Band structure and localization of electronic states in a fivefold symmetric quasicrystal model

A fivefold symmetric quasilattice is constructed by the self-similar transformation on Gummelt two-color decagon and a single electron tight-binding model is proposed. We reduce the Hamiltonian to five identical subsets and analyze the spectral properties. By numerical calculation, three kinds of wave functions are found, which correspond to extended, localized and intermediate states, respectively.