Spectral characteristics of the impurity band in the structural disorder model

Abstract

The density and character of the quantum states in the impurity band arising from broadening of the local impurity level are studied. When the impurity concentration is small, the energy levels and states in the impurity band admit an apparent geometric systematics in the main approximation. In this systematics, the wave functions are localized at one or two centers, though the energy levels depend on the positions of orther centers. The density of states and the space correlators calculated in the main approximation are of universal nature, i.e., are represented in a certain scale as universal functions independent of the concentration. In the immediate vicinity of the local level, where in terms of the geometric systematics the density of states has a gap, different states become significant, which collectivize a larger number of centers. They fill the gap, the filling degree essentially depending on the impurity concentration. The general structure of the impurity band spectrum is discussed.