One-electron states in materials with structural disorder

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Abstract
A theoretical study of the one-electron states in materials composed of a single atomic species but structurally disordered is developed. The disorder is characterised probabilistically through the joint probability density of finding a given configuration; the 'uniform' case is used in calculations. The influence of system dimensionality, atomic scattering strength and density are examined as they affect the density of electron states per unit volume and localisation as a function of energy. The calculations are variational and designed to study trends. Band tails are obtained numerically for the case of an electron-atom interaction which is fully rotationally symmetric, short ranged and repulsive. Furthermore, the calculated results are interpreted as implying that all one-dimensional states are localised, in two dimensions the implication is of localised and delocalised states while in three dimensions localised and delocalised states are deduced but it is also suggested than an intermediate 'percolative' regime may exist. The energies separating the various localisation regimes are estimated and vary continuously with coupling constant.