Comparison of electronic properties of quasiperiodic and periodic lattices in two and three dimensions

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Abstract
The density of states (DOS) in two- and three-dimensional Penrose lattices with sites at vertices of rhombi were calculated in a one-orbital, tight-binding model. The DOS for the two-dimensional model showed much fine structure, indicative of the multitude of gaps thought to exist in quasicrystal spectra. The three-dimensional model showed a much smoother DOS, whose bumps were well matched by those for a periodic Penrose-derived lattice. In all cases, all states were quite delocalized. I conclude that the gross electronic properties of quasilattices are little influenced by their quasiperiodic nature, especially in three dimensions.