Critical parameters for the one-dimensional systems with long-range correlated disorder

Abstract

We study the metal–insulator transition in a tight-binding one-dimensional (1D) model with long-range correlated disorder. In the case of diagonal disorder with site energy within [ − W / 2 , W / 2 ] and having a power-law spectral density S ( k ) ∝ k − α , we investigate the competition between the disorder and correlation. Using the transfer-matrix method and finite-size scaling analysis, we find out that there is a finite range of extended eigenstates for α > 2 , and the mobility edges are at ± E c = ± | 2 − W / 2 | . Furthermore, we find the critical exponent ν of localization length ( ξ ∼ | E − E c | − ν ) to be ν = 1 + 1.4 e 2 − α . Thus our results indicate that the disorder strength W determines the mobility edges and the degree of correlation α determines the critical exponents.