Journal article

Publication year: 2002

Journal: Physical Review B

Volume number: 66

Issue number: 3

ISSN: 2469-9950

eISSN: 2469-9969

Open access status: Green

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

Publisher: American Physical Society

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.

Harvard Citation style: Kantelhardt, J. and Bunde, A. (2002) Sublocalization, superlocalization, and violation of standard single-parameter scaling in the Anderson model, Physical Review B, 66(3), Article 035118. https://doi.org/10.1103/PhysRevB.66.035118

APA Citation style: Kantelhardt, J., & Bunde, A. (2002). Sublocalization, superlocalization, and violation of standard single-parameter scaling in the Anderson model. Physical Review B. 66(3), Article 035118. https://doi.org/10.1103/PhysRevB.66.035118