys. 14 (1961), 43[CrossRef].
4. T. Matsubara and Y. Toyozawa, Prog. Theor. Phys. 26 (1961), 739[PTP].
5. For instance, D. A. Greenwood, Proc. Phys. Soc. 71 (1958), 585.
6. W. Kohn and J. M. Luttinger, Phys. Rev. 108 (1957), 590[APS].

Citing Article(s) :

1. Progress of Theoretical Physics Vol. 35 No. 3 (1966) pp. 357-379 :

   Note on Electronic State of Random Lattice. II

   Fumiko Yonezawa and Takeo Matsubara

2. Progress of Theoretical Physics Vol. 35 No. 5 (1966) pp. 759-776 :

   Note on Electronic State of Random Lattice. III

   Fumiko Yonezawa and Takeo Matsubara

3. Progress of Theoretical Physics Vol. 36 No. 4 (1966) pp. 695-711 :

   Contribution to the Theory of Impurity Band Conduction. I

   Takeo Matsubara and Takahito Kaneyoshi

4. Progress of Theoretical Physics Vol. 37 No. 6 (1967) pp. 1346-1347 :

   First-Order Self-Energy Expressed in the Form of a Continued Fraction

   Takeo Matsubara and Fumiko Yonezawa

5. Progress of Theoretical Physics Vol. 39 No. 5 (1968) pp. 1153-1164 :

   Coarse-Grained Quantities in Aperiodic Systems. III

   Kenkichi Okada and Hirotsugu Matsuda

6. Progress of Theoretical Physics Vol. 40 No. 3 (1968) pp. 435-451 :

   Classical Spins in Superconductors

   Hiroyuki Shiba

7. Progress of Theoretical Physics Vol. 40 No. 4 (1968) pp. 734-757 :

   A Systematic Approach to the Problems of Random Lattices. I

   Fumiko Yonezawa

8. Progress of Theoretical Physics Vol. 40 No. 4 (1968) pp. 900-901 :

   Exact First Order Self-Energy of a Lattice with Random Impurities

   Melvin Stavn

9. Progress of Theoretical Physics Vol. 42 No. 6 (1969) pp. 1284-1303 :

   Theory of Hall Effect. II

   Hidetoshi Fukuyama

10. Progress of Theoretical Physics Vol. 44 No. 4 (1970) pp. 879-898 :

    Hall Effect and Orbital Magnetism of Binary Alloys

    Hidetoshi Fukuyama

11. Progress of Theoretical Physics Supplement No.53 (1973) pp. 1-76 :

    Coherent Potential Approximation

    Fumiko Yonezawa and Kazuo Morigaki

12. Progress of Theoretical Physics Supplement No.53 (1973) pp. 139-201 :

    Density of States in Aperiodic Solids

    Hiroshi Hasegawa

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