Perturbation-theoretic studies of the anomalous electronic structure and transport properties of quasicrystals.

Abstract

The question of whether scattering by the almost periodic lattice potentials of recently discovered metallic quasicrystals is able to explain the observed short mean free paths (about 1 A\r{}) in these materials is discussed. It is shown that scattering by a three-dimensional almost periodic potential cannot account for such resistivities, but a model which includes structural defects in the three-dimensional Penrose tiling and large scattering of electrons due to s-d resonant scattering can account for the experimental observations. It is also shown in perturbation theory that if a dc current is set up in the crystal (e.g., by an electric field which is switched on and then quickly switched off), the current will decay slowly to zero with an anomalous logarithmic dependence on time for one- and three-dimensional quasicrystals. This is most likely due to the extremely long-wavelength Fourier components possessed by the quasiperiodic potential. The same phenomena are not found for two-dimensional quasicrystals.