Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one dimensionality

TL;DR

This paper demonstrates how specific off-diagonal disorder configurations in tight-binding chains can create absolutely continuous energy bands with extended states, revealing a novel sensitivity of localization phenomena to system parameters.

Contribution

It provides an exact analytical framework for generating extended states in disordered chains through tailored off-diagonal correlations, extending understanding beyond traditional Anderson localization models.

Findings

Absolutely continuous energy bands can be engineered in disordered chains.

Extended eigenstates are achieved through specific ratios of hopping integrals.

The model reveals a sensitive dependence of localization on system parameters.

Abstract

It is shown that, an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side coupled to a suitable subset of sites in the backbone, and if the nearest neighbor hopping integrals, in the backbone and in the side coupled cluster bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone, and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or, a singular continuous one for deterministically disordered lattices) with exponentially (or power law ) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization [P. W. Anderson, Phys. Rev. 109, 1492 (1958)], pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) [Dunlap et al., Phys. Rev. Lett. 65, 88 (1990)].