Numerical Study of Electron Localization in Anderson Model for Disordered Systems: Spatial Extension of Wavefunction

Abstract

The electron localization is investigated numerically in the Anderson model of disordered two dimensional square lattices. The spatial behaviors of wavefunctions are examined for large systems composed of 10⁴ sites. Computations are carried out to see the Anderson transition at the band center and to see the localization near the mobility edge.
Sharp transition at the band center is recognized and the electron localization is clearly visualized. The spatial decay rate of localized wavefunction is evaluated in the localized region and its dependence on energy or the degree of disorder is determined.