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arXiv · 1001.2568

Scattering and transport statistics at criticality

J. A. Mendez-Bermudez·Victor A. Gopar·Imre Varga
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Abstract

We study numerically scattering and transport statistical properties of the one-dimensional Anderson model at the metal-insulator transition described by the Power-law Banded Random Matrix (PBRM) model at criticality. Within a scattering approach to electronic transport, we concentrate on the case of a small number of single-channel attached leads. We observe a smooth transition from localized to delocalized behavior in the average scattering matrix elements, the conductance probability distribution, the variance of the conductance, and the shot noise power by varying $b$ (the effective bandwidth of the PBRM model) from small ($b\ll 1$) to large ($b>1$) values. We contrast our results with analytic random matrix theory predictions which are expected to be recovered in the limit $b\to \infty$. We also compare our results for the PBRM model with those for the three-dimensional (3D) Anderson model at criticality, finding that the PBRM model with $b \in [0.2,0.4]$ reproduces well the scattering and transport properties of the 3D Anderson model.

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J. A. Mendez-Bermudez, Victor A. Gopar, Imre Varga. 2010-10-30. Scattering and transport statistics at criticality. https://doi.org/10.1103/physrevb.82.125106

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