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This article is not a review in the conventional sense. Rather, it is a monographic study of the implications of detection in Al-Cu-Fe quasicrystals of the electronic heat capacity contributions associated with the two-level electron excitations. Our aim was to reveal correlations between these contributions, on the one hand, and specific features of electron transport, magnetic susceptibility, Hall-effect, tunnelling and optical spectra, on the other hand. It is shown that the full range of these features can be understood in the framework of the unified conceptual scheme based on two-level electron excitations.

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This study was supported by the Russian Foundation for Basic Research (project no. 10-02-00602-a).The heat capacity of icosahedral quasicrystals Al63Cu25Fe12 and Al62Cu25.5Fe12.5 has been studied at high temperatures up to 1700 K, which is by almost 400 K higher than the melting point of the material. It has been shown that the melt exhibits an excess heat capacity with respect to that determined by the Dulong-Petit law and that is a direct extension of the excess heat capacity of the solid state. It has been concluded that the excess heat capacity is related, as a whole, to the short-range order in the quasicrystal structure. This circumstance allows the identification of the orbital hybridization as the most probable mechanism of formation of the pseudogap in the electronic structure of the quasicrystals