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Anderson transitions

Ferdinand Evers and Alexander D. Mirlin

Ferdinand Evers

  • Institut für Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany

Alexander D. Mirlin

  • Institut für Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany; Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany; and Petersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia

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Rev. Mod. Phys. 80, 1355 – Published 17 October, 2008

DOI: https://doi.org/10.1103/RevModPhys.80.1355

Abstract

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. The term “Anderson transition” is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states. The emphasis is put on recent developments, which include multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians. Analytical approaches are complemented by advanced numerical simulations.

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Rev. Mod. Phys. 80, 1355– Published 17 October, 2008

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