The electronic structure of a disordered network

Abstract

A study is made of the electronic structure of a network by adapting the free-electron model. In this model, a tight-binding structure is represented by free electrons constrained to move upon lines joining the bonded atoms of the network. A Boltzmann equation is then derived for the joint probability distribution of the wavefunction and its logarithmic derivative. In the Fokker-Planck approximation this equation reduces to that derived by Halperin for a one-dimensional random white-gaussian noise potential. This model strongly suggests that localization persists in a network long after percolation is possible.