Magnetoconductivity of quasicrystals in the insulating regime

Magnetoconductivities of icosahedral ${\mathrm{Al}}_{70.5}$ ${\mathrm{Pd}}_{21}$ ${\mathrm{Re}}_{8.5}$ alloys whose zero-field conductivity σ(T)→0 as T→0 K [σ∼0.1 (Ω cm${)}^{\mathrm{-}1}$ at 0.45 K] have been measured. At low temperature and low field, both positive and negative contributions to magnetoconductivity are prominently present. The magnetoconductivity trend is distinctly different from those seen in disordered metals and insulators. The observed features are interpreted in light of anomalous diffusion of slowly decaying electron wave functions in insulating quasicrystals.