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 but they suggest that a second parameter is required to describe the scaling behavior of the amplitude fluctuations in 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 and In 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 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