The electronic structure of a two-dimensional Penrose lattice is calculated within the tight-binding Hamiltonian. By means of the cluster Bethe-lattice method, we study the dependence of the local density of states (LDS) on the cluster size for two different geometries. We find that very large clusters are necessary to obtain the main features of the LDS. The method is applied to a single-component system and to an ordered binary alloy.

• Received 20 May 1987

DOI:https://doi.org/10.1103/PhysRevB.36.7342