The influence of phasons, magnetic field, and substitutional chemical disorder on the electronic spectrum and wave functions of icosahedral quasicrystals is investigated by means of tight-binding approximation and level statistic method. The localization of the wave functions has been studied and we show that they are “critical.” Phasons smear the electronic spectrum and reduce localization of the critical wave functions. A magnetic field shifts the boundaries of the spectrum, smears it, and lifts its degeneracy. At small magnetic fields $(<\mathrm{}10\mathrm{}\hspace{0.5em}\mathrm{T})$ the wave functions also become less localized. 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.

• Received 21 April 2000

DOI:https://doi.org/10.1103/PhysRevB.62.14040