Electrons in Quasicrystals

Quasicrystals, discovered by Dan Shechtman in 1982, provide unique materials with long-range aperiodic order. Their electronic structure and the electronic transport in quasicrystalline alloys has been a focus of research, motivated by trying to understand the formation and stability of quasicrystals, and their pronounced transport anomalies. This brief review on the motion of electrons concentrates on one perspective of this problem. It focuses on results obtained for simple models which capture the essence of the aperiodic order, rather than on results which attempt a realistic description of quasicrystalline alloys by employing empirical interaction potentials.