Electronic structure and transport properties of decagonal Al-Cu-Co alloys

The electronic structure of the decagonal phase Al-Cu-Co and of related crystalline phases has been calculated using the self-consistent tight-binding linear-muffin-tin-orbital technique. The description of the atomic structure is based on different variants of the model proposed by Burkov [Phys. Rev. Lett. 67, 614 (1991); Phys. Rev. B 47, 12 325 (1993)]. The chemical decoration of these models is optimized on the basis of the electronic structure calculations. This is shown to be important for describing correctly the positions of the $d$ bands of Co and Cu. The observed shift of the Co $d$ band to relatively high binding energies is related to a particular type of order. We also show that the Cu and Co $d$-band shifts play a more important role for the stabilization of the decagonal phase than the formation of a pseudogap in the Al $\mathrm{sp}$ band. Satisfactory agreement with photoemission and x-ray emission and adsorbtion spectra is obtained for a special chemical order with preferred Co-Co coordination. The low-temperature conductivity is investigated within the Boltzmann formalism. A strong anisotropy $({\sigma }_p/{\sigma }_q\approx 50)$ of the conductivity in the model with idealized coordinates results from a pronounced anisotropy of the band structure. It is shown that thermal disorder breaks the coherence of the electronic eigenstates in the quasiperiodic plane and leads to an enhancement of the conductivity and a reduction of the anisotropy ratio.