Electronic spectrum and localization of electronic states in three-dimensional quasicrystals

The influence of phasons, magnetic field, and substitutional atomic disorder on the electronic spectrum and wave functions of icosahedral quasicrystals is investigated in a tight-binding approximation and level statistic (LS) method. The localization of the wave functions has been studied and their “critical” behavior has been detected. Phasons smooth the electronic spectrum and produce a greater delocalization of the critical wave functions. A magnetic field shifts the boundaries of the spectrum, smoothes the spectrum, lifts the degeneracy and also delocalizes the wave functions. The small degree of chemical substitutional disorder delocalizes the wave functions, but at greater degree the disorder leads to the Anderson type localization. The results show that the localization of electronic states in an ideal quasicrystal exists due to their coherent interference at the Fermi level which is caused by the specific symmetry and aperiodic long-range order.