Evidence for a marginally conducting state in AlCuFe and AlPdMn quasicrystals

In a quasiperiodic system without defects the dissipative part of the conductivity is expected to vary as Re σ0(ω)∝ω1−2β at low frequency ω (0<β<1). β is the diffusion exponent in the perfect structure such that the spreading of wavepackets is L(t)∝tβ at large time t. Under certain conditions disorder induces a current relaxation in a time τ and we express the conductivity, with defects, in terms of τ and of the conductivity without defects, Re σ0(ω). For AlCuFe and AlPdMn quasicrystals a coherent interpretation of the conduction properties is obtained. We extract the values of τ and get β≃0. It means that quantum diffusion is slow or marginal in the perfect systems.