Influence of phason flips, magnetic field, and chemical disorder on the localization of electronic states in an icosahedral quasicrystal

The influence of phasons, magnetic held, and substitutional chemical disord er on the electronic spectrum and wave functions of icosahedral quasicrysta ls is investigated by means of tight-binding approximation and level statis tic method. The localization of the wave functions has been studied and we show that they are "critical." Phasons smear the electronic spectrum and re duce localization of the critical wave functions. A magnetic held shifts th e boundaries of the spectrum, smears it, and lifts its degeneracy. At small magnetic fields (< 10 T) the wave functions also become less localized. Th e small degree of chemical substitutional disorder delocalizes the wave fun ctions, but at greater degree the disorder leads to the Anderson type local ization. The results show that the localization of electronic states in an ideal quasicrystal exists due to their coherent interference at the Fermi l evel which is caused by the specific symmetry and aperiodic long-range orde r.