"Cluster-Bethe-lattice" method: Electronic density of states of amorphous and crystalline homopolar solids

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Abstract
A new method is developed to study the electronic density of states of infinite networks of atoms. The method involves treating part of the system exactly as a cluster and simulating the effects of the rest of the environment by connecting a Bethe lattice (Cayley tree) to the surface of the cluster. Calculations show that the local ringlike topologies of each atom are of primary importance in determining structure in the electronic density of states. The densities of states of the diamond, BC-8, and ST-12 structures are studied in detail using this method. These calculations are in excellent agreement with the exact results. Because of this, the method is used to obtain the density of states of the Polk and Connell random-network models. These models give the same radial distribution functions but exhibit striking differences in their densities of states which are interpreted in terms of topology.