Localization-delocalization transition in one-dimensional system with long-range correlated diagonal disorder

Abstract

We show that the electronic states in a one-dimensional (1D) Anderson model of diagonal disorder with long-range correlation proposed by de Moura and Lyra exhibit localization-delocalization phase transition in varying the energy of electrons. Using transfer matrix method, we calculate the average resistivity \(\) and investigate how it changes with the size of the system N. For given value of α (> 2) we find critical energies Ec1 and Ec2 such that the resistivity decreases with N as a power law \(\) ∝ N- γ for electron energies within the range of [Ec1, Ec2], and exponentially grows with N outside this range. Such behaviors persist in approaching the transition points and the exponent γ is in the range from 0.92 to 0.96. The origin of the delocalization in this 1D model is discussed.