Anomalous Anderson localization

We propose a generalized Anderson model and study numerically the localization phenomena in one dimension. In our model, not all the sites take on-site random site energy. The on-site energy epsilon(n) on the nth site is assigned as follows. If n + P - 1 = 0 (mod P). where P is a positive integer, epsilon(n) is assumed to be randomly distributed between - W/2 and W/2. On the other lattice sites. the site energy is fixed, say epsilon(n) = 0. The localization length xi defined as \t\(2) = e(-2L/xi), where t is the transmission coefficient. is calculated using the transfer matrix method. It is found that the single-electron states with wave vectors k = pi/P, 2 pi/P,...,(P - 1)pi/P are no longer localized as in the standard Anderson model. Compared with the smooth localization length spectrum of the Anderson model, there appear P - 1 sharp peaks periodically located at P - 1 values of wave vector on the localization length spectrum of the generalized Anderson model with parameter P. (C) 2000 Elsevier Science B.V. All rights reserved.