THE ELECTRONIC-SPECTRUM OF A 3-DIMENSIONAL QUASI-CRYSTAL

The electronic spectrum of an icosahedral quasicrystal with a central- atom decoration of the Amman-Mackay network is investigated in the tig ht-binding approximation. The quasicrystal is described as a structura l limit of the optimal cubic approximants with increasing period. The electronic spectra for the first four optimal cubic approximants do no t contain the hierarchical gap structure which is typical for the Cant er set of the spectrum of a one-dimensional quasicrystal. At the same time, as the order of the approximant increases, the spectrum becomes singular throughout the entire energy scale. (C) 1998 American Institu te of Physics. [S0021-3640(98)00808-1]