Fractal Character of Eigenstates in Disordered Systems

C. M. Soukoulis and E. N. Economou
Phys. Rev. Lett. 52, 565 – Published 13 February 1984
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Abstract

Electronic eigenfunctions are studied on the tight-binding model of disordered systems at dimensionalities d=1,2,3. It is found that the eigenfunctions have a self-similar (fractal) behavior up to length scales roughly equal to the localization length. For d=3, above the mobility edge, the fractal character persists up to length scales about equal to the correlation length ξ. The dependence of the fractal dimensionality D on disorder W is presented. The fractal character of the wave function is suggested as a new method for finding mobility edges.

  • Received 21 November 1983

DOI:https://doi.org/10.1103/PhysRevLett.52.565

©1984 American Physical Society

Authors & Affiliations

C. M. Soukoulis and E. N. Economou*

  • Corporate Research Science Laboratory, Exxon Research and Engineering Co., Annandale, New Jersey 08801

  • *Permanent address: Department of Physics, University of Crete, and Research Center of Crete, Heraklio, Crete, Greece.

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Issue

Vol. 52, Iss. 7 — 13 February 1984

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