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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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SCALING HYPOTHESIS

SCALING HYPOTHESIS

Chapter:
(p.102) 6 SCALING HYPOTHESIS
Source:
Electrons and Disorder in Solids
Author(s):

V.F. Gantmakher

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198567561.003.0006

This chapter presents phenomenological scaling theory of quantum metal-insulator transition of non-interacting electrons. It confirms the existence of the transition in 3D-system; and elucidates the relation between the correlation length and the conductance, the shape of the critical region, and the temperature dependence of the conductance inside it (T1/3-law). For 2D-systems, it predicts that there is no transition, only a weak-to-strong localization crossover.

Keywords:   conductance, correlation length, critical region, quantum phase transition, T1/3-law, weak-to-strong localization crossover

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