Inhomogeneous Fixed Point Ensembles Revisited

Abstract

The density of states of disordered systems in the Wigner-Dyson classes approaches some finite non-zero value at the mobility edge, whereas the density of states in systems of the chiral and Bogolubov-de Gennes classes shows a divergent or vanishing behavior in the band centre. Such types of behavior were classified as homogeneous and inhomogeneous fixed point ensembles within a real-space renormalization group approach. For the latter ensembles the scaling law $\mu =d\nu -1$ was derived for the power laws of the density of states $\rho \propto |E{|}^{\mu }$ and of the localization length $\xi \propto |E{|}^{-\nu }$. This prediction from 1976 is checked against explicit results obtained meanwhile.

Submitted to 'World Scientific' for the volume 'Fifty Years of Anderson Localization'. 12 pages

References in corpus (13)

• Classification of topological insulators and superconductors in three spatial dimensions
• Anderson Transitions
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• Electron transport in disordered graphene
• Effect of Disorder on Transport in Graphene
• Quantum criticality and minimal conductivity in graphene with long-range disorder
• On electron (anti)localization in graphene
• Particle-hole symmetric localization in two dimensions
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Cited by in corpus (1)

• Disorder-driven destruction of a non-Fermi liquid semimetal via renormalization group