Comportamento de escala nas vizinhanças da transição de Anderson de sistemas com desordem correlacionada

Abstract

The Anderson localization theory is the most important formalism to understand noninteracting electrons moving in disordered systems. The scaling theory predicts in low dimensional systems the absence of a localization-delocalization transition for any degree of uncorrelated disorder. However, in the two-dimensional model, distinct dynamical regimes can be observed according to the disorder intensity. More recently, the Anderson model with correlated disorder have been shown to break up the scaling theory predictions. It was numerically and experimentally proved that long range correlations can be induce a metal-insulator transition with mobility edges separating localized from extended states. In this work, we contribute along these lines. We study the nature of one-electron states in one-dimensional and two-dimensional Anderson models with long-range correlations in the disorder distribution. The long-range correlations was introduced by using a discrete Fourier method which produces a distribution of the energies in the sites with spectral density S(k)α 1/kα. In one-dimension, we study the static and dynamic case calculating the participation number function ξ and the wave-packet mean square displacement. In both the cases, we identify distinct regimes depending on the correlation degree α. For the 2d model, we investigate the behavior of the relative fluctuation of the participation number that is used to monitor the critical point. Our numerical data suggest that the localization length exponent governs the data collapse of the relative fluctuations as a function of the energy η(E). We still obtained the phase diagram that shows regions of extended, critical and localized states.