Density of states and localization length in weakly disordered peierls chains

Abstract

The electron density of states and localization length are calculated for weakly disordered dimerized tight-binding chains. Pure bond disorder causes a singular density of states for small bond gaps, and a singular localization length for zero bond gap, whereas larger bond gaps are transformed into pseudogaps. A site gap for diatomic chains is preserved under bond disorder. Site disorder destroys any gap and does not create singularities in the density of states or localization length. These results are compared with those obtained from the continuum approximation with Gaussian disorder, which is not strictly justified for short-ranged disorder potentials. However, the continuum results are valid for weakly disordered chains provided the bond and site disorders in the chain correspond to bond-gap and combined site and site-gap disorders in the continuum model, respectively.