The three-dimensional Anderson model of localization with binary random potential

TL;DR

This study investigates the three-dimensional two-band Anderson model of localization, analyzing metal-insulator transitions and phase diagrams, and finds results consistent with universal critical exponents observed in single-band models.

Contribution

It extends the Anderson localization framework to a two-band model and compares theoretical phase diagrams with experimental data on amorphous metallic alloys.

Findings

Identification of metal-insulator transition points

Phase diagrams of extended and localized states

Critical exponents consistent with universal value ~1.6

Abstract

We study the three-dimensional two-band Anderson model of localization and compare our results to experimental results for amorphous metallic alloys (AMA). Using the transfer-matrix method, we identify and characterize the metal-insulator transitions as functions of Fermi level position, band broadening due to disorder and concentration of alloy composition. The appropriate phase diagrams of regions of extended and localized electronic states are studied and qualitative agreement with AMA such as Ti-Ni and Ti-Cu metallic glasses is found. We estimate the critical exponents nu_W, nu_E and nu_x when either disorder W, energy E or concentration x is varied, respectively. All our results are compatible with the universal value nu ~ 1.6 obtained in the single-band Anderson model.