Electron spectrum of the disordered binary linear chain

Abstract

Within the tight-binding model, numerical calculations of one-electron spectra of long disordered two-component linear chains are performed. The general structure of the spectrum is obtained. It is shown that in the region of a localized level, the spectrum has a clear hierarchy and self-similarity properties typical for fractals. The distribution of intervals between levels within the quasi-continuous spectrum is determined. It is shown that this distribution has a random exponential character without a dip in the region of small intervals. The change of the general form of the density of states in the quasi-continuous region of the spectrum was found. It is demonstrated that there appear sets of features, consisting of resonant minima and maxima, which condense at the band edges. With increasing the difference of energy levels of components, such features are gradually transformed into forbidden bands with widths depending linearly on the concentration. It is established that the positions of these features do not depend on the parameters of the components and on their concentration, but are determined by the self-energies of short chains of atoms of the main component. The general structure of the spectrum at commensurable concentrations of different atoms is also found.