Spectral limits in disordered systems

Abstract

The spectral limits of a disordered system are given in a tight binding model, using general criteria for the localization of eigenvalues of matrices. The width of the electronic density of states is directly related to the short range order of the system and various cases of disorder are discussed. The shape of the density of states near the band edges is studied, using an expansion in its moments. Special attention is paid to some amorphous materials whose structure can be described by an ideal random covalent network. Sharp band edges are found in agreement with recent experiments on amorphous Si and Ge.