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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

This chapter is dedicated to electron transitions between localized states. After a description of the states with the help of localization radius and the general expression for the transition probability between two states — the hopping conductivity theory — is presented. The theory is based on Abrahams-Miller network of random resistances modelling an insulator and the percolation theory. Three types of hopping conductivity are presented: nearest-neighbour hopping, variable-range hopping with Coulomb gap at the Fermi level (Efros-Shklovskii law), and variable-range hopping without Coulomb gap (Mott law). They can be distinguished by the temperature dependence of the activated conductance.

Keywords:   Abrahams-Miller network, activated conductance, insulator, localized state, Mott law, nearest-neighbour hopping, percolation, variable-range hopping

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