ELECTRON SPECTRUM AND WAVE-FUNCTIONS OF ICOSAHEDRAL QUASI-CRYSTALS

Electron spectra and wave functions of icosahedral quasicrystals have been investigated in the tight-binding approximation using the two-fra gment structural model (the Amman-MacKay network) with ''central'' dec oration. A quasicrystal has been considered as a limiting structure in a set of optimal cubic approximants with increasing lattice constants . The method of level statistics indicates that the energy spectrum of an icosahedral quasicrystal contains a singular (nonsmooth) component . The density of electron states has been calculated for the first fou r optimal cubic approximants of the icosahedral quasicrystal, and the respective Lebesgue measures of energy spectra of these approximants h ave been obtained. Unlike the case of a one-dimensional quasiperiodic structure, the energy spectrum of an icosahedral quasicrystal does not contain a hierarchical gap structure typical of the Canter set of mea sure zero in a one-dimensional quasicrystal. Localization of wave func tions in an icosahedral quasicrystal has been studied, and their ''cri tical'' behavior has been detected. The effect of disorder due to subs titutional impurities on electron properties of icosahedral quasicryst als has been investigated. This disorder makes the electron spectrum ' 'smoother'' and leads to a tendency to localization of wave functions. (C) 1998 American Institute of Physics. [S1063-7761(98)01803-4].