Ja n 20 01 Electronic properties of ternary quasicrystals

The electronic 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 present in detail the existence of a special kind of critical states called marginal critical states in these QCs. By the use of the exact 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 existence makes a QC less conductive.