Explanation of delocalization in the continuous random-dimer model

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. Sánchez, E. Maciá, and F. Domínguez-Adame, Phys. Rev. B 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.

Extended states and dynamical localization in semiconductor superlattices

“…7,8 In Ref. 9, it was shown that delocalized electronic states arise in spite of the inherent disorder due to resonant phenomena taking place at dimer quantum-wells of the same thickness. These resonances lead to a transmission coefficient of different segments forming the SL close to unity, no matter what the length of the segment is.…”

Delocalization in continuous disordered systems

“…Recently the interest has increased substantially in order to find theoretical evidence for the breaking of Anderson localization by internal correlations in disordered systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] . For instance, in ref.…”

“…8 . Using the inter-relation between a disordered Kronnig-Penney system and the dimer model (Poincaré map) [9][10][11][12] an infinite set of such delocalized states exist. The generalization of the dimer model to the N-mer case was considered, for instance, in refs.…”

Extended states in a one-dimensional generalized dimer model

“…Note that the m ij matrix elements contain all the physical information about the system that we are considering as a sample. If we consider a piece of a chain with N sites of equal energy ǫ 0 embedded in a host lattice of site energy 0, sometimes referred in the literature as an N -mer, equation (15) becomes…”