ELECTRONIC-STRUCTURE AND STABILITY OF QUASI-CRYSTALS - QUASI-PERIODIC DISPERSION-RELATIONS AND PSEUDOGAPS

We present calculations of the electronic structure for higher-order rational approximations to quasicrystals with up to 12380 atoms in the unit cell, based on a tight-binding linear-muffin-tin-orbital technique. The dispersion relations of the electronic states of quasicrystals are related to those of quasiperiodic free-electron model. Highly degenerate free-electron states are found close to the Fermi level. Their wave vectors define the analog of a Brillouin zone; the "Brillouin-zone"-Fermi-sphere interaction leads to the formation of a pseudogap at the Fermi level.