Abstract
The transition between localized and extended electronic states in disordered materials is considered by the use of two different models. The mathematical analogy between this transition and phase transitions and critical points in fluids and magnets is stressed and exploited. The localization probability and range in the neighborhood of the transition are shown to have critical exponent type behavior with the exponents 13/6 and -2/3, respectively. A preliminary discussion of electron mobility in disordered materials is also presented.
Research supported by NSF Grant GP-28135, ACS PRF Grant 5767-AC6, and ARPA facilities for materials research at The University of Chicago
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References
For a review and further references see E. N. Economou, M. H. Cohen, K. F. Freed, and E. S. Kirkpatrick in Amorphous and Liquid Semiconductors, J. Taue, ed,, (Plenum, New York) to be published.
N. F. Mott and E. A. Davis, Electronic Processes in Noncrystal-line Materials (Clarendon Press, Oxford, 1971),
I. M. Lifshitz, Adv. Phys. 13, 403 (1964).
M. H. Cohen, H. Fritzsche, and S. R. Ovshinsky, Phys. Rev. Letters 22, 1065 (1969).
P. W. Anderson, Phys. Rev. 109, 1492 (1958).
J. M. Ziman, J. Phys. C. 1, 1532 (1968).
V.K.S. Shante and S. Kirkpatrick, Adv. Phys. 20, 325 (1971).
S. F. Edwards, J. Phys. C. 3, L30 (1970); J. Non-Cryst, Solids 4, 417 (1970).
K. F. Freed and M. H. Cohen, Phys. Rev. B3, 3400 (1971).
F. Yonezawa and T. Matsubara, Progr. Theoret. Phys. (Kyoto) 35, 357, 759 (1966); P. Soven, Phys. Rev. 156, 809 (1967); D. W. Taylor, ibid. 156, 1017 (1967); P. L. Leath, ibid. 171, 725 (1968); B. Veclicky, S. Kirkpatrick and H. Ehrenreich, ibid. 175, 747 (1968); P. Soven, ibid. 178, 1136 (1969); and S. Kirkpatrick, B. Velicky and H. Ehrenreich, ibid. B1, 3250 (19 70).
S. F. Edwards and Y. B. Gulyaev, Proc. Phys. Soc. (London) 83, 495 (1964).
B. Halperin and M. Lax, Phys. Rev. 148, 722 (1966); J. Zittartz and J. S. Langer, ibid. 148, 741 (1966).
K. F, Freed, J. Phys, C, 4, L331 (1971); Phys. Rev. B5, 4802 (1972).
E. N. Economou and M. H. Cohen, Phys. Rev. B5, 2931 (1972).
K. F. Freed, Advan. Chem, Phys. 22, 1 (1972).
R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals ( McGraw-Hill, New York, 1965 ).
S. F. Edwards, Proc. Phys. Soc. (London) 85, 613 (1965); Natl. Bur. Std. (U.S.) Misc. Publ. 273, 225 (1966).
R. M. White and P. W. Anderson, Phil. Mag. 25, 737 (1972).
T. Lukes (private communication).
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Freed, K.F. (1973). Properties of Localized States in Disordered Materials. In: Herman, F., McLean, A.D., Nesbet, R.K. (eds) Computational Methods for Large Molecules and Localized States in Solids. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2013-5_30
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DOI: https://doi.org/10.1007/978-1-4684-2013-5_30
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