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

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.