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

J. Ruiz·E. Jódar·V. Gasparian
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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 $δ$ 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.

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J. Ruiz, E. Jódar, V. Gasparian. 2006-10-23. Global Partial Density of States: Statistics and Localization Length in Quasi-one Dimensional disordered systems. https://doi.org/10.1103/physrevb.75.235123

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