The effect of disorder on the electronic states in some model systems

A system is considered for which the diagonal matrix elements of the hamiltonian with respect to a basis of localized orbitals are fixed, while the nearest-neighbour off-diagonal elements are a random variable with a given continuous probability distribution. The spatial average of the system's Green's function is calculated by means of a two-site extension of the coherent potential approximation in which the self-energy has both diagonal and off-diagonal elements. The density of states and spectral density are calculated for various amounts of disorder, and the mean lifetimes of the quasi-particle Bloch states are derived from the latter.