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Electronic Structure of Disordered Materials

  • E. N. Economou
  • Morrel H. Cohen
  • Karl F. Freed
  • E. S. Kirkpatrick
Chapter

Abstract

It has been known since the work of Bloch (1928) that there are universal features in the electronic structures of crystals. The most important of these are energy bands separated by gaps, crystal momentum as a good quantum number, and the form of the wave function; they provide the conceptual foundations of much of solid state physics.

Keywords

Extended State Percolation Theory Localization Length Mobility Edge Anderson Transition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Anderson, P. W., (1958), Phys. Rev., 109, 1492.ADSCrossRefGoogle Scholar
  2. Austin, I. G. and Mott, N. F., (1969), Adv. Phys., 18, 41.ADSCrossRefGoogle Scholar
  3. Banyai, L., (1964), Physique de Semi-Conducteurs, p. 417. Dunod, Paris.Google Scholar
  4. Bloch, F., (1928), Z. Physik, 52, 555.ADSCrossRefGoogle Scholar
  5. Bonch-Bruevich, V. L., (1964), Fizika tuerd Tela, 5, 1852. (Translation: (1964) Soviet Phys. Solid St, 5, 1353 ).Google Scholar
  6. Borland, R. E., (1961), Proc. Phys. Soc., 78, 926.MathSciNetADSCrossRefGoogle Scholar
  7. Borland, R. E., (1963), Proc. R. Soc., A274, 529.Google Scholar
  8. Borland, R. E. and Bird, N. F., (1964), Proc. Phys,. Soc., 83, 23.ADSCrossRefGoogle Scholar
  9. Brillouin, L., (1953), Wave Propagation in Periodic Structures, 2nd ed. Dover, New York.zbMATHGoogle Scholar
  10. Broadbent, S. R. and Hammersley, J. M., (1957), Proc. Cambridge Phil Soc., 53, 629.MathSciNetADSCrossRefzbMATHGoogle Scholar
  11. Brodsky, M. H. and Title, R. S., (1969), Phys. Rev. Letters, 23, 581.ADSCrossRefGoogle Scholar
  12. Brodsky, M. H., (1971), J. Vac. Science and Technology, 8, 125.ADSCrossRefGoogle Scholar
  13. Brouers, F., (1970), J. Non-Cryst. Solids, 4, 428.ADSCrossRefGoogle Scholar
  14. Cohen, M. H., Fritzsche, H. and Ovshinsky, S. R., (1969), Phys. Rev. Letters, 22, 1065.ADSCrossRefGoogle Scholar
  15. Cohen, M. H., (1970), J. Non-Cryst. Solids, 4, 391.ADSCrossRefGoogle Scholar
  16. Coopersmith, M. H., (1965) Phys. Rev., 139, 1359.ADSCrossRefGoogle Scholar
  17. Coopersmith, M. H. and Neustadter, H. E., (1967), Phys. Rev., 161, 168.ADSCrossRefGoogle Scholar
  18. Cutler, M. and Mott, N. F., (1969), Phys. Rev., 181, 1336.ADSCrossRefGoogle Scholar
  19. Davis, E. A. and Mott, N. F., (1970), Phil Mag., 22, 903.ADSCrossRefGoogle Scholar
  20. Domb, G, (1963), J. Chem. Phys., 38, 2957.ADSCrossRefGoogle Scholar
  21. Donovan, T. M., Spicer, W. E., Bennett, J. M. and Ashley, E. J., (1970a),Phys. Rev., B2, 397.Google Scholar
  22. Donovan, T. M., Ashley, E. J. and Spicer, W. E., (1970b), Physics Letters, 32A, 85.Google Scholar
  23. Economou, E. N., Kirkpatrick, S., Cohen, M. H. and Eggarter, T. P., (1970a), Phys. Rev. Letters, 25, 520.ADSCrossRefGoogle Scholar
  24. Economou, E. N. and Cohen, M. H., (1970b), Phys. Rev. Letters, 25, 1445.ADSCrossRefGoogle Scholar
  25. Economou, E. N. and Cohen, M. H., (1972), Phys. Rev., 5B, 2931.ADSCrossRefGoogle Scholar
  26. Economou, E. N., (1971a), Solid State Comm., 9, 1317.ADSCrossRefGoogle Scholar
  27. Economou, E. N. and Cohen, M. H., (1971b), Phys. Rev., 4B, 396.Google Scholar
  28. Economou, E. N. and Cohen, M. H., (1970c), Phys. Rev. Letters, 24, 218.ADSCrossRefGoogle Scholar
  29. Economou, E. N. and Papatriantafillou, C., (1972b) Solid State Comm., 11, 197.ADSCrossRefGoogle Scholar
  30. Edwards, S. F., (1961), Phil Mag., 6, 617.ADSCrossRefzbMATHGoogle Scholar
  31. Edwards, S. F., (1962), Proc. R. Soc., A267, 518.Google Scholar
  32. Edwards, S. F., (1970a), J. Phys., C3, L30.Google Scholar
  33. Edwards, S. F., (1970b), J. Non-Cryst. Solids, 4, 417.ADSCrossRefGoogle Scholar
  34. Edwards, S. F. and Gulyaev, Y. B., (1964), Proc. Phys. Soc. (London), 83, 495.ADSCrossRefGoogle Scholar
  35. Edwards, S. F., (1965), Proc. Phys. Soc. ( London ), 85, 613.Google Scholar
  36. Edwards, S. F., (1966), Natl Bur. Std. (U.S.) Misc. Publ., 273, 225.Google Scholar
  37. Edwards, S. F. and Freed, K. F., (1970c), J. Phys., C3, 739.ADSGoogle Scholar
  38. Edwards, S. F. and Freed, K. F., (1969), J. Phys., A2,145.ADSGoogle Scholar
  39. Eggarter, T. P. and Cohen, M. H., (1970), Phys. Rev. Letters, 25, 807.ADSCrossRefGoogle Scholar
  40. Feynman, R. P. and Hibbs, A. R., (1965), Quantum Mechanics and Path Integrals, McGraw-Hill, New York.zbMATHGoogle Scholar
  41. Fröhlich, H., (1947), Proc. Roy. Soc. (London), A188, 521.Google Scholar
  42. Foldy, L. L., (1945), Phys. Rev., 67, 107.MathSciNetADSCrossRefzbMATHGoogle Scholar
  43. Freed, K. and Cohen, M. H., (1971a), Phys. Rev., 33, 3400.Google Scholar
  44. Freed, K. F., (1971b), J. Chem Phys, 55, 3910.ADSCrossRefGoogle Scholar
  45. Fritzsche, H., (1971), present volume.Google Scholar
  46. Frisch, H. L. and Lloyd, S. P., (1960), Phys. Rev., 120, 1175.ADSCrossRefzbMATHGoogle Scholar
  47. Frisch, H. L. and Hammersley, J. M., (1963), S.I.A.M., 11, 894.MathSciNetGoogle Scholar
  48. Frisch, H. L., Sonnenblick, E., Vyssotsky, V. A. and Hammersley, J. M., (1961), Phys. Rev., 124, 1021.ADSCrossRefGoogle Scholar
  49. Gelfand, I. M. and Taglow, A. M., (1960), J. Math. Phys., 1, 48.ADSCrossRefGoogle Scholar
  50. Grigorivici, R., (1968), Materials Res. Bulletin, 3, 13.CrossRefGoogle Scholar
  51. Gubanov, A. I., (1963), Quantum Electron Theory of Amorphous Conductors, Academy of Sciences Press, Moscow (Translation: Consultants Bureau, New York, 1965 ).Google Scholar
  52. Halperin, B. I. and Lax M., (1966), Phys. Rev., 148, 722.ADSCrossRefGoogle Scholar
  53. Halperin, B. I., (1967), Adv. Chem. Phys., 13, 123.CrossRefGoogle Scholar
  54. Hori, J., (1966), Progr. Theor. Phys., Suppl. No. 36, 3.MathSciNetADSCrossRefGoogle Scholar
  55. Jalickee, J. B., Siegert, A. J. F. and Vezzetti, D. J., (1969), J. Math. Phys., 10, 1442.MathSciNetADSCrossRefGoogle Scholar
  56. Jones, R. and Lukes, T., (1969), Proc. Roy. Soc., A309, 457.ADSCrossRefGoogle Scholar
  57. Kane, E. O., (1963), Phys. Rev., 131, 79.ADSCrossRefzbMATHGoogle Scholar
  58. Kirkpatrick, S., Velicky, B. and Ehrenreich, H., (1970), Phys. Rev., B1, 3250.ADSCrossRefGoogle Scholar
  59. Kirkpatrick, S., Economou, E. N., Cohen, M. H. and Papatriantafillou, C., (1971) unpublished.Google Scholar
  60. Kubo, R., (1962), J Phys. Soc. (Japan), 17, 1100.MathSciNetADSCrossRefzbMATHGoogle Scholar
  61. Kubo, R., (1956), Can. J. Physics, 34, 1274.MathSciNetADSCrossRefGoogle Scholar
  62. Kubo, R., (1957), J. Phys. Soc. (Japan), 12, 570.MathSciNetADSCrossRefGoogle Scholar
  63. Landauer, R. and Heiland, J. G, (1954), J. Chem. Phys., 22, 1655ADSCrossRefGoogle Scholar
  64. Lax, M. and Phillips, J. C., (1958a), Phys. Rev., 110, 41.MathSciNetADSCrossRefzbMATHGoogle Scholar
  65. Lax, M., (1958b), Phys. Rev., 109, 1921.MathSciNetADSCrossRefzbMATHGoogle Scholar
  66. Lax, ML, (1951), Reviews Mod. Phys., 23, 287.MathSciNetADSCrossRefzbMATHGoogle Scholar
  67. Lifshitz, I. M., (1964a), Adv. Phys., 13, 483.ADSCrossRefGoogle Scholar
  68. Lifshitz, I. M., (1964b), Usp. Fiz. Nauk, 83, 617 (Translation: Soviet Phys. Usp. 7, 549 (1965)).MathSciNetGoogle Scholar
  69. Llyod, P., (1969), J. Phys., C2, 1717.ADSGoogle Scholar
  70. Makinson, R. E. B. and Roberts, A. P., (1962), Proc. Phys. Soc., 79, 630.MathSciNetADSCrossRefGoogle Scholar
  71. Mortensen, R. E., (1969) J. Stat. Phys., 1, 271.ADSCrossRefGoogle Scholar
  72. Moss, S. C. and Graczyk, J. F., (1970), Proceedings, Tenth International Conference on the Physics of Semiconductors, Cambridge, Mass.Google Scholar
  73. Mott, N. F., (1967a), Adv. Phys., 16, 49.ADSCrossRefGoogle Scholar
  74. Mott, N. F. and Twose, W. D., (1961), Adv. Phys., 10, 107.ADSCrossRefGoogle Scholar
  75. Mott, N. F., (1966), Phil Mag., 13, 989.ADSCrossRefGoogle Scholar
  76. Mott, N. F., (1968a), J. Non-Cryst. Solids, 1, 1.ADSCrossRefGoogle Scholar
  77. Mott, N. F. and Allgaier, R. S., (1967b), Phys. Stat. Sol., 21, 343.ADSCrossRefGoogle Scholar
  78. Mott, N. F., (1968b), Phil Mag., 17, 1259.ADSCrossRefGoogle Scholar
  79. Mott, N. F. and Davis, E. A., (1968c), Phil Mag., 17, 1269.ADSCrossRefGoogle Scholar
  80. Mott, N. F., (1969a), Phil Mag., 19, 835.ADSCrossRefGoogle Scholar
  81. Mott, N. F., (1968d), Revs. Mod. Phys., 40, 677.ADSCrossRefGoogle Scholar
  82. Mott, N. F., (1969b), Contemp. Phys., 10, 125.ADSCrossRefGoogle Scholar
  83. Mott, N. F., (1968c), Festkorperprobleme, 9, 22.Google Scholar
  84. Mott, N. F., (1970), Phil Mag., 22, 7.ADSCrossRefGoogle Scholar
  85. Neustadter, H. E. and Coopersmith, M. H., (1969), Phys. Rev. Letters, 23, 585.ADSCrossRefGoogle Scholar
  86. Polk, D. E., (1971), J. Non-Cryst. Solids, 5, 365.ADSCrossRefGoogle Scholar
  87. Schilder, M., (1970), J. Stat Phys., 1, 475.ADSCrossRefGoogle Scholar
  88. Schwartz, L., (1970), Thesis, Harvard; Schwartz, L. and Ehrenreich, H., (1971), Ann Phys. (N.Y.), 64, 100.ADSCrossRefGoogle Scholar
  89. Shante, V. K. S. and Kirkpatrick, S., (1971a) Adv. in Physics, 30, 325.ADSCrossRefGoogle Scholar
  90. Siegert, A. J. F., (1963), statistical Physics Vol. Ill of Brandeis Lectures W. A. Benjamin, New York.Google Scholar
  91. Soven, P., (1967), Phys. Rev., 156, 809.ADSCrossRefGoogle Scholar
  92. Sykes, M. F. and Essam, J. W., (1964), Phys. Rev., 133, A310.ADSCrossRefGoogle Scholar
  93. Thouless, D., (1970), J. Phys., C3, 1559.ADSGoogle Scholar
  94. Velicky, B., Kirkpatrick, S. and Ehrenreich, H., (1968), Phys. Rev., 175, 747.ADSCrossRefGoogle Scholar
  95. Wall, H. S., (1948), Analytic Theory of Continued Fractions, D. VanNostrand, New York.zbMATHGoogle Scholar
  96. Watson, K. M., (1957), Phys. Rev., 105, 1388.MathSciNetADSCrossRefzbMATHGoogle Scholar
  97. Wilhams, F. W. and Matthews, N. F. J., (1969), Phys. Rev., 180, 864.ADSCrossRefGoogle Scholar
  98. Ziman, J. M., (1961), Phil Mag., 6, 1013.ADSCrossRefzbMATHGoogle Scholar
  99. Ziman, J. M., (1968), J. Phys., C1, 1532.ADSGoogle Scholar
  100. Ziman, J. M., (1969), J. Phys., C2, 1230.Google Scholar
  101. Zittartz, J. and Langer, J. S., (1966), Phys. Rev., 148, 741.ADSCrossRefzbMATHGoogle Scholar

Copyright information

© Plenum Publishing Company Ltd 1974

Authors and Affiliations

  • E. N. Economou
    • 1
  • Morrel H. Cohen
    • 2
  • Karl F. Freed
    • 2
  • E. S. Kirkpatrick
    • 2
  1. 1.Department of Physics and Center for Advanced StudiesUniversity of VirginiaCharlottesvilleUSA
  2. 2.James Franck InstituteThe University of ChicagoChicagoUSA

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