Statistical properties of a localization-delocalization transition induced by correlated disorder

TL;DR

This paper analytically investigates the statistical properties of resistance, conductance, and transmission in a 1D Anderson model with correlated disorder, revealing how correlation affects the localization-delocalization transition.

Contribution

It provides exact probability distributions and moments for these variables, demonstrating the impact of long-range correlations on the transition.

Findings

Resistance distribution remains unchanged across the transition.

Average resistance growth rate decreases near the critical Hurst exponent.

Distributions become size-independent in the metallic regime.

Abstract

The exact probability distributions of the resistance, the conductance and the transmission are calculated for the one-dimensional Anderson model with long-range correlated off-diagonal disorder at E=0. It is proved that despite of the Anderson transition in 3D, the functional form of the resistance (and its related variables) distribution function does not change when there exists a Metal-Insulator transition induced by correlation between disorders. Furthermore, we derive analytically all statistical moments of the resistance, the transmission and the Lyapunov Exponent. The growth rate of the average and typical resistance decreases when the Hurst exponent $H$ tends to its critical value ($H_{cr}=1/2$) from the insulating regime. In the metallic regime $H\geq1/2$, the distributions become independent of size. Therefore, the resistance and the transmission fluctuations do not diverge with system size in the thermodynamic limit.