Localization Properties of the Periodic Random Anderson Model

TL;DR

This paper investigates how periodicity influences localization and extended states in a one-dimensional Anderson model with mixed random and non-random potentials, revealing resonance energies where localization behavior changes.

Contribution

It introduces a model with simple periodicity in disordered systems and analyzes the emergence of resonance energies affecting localization properties.

Findings

Resonance energies are linked to the lattice constant of the non-random lattice.

Extended states occur at resonance energies when a random site is surrounded by non-random sites.

Localization length increases at resonance energies, but states remain localized in other cases.

Abstract

We consider diagonal disordered one-dimensional Anderson models with an underlying periodicity. We assume the simplest periodicity, i.e., we have essentially two lattices, one that is composed of the random potentials and the other of non-random potentials. Due to the periodicity special resonance energies appear, which are related to the lattice constant of the non-random lattice. Further on two different types of behaviors are observed at the resonance energies. When a random site is surrounded by non-random sites, this model exhibits extended states at the resonance energies, whereas otherwise all states are localized with, however, an increase of the localization length at these resonance energies. We study these resonance energies and evaluate the localization length and the density of states around these energies.