Quantum diffusion of electrons in quasiperiodic and periodic approximant lattices in the rare earth-cadmium system

Icosahedral quasicrystals are characterised by the absence of a distinct Drude peak in their low-frequency optical conductivity and the same is true of their crystalline approximants. We have measured the optical conductivity of i-GdCd7.98, an icosahedral quasicrystal, and two approximants, GdCd6 and YCd6. We find that there is a significant difference in the optical properties of these compounds. The approximants have a zero frequency peak, characteristic of a metal, whereas the quasicrystal has a striking minimum. This is the first example where the transport properties of a quasicrystal and its approximant differ in such a fundamental way. Using a generalised Drude model introduced by Mayou, we find that our data are well described by this model. It implies that the quantum diffusion of electron wave packets through the periodic and quasiperiodic lattices is responsible for these dramatic differences: in the approximants, the transport is superdiffusive, whereas the quasicrystals show subdiffusive motion of the electrons.