Understanding delocalization in the Continuous Random Dimer model

TL;DR

This paper explains the emergence of extended states in the Continuous Random Dimer model by analyzing transmission properties and their independence from the number of host sites, providing new insights into correlated disorder effects.

Contribution

It offers an exact explanation for bands of extended states in the model and explores their dependence on concentration and potential generalizations.

Findings

Transmission coefficient at resonant energy is independent of host site number.

Bands of extended states exist for every realization of the model.

Bandwidths depend on the concentration of dimers.

Abstract

We propose an explanation of the bands of extended states appearing in random one dimensional models with correlated disorder, focusing on the Continuous Random Dimer model [A.\ S\'{a}nchez, E.\ Maci\'a, and F.\ Dom\'\i nguez-Adame, Phys.\ Rev.\ B {\bf 49}, 147 (1994)]. We show exactly that the transmission coefficient at the resonant energy is independent of the number of host sites between two consecutive dimers. This allows us to understand why are there bands of extended states for every realization of the model as well as the dependence of the bandwidths on the concentration. We carry out a perturbative calculation that sheds more light on the above results. In the conclusion we discuss generalizations of our results to other models and possible applications which arise from our new insight of this problem.