Electronic structure and conductivity in a model approximant of the icosahedral quasicrystal Al-Cu-Fe

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Abstract
We present the calculated self-consistent electronic structure and conductivity in a hypothetical model [1/1] approximant of the icosahedral phases Al-Cu-Fe. Two main features characterize the density of states. First, a well-pronounced pseudogap, commonly attributed to electron scattering by the lattice structure (the Hume-Rothery phenomenon), is found in the vicinity of the Fermi level. That pseudogap stabilizes the quasicrystalline structure but does not have a strong effect on the transport properties. Its width is about 0.035 Ry. Second, the density of states consists of a set of very fine spiked peaks. The width of each peak is about 0.001 Ry. The origin of this structure is the strong hybridization between atomic orbitals, due to the high local symmetry of quasicrystalline structure, and the variation in the height and width of the spikes is accentuated by the presence of the d states of the transition metals. Such a fine structure has little effect on the energetic stability but is crucial for the transport properties, both for their absolute values at 0 K and for their temperature dependence.