Delocalization and wave-packet dynamics in one-dimensional diluted Anderson models

TL;DR

This paper investigates how periodic dilution affects electron eigen-states and wave-packet dynamics in a one-dimensional Anderson model, revealing conditions for extended states and their impact on wave spreading.

Contribution

It introduces a detailed analysis of extended states in a diluted Anderson model using renormalization and transfer matrix methods, highlighting the role of symmetry in the diluting function.

Findings

Extended states depend on the symmetry of the diluting function

Density of states features are linked to the symmetry properties

Wave-packet spreading is sub-diffusive due to extended states

Abstract

We study the nature of one-electron eigen-states in a one-dimensional diluted Anderson model where every Anderson impurity is diluted by a periodic function $f(l)$ . Using renormalization group and transfer matrix techniques, we provide accurate estimates of the extended states which appear in this model, whose number depends on the symmetry of the diluting function $f(l)$. The density of states (DOS) for this model is also numerically obtained and its main features are related to the symmetries of the diluting function $f(l)$. Further, we show that the emergence of extended states promotes a sub-diffusive spread of an initially localized wave-packet.