Electronic properties of a two-dimensional quasicrystal model based on octagonal covering structure

A two-dimensional quasilattice with eight-fold rotational symmetry is formed by covering of identical octagonal clusters; a tight-binding Hamiltonian is presented based on it. We study the electronic properties by analyzing the energy spectrum and wave functions. The main energy levels are obtained and the gaps are labeled. The wave functions with different localization features are found and the self-similar distribution is shown.