Electronic properties of icosahedral systems: Energy spectrum, wave functions, and dc conductance

The electronic properties of three-dimensional quasicrystals in the icosahedral Danzer model are calculated by using tight-binding Hamiltonians for a vertex and a center model of a finite system. Results are compared with calculations on the two-dimensional Penrose lattice. The energy spectrum, wave functions, and Fermi-energy dependence of the dc conductance at zero temperature are analyzed. Different types of states are found. Most of the states are not degenerate or weakly degenerate and show low conductance. Some very highly degerate states have zero conductance suggesting that they are strongly localized. By integrating the zero condunctance over the Fermi distribution we show that very small differences in the Fermi energy of the system can cause a completely different temperature dependence of the conductance.