Anderson Transitions: Criticality, Symmetries, and Topologies

Abstract

The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed. We focus on the character of criticality as well as on underlying symmetries and topologies that are crucial for understanding phase diagrams and the critical behavior.

36 pages. Published in "50 Years of Anderson Localization", ed. by E. Abrahams (World Scientific, 2010); reprinted in IJMPB

References in corpus (22)

• The electronic properties of graphene
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Weak localisation magnetoresistance and valley symmetry in graphene
• Localization of ultrasound in a three-dimensional elastic network
• Electron transport in disordered graphene
• Effect of Disorder on Transport in Graphene
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• Exact relations between multifractal exponents at the Anderson transition
• Low energy theory of disordered graphene
• On electron (anti)localization in graphene
• Landauer conductance and twisted boundary conditions for Dirac fermions in two space dimensions
• Electron transport in disordered Luttinger liquid
• Conductivity of disordered graphene at half filling
• Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect
• Density of quasiparticle states for a two-dimensional disordered system: Metallic, insulating, and critical behavior in the class D thermal quantum Hall effect
• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
• Wave function statistics at the symplectic 2D Anderson transition: bulk properties
• Boundary multifractality in critical 1D systems with long-range hopping

Cited by in corpus (17)

• Coulomb interaction in graphene: Relaxation rates and transport
• Wave function multifractality and dephasing at metal-insulator and quantum Hall transitions
• Majorana fermions on a disordered triangular lattice
• Coherent forward scattering as a signature of Anderson metal-insulator transitions
• Graphene with vacancies: supernumerary zero modes
• Disorder and interaction in chiral chains: Majoranas vs complex fermions
• Analytical and numerical study of uncorrelated disorder on a honeycomb lattice
• Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes
• Probing the topological Anderson transition with quantum walks
• Sinai Diffusion at Quasi-1D Topological Phase Transitions
• Edge states and topological properties of electrons on the bismuth on silicon surface with giant spin-orbit coupling
• Impurities and electronic localization in graphene bilayers
• Statistics of Conductances and Subleading Corrections to Scaling near the Integer Quantum Hall Plateau Transition
• Partial preservation of chiral symmetry and colossal magnetoresistance in adatom doped graphene
• Topological phase diagram of the disordered 2XY model in presence of generalized Dzyaloshinskii-Moriya Interaction
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Enhanced spin Hall effect in strong magnetic disorder