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Conductor-Insulator Quantum Phase Transitions$
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Vladimir Dobrosavljevic, Nandini Trivedi, and James M. Valles, Jr.

Print publication date: 2012

Print ISBN-13: 9780199592593

Published to Oxford Scholarship Online: September 2012

DOI: 10.1093/acprof:oso/9780199592593.001.0001

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Anderson Localization

Anderson Localization

(p.86) 3 Anderson Localization
Conductor-Insulator Quantum Phase Transitions

Keith Slevin

Tomi Ohtsuki

Oxford University Press

This chapter reviews briefly the theory of the Anderson localisation of electrons. In disordered materials at low temperatures, quantum interference may lead to the suppression of diffusion. If this occurs, the material becomes an insulator at zero temperature and zero frequency even though the density of states at the Fermi level is finite. This transition from metal to insulator is called the Anderson transition. Anderson localisation occurs particularly easily in low dimensional systems. After describing very briefly some elements of the theory of Anderson localisation, the chapter focuses on numerical simulations of Anderson localisation using the transfer matrix method, and the analysis and interpretation of the results using finite size scaling. After mentioning other approaches such as diagonalisation, this chapter closes by describing some of the experimental signatures of Anderson localisation.

Keywords:   Anderson localisation, Anderson transition, quantum interference, weak localisation, scaling theory, transfer matrix, Lyapunov exponents, finite size scaling

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