The theory of electronic structure of disordered networks

Abstract

A study is made of the electronic structure of a network with arbitrary disorder using free-electron and tight-binding models. In the free-electron model, propagator techniques are used to describe the probability distribution of the wavefunction's logarithmic derivative along an arbitrary path in the network. The tight-binding model is developed by analogy to the free-electron model. In both models coupled self-consistent integral equations are found to describe steady-state probability distributions when the effects of closed loops in the network are ignored. A discussion of the equivalence of the two models is given.