Inhomogeneous Electronic Localization in Icosahedral Quasicrystals

Abstract

The lattice structure of i-phases opened in 1984 by Shechtman [1] is based on an icosahedron a polyhedron having symmetry of the fth order, which cannot serve as a unit cell of a periodic crystal. It was evident from the very start that in the course of formation of thermodynamically stable i-phases, a minimum of free energy is possible to achieve only owing to a gain in the kinetic energy of free carriers. To this end, two mechanisms were proposed: structure-induced pseudogap in the density of states of the conduction band, which is traceable to the presence of a long aperiodic order, and electron localization, connected with either short-range order or a peculiar type of disorder. The hypothesis of pseudogap has experimentally been shown to agree well with the estimates of electronic parameters of i-phases in the limit of low temperatures. These phases possess an anomalously low (≈ 10 cm−3) concentration of conductive electrons and, consequently, anomalously low values of the metal-like conductivity, Pauli susceptibility and electronic heat capacity. The experimentally observed powerful thermal e ects, namely, thermally induced charge carriers, conductivity (negative TCR), and paramagnetism, were noticed long ago to badly agree with the hypothesis of pseudogap. The width of a pseudogap (≈ 1 eV) is too large to be the source of these e ects, which meanwhile may well originate from the localized electron states with characteristic energies of excitation on the order of ≈ 10÷ 50 meV. Yet, no direct experimental evidence of such states was obtained either by high-resolution photoelectron spectroscopy or via analysis of transport properties [2]. Finally, the hypothesis of structure-induced pseudogap seemed to be a single option. In the next years, however, several experimental observations served to revive the idea of localized states as an essential factor of the thermodynamic stability of aperiodic structures.