One-dimensional tight-binding models with correlated diagonal and off-diagonal disorder

TL;DR

This paper investigates localization phenomena in one-dimensional tight-binding models with both diagonal and off-diagonal disorder, deriving analytical expressions and exploring effects of correlations and disorder strength.

Contribution

It provides a comprehensive analysis of localization in 1D models with correlated diagonal and off-diagonal disorder, including new analytical formulas for localization length.

Findings

Derived a general analytical expression for localization length with small disorder.

Compared approximate analytical estimates with numerical data for strong uncorrelated disorder.

Extended the random dimer model to include off-diagonal disorder with short-range correlations.

Abstract

We study localization properties of electronic states in one-dimensional lattices with nearest-neighbour interaction. Both the site energies and the hopping amplitudes are supposed to be of arbitrary form. A few cases are considered in details. We discuss first the case in which both the diagonal potential and the fluctuating part of the hopping amplitudes are small. In this case we derive a general analytical expression for the localization length, which depends on the pair correlators of the diagonal and off-diagonal matrix elements. The second case we investigate is that of strong uncorrelated disorder, for which approximate analytical estimates are given and compared with numerical data. Finally, we study the model with short-range correlations which constitutes an extension with off-diagonal disorder of the random dimer model.