The conductivity a of a series of AlCuFe and AlPdMn quasicrystals and approximant phases can be written a(T) ==G4K'^5O{T).The cr4K term is very low, decreases with improvement of structural quality, and varies strongly with composition. Sa(T) is independent of the sample and increases anomalously with temperature up to 1000 K, with (TioooK/cr4K greater than 10. The results are interpreted by electronic hopping between structural entities separated by about 30 A. Within a band picture, this process would correspond to interband transitions. PACS numbers: 61.44.+p, 7I.30.+h, 72.15.Eb The AlCuFe, AlCuRu, and AlPdMn systenms make accessible very high structural quality quasicrystalline (QC) phases [1], and also allow us to get very close approximants in the case of AlCuFe [2]. For these QC phases, anomalous transport [3-6] and optical properties [7] were measured, with high resistivity values up to 30000 fuCl cm, close to a metal-insulator transition. A low density of states at the Fermi level, a small number of carriers, strong electron interactions, and a diamagnetic behavior also are indications of the proximity of this transition. The temperature and magnetic field dependences of conductivity at low temperature are well described [8] by quantum interference effects [9], which was at first surprising in view of the strong resistivities. Further, the increase of resistivity due to removing defects seems to be a common feature of these systems, and has not yet received satisfactory explanation. Moreover, we note that from published results in AlCuFe [5,10], the drastic changes of resistivity with concentration and structural quality are observed for samples having all the same density of states, within a few percent.On the theoretical side, except for the structural model of Phillips and Rabe [11], electronic properties have been studied by similarity with Hume-Rothery alloys [12]. In particular the existence of a pseudogap near the Fermi level due to diffraction by Bragg planes seems determined, and has been confirmed by ab initio calculations on approximant phases [13,14]. The scattering by d states was also shown to be important [15]. The band structure due to the strong interaction between the Fermi surface and the Brillouin zone is peculiar: In particular it was suggested that the properties could vary rapidly with the Fermi energy on a scale of a tenth of an eV [5,13] and that the band structure could be very sensitive to temperature via the variation of the Debye-Waller factor [16]. However, these theories do not fully take into account the QC character of the systems. Studies on tightbinding (ID and 2D) models [13,17] have shown that the eigenstates are critical. They are mainly localized around local environments with reappearances in similar arrangements of the structure, but the envelope of the wave function decreases like \/r". Sire and co-workers [18] have shown that the propagation of a wave packet in the 2D lattice is then neither ballistic nor diffusive. This bad propagation is consistent with f...
