Anderson Transitions

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.

63 pages, 39 figures, submitted to Rev. Mod. Phys

References in corpus (11)

• Electric Field Effect in Atomically Thin Carbon Films
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological delocalization of two-dimensional massless Dirac fermions
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions
• $f(\alpha )$ Multifractal spectrum at strong and weak disorder
• Dynamical scaling of the quantum Hall plateau transition
• Multifractality of Hamiltonians with power-law transfer terms
• Long range disorder and Anderson transition in systems with chiral symmetry
• Two-level correlation function of critical random-matrix ensembles

Cited by in corpus (1)

• Corner Multifractality for Reflex Angles and Conformal Invariance at 2D Anderson Metal-Insulator Transition with Spin-Orbit Scattering