Sublocalization, superlocalization, and violation of standard single-parameter scaling in the Anderson model

Jan W. Kantelhardt and Armin Bunde
Phys. Rev. B 66, 035118 – Published 30 July 2002
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Abstract

We discuss the localization behavior of localized electronic wave functions in the one- and two-dimensional tight-binding Anderson model with diagonal disorder. We find that the distributions of the local wave-function amplitudes at fixed distances from the localization center are well approximated by log-normal fits which become exact at large distances. These fits are consistent with the standard single-parameter scaling theory for the Anderson model in d=1, but they suggest that a second parameter is required to describe the scaling behavior of the amplitude fluctuations in d=2. From the log-normal distributions we calculate analytically the decay of the mean wave functions. For short distances from the localization center we find stretched exponential localization (“sublocalization”) in both d=1 and d=2. In d=1, for large distances, the mean wave functions depend on the number of configurations N used in the averaging procedure and decay faster than exponentially (“superlocalization”), converging to simple exponential behavior only in the asymptotic limit. In d=2, in contrast, the localization length increases logarithmically with the distance from the localization center and sublocalization occurs also in the second regime. The N dependence of the mean wave functions is weak. The analytical result agrees remarkably well with the numerical calculations.

  • Received 19 January 2002

DOI:https://doi.org/10.1103/PhysRevB.66.035118

©2002 American Physical Society

Authors & Affiliations

Jan W. Kantelhardt1,2 and Armin Bunde1

  • 1Institut für Theoretische Physik III, Justus-Liebig-Universität Giessen, D-35392 Giessen, Germany
  • 2Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215

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Vol. 66, Iss. 3 — 15 July 2002

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