A new technique to calculate the electronic structure of two-dimensional quasicrystals

Abstract The electronic structure of a two-dimensional Penrose lattice has been investigated in the tight-binding limit using a new theoretical approach based on multiple-scattering theory. We have studied in particular the vertex model of the lattice and calculated the density and integrated density of electronic states. The method used is effectively for an infinite structure and leads to no distortions from edge effects or periodic continuation. The vertex model, which is based on fat and thin rhombi, has three nearest interatomic distances: the short diagonal of a thin rhombus, the edge of a rhombus, and the short diagonal of a fat rhombus. We have investigated the effect of interactions involving these various distances in the density of states, giving results which are similar to those using other methods. It is stressed that the method is capable of considerable generalization.