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Electrons and Disorder in Solids$
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V. F. Gantmakher

Print publication date: 2005

Print ISBN-13: 9780198567561

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198567561.001.0001

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Electrons and Disorder in Solids

V.F. Gantmakher

Oxford University Press

In this chapter, various data on localization in one and three dimensional (1D and 3D) systems are gathered into a unified pattern. Using the Landauer formula, it is shown that random potential always localizes electrons in 1D, although the requirements to the randomness are rather severe; correlations can break localization. All the models of disordered 3D, those named after Anderson, Mott, and that of structural disorder, point to a metal-insulator transition at critical level of disorder. The Anderson transition happens in the system of noninteracting electrons, the driving force of the Mott transition is electron-electron interaction. However, they look very much alike experimentally and have the same numerical criterion — the ratio of localization radius to mean distance between electrons. Another important question remains unsolved: whether the transition is continuous, i.e., whether the conductivity goes to zero smoothly or jumps to zero from the minimum metal conductivity value.

Keywords:   Anderson transition, continuous transition, Landauer formula, metal-insulator transition, minimum metal conductivity, Mott transition, one-dimensional systems, phase transition

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