Global Partial Density of States: Statistics and Localization Length in Quasi-one Dimensional disordered systems

TL;DR

This paper analyzes the statistical distribution of the global partial density of states in quasi-one-dimensional disordered systems, establishing a link between disorder strength, localization length, and phase transition from metal to insulator.

Contribution

It introduces analytical methods for calculating Green functions in disordered Q1D models and relates the variance crossing of GPDOS to the localization length and disorder crossover.

Findings

Variance of GPDOS distributions crosses at the metal-insulator transition

Critical disorder value $w_c$ determines the localization length

Analytical expressions for Green functions in disordered models are derived

Abstract

We study the distributions functions for global partial density of states (GPDOS) in quasi-one-dimensional (Q1D) disordered wires as a function of disorder parameter from metal to insulator. We consider two different models for disordered Q1D wire: a set of two dimensional $\delta$ potentials with an arbitrary signs and strengths placed randomly, and a tight-binding Hamiltonian with several modes and on-site disorder. The Green functions (GF) for two models were calculated analytically and it was shown that the poles of GF can be presented as determinant of the rank $N\times N$, where $N$ is the number of scatters. We show that the variances of partial GPDOS in the metal to insulator crossover regime are crossing. The critical value of disorder $w_c$ where we have crossover can be used for calculation a localization length in Q1D systems.