CLUSTERS AND LOCALIZATION OF ELECTRONS IN QUASI-CRYSTALS

We analyze the relationship between the tendency to electron localizat ion, which is observed in many quasicrystals and approximants, and the local atomic order. Starting from the structural models, we consider atomic clusters that are embedded in a metallic medium, and we study t heir scattering properties within the multiple-scattering formalism. W e show that these local environments can lead to virtual bound states for electrons, i.e., resonances of the wave function in clusters of di fferent length scale. That is consistent with the tendency to localiza tion shown by transport measurements or band-structure calculations. I n agreement with the Hume-Rothery picture of quasicrystals, this tende ncy to localization has a small effect on the total energy.