Abstract
Electronic structure in three-dimensional quasicrystals is discussed both for simple tight-binding models of Penrose lattice and rationally approximated AlMn alloys. In three-dimensional Penrose lattice, there are several infinitelly degenerated states though they are not generic in quasi-periodicity. The electronic structure in the latter system is calculated by the LMTO-ASA method with the local density functional theory. The density of states in AlMn alloys consists of a set of spiky peaks, and the stability and the role of the vacant center of the Mackay icosahedron are discussed.
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