Electronic properties of two-dimensional quasicrystals with near-neighbor interactions

Abstract

We study the electronic properties of the vertex model of two-dimensional Penrose lattices in the framework of the tight-binding Hamiltonian with near-neighbor interactions. For Penrose tiling, the first three shortest interatomic distances are the short diagonal of a thin rhombus, the edge of a rhombus, and the short diagonal of a fat rhombus. In this paper the effects of different ranges of interactions on the energy spectrum, degenerate confined state, and localization of electronic states are studied in detail. A similarity transformation is introduced to reduce the Hamiltonian, and the degeneracies of eigenstates are analytically determined. It is found that if first- and second-neighbor interactions are considered, three kinds of wave functions (extended, localized, and intermediate states) coexist. If third-neighbor interactions are included, the degeneracy of zero-energy eigenstates and localized electronic states completely disappear, and only extended and intermediate states are observed.