Universality and Scaling Law of Localization Length in One-Dimensional Anderson Localization

Abstract

The localization length ξ for four kinds of the 1D random potentials (a δ-function type and three Kronig-Penny types) has been calculated numerically as a function of the electron energy and two parameters specifying the randomness of the potential (the maximum strength of the potential and the average interval a between neighbouring impurities). A length parameter s is introduced which is related to the fluctuation of the potential. We have found that ξ/s depends only on ks for ka<1, where k is the electron wave number. The function relating ξ/s to ks is found to be universal for the four kinds of the potential considered here.