Determination of spatially hybridized charge distribution and its effect on electron transport in the Al-Cu-Ru-Si 1/1-approximant - Theoretical basis for the Hume-Rothery rule

The origin of the pseudogap across the Fermi level was investigated by analyzing the electronic structure calculated in the framework of the LMTO-ASA method for the RT-type Al-Mg-Zn and MI-type Al-Cu-Ru-Si 1/1-approximants. The pseudogap in the former is proved to originate from the interaction of electronic states with the Brillouin zone planes associated with reciprocal lattice vectors matching with the Fermi sphere in the extended zone scheme, in the latter, the Fermi surface-Brillouin zone interaction coupled with the hybridization effect between the Al-3p and transition metal d-states produces a deep pseudogap at the Fermi level. The real-space charge distribution for electrons at the Fermi level is calculated for the Al-Cu-Ru-Si 1/1-approximant. The charge distribution thus obtained could explain not only the possession of a large resistivity of this approximant but also evidenced that the icosahedral clusters play a key role in reducing the electronic energy in favor of quasicrystalline and approximant phases.