Limited conductivity in an octagonal quasicrystal

Abstract

Conductivity of an s-band model on the octagonal tiling is studied. Using perturbation theory it is shown that there is only one channel available for electronic transport, when the kinetic term in the Hamiltonian is small. This feature is independent of the size of the approximant and reveals a microscopic mechanism that is capable of severely limiting conduction processes in a quasicrystal. Numerical evidence indicates that the same result is valid even in case of realistic kinetic energies at some values of the Fermi energy.