Journal
REVIEWS OF MODERN PHYSICS
Volume 80, Issue 4, Pages 1355-1417Publisher
AMER PHYSICAL SOC
DOI: 10.1103/RevModPhys.80.1355
Keywords
Anderson model; Dirac equation; fractals; metal-insulator transition; quantum Hall effect; reviews; wave functions
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Funding
- Center for Functional Nanostructures of the Deutsche Forschungsgemeinschaft
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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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