Electronic structure and stability of quasicrystals: Quasiperiodic dispersion relations and pseudogaps

We present calculations of the electronic structure for higher-order rational approximations to quasicrystals up to 12 380 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.