2 9 Ja n 20 01 Electronic properties of ternary quasicrystals

The one-electron properties of type II quasicrystals (QCs) in one dimension, namely ternary QCs which are generated by the cut-and-projection method, are analyzed. In particular, we show in detail the presence of a special kind of critical states called marginal critical states in these QCs. By the use of a real-space renormalization-group method, it is shown that the scaling properties of marginal critical states are characterized by stretched exponentials. These states are virtually localized, so that their presence makes a QC less conductive.