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

The density of states in two- and three-dimensional Penrose lattices with sites at vertices of rhombs were calculated in a one-orbital, tight-binding model. The DOS for the 2D model showed much fine structure, indicative of the multitude of gaps thought to exist in quasicrystal spectra. The 3D 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.