Electronic properties of quasicrystals an experimental review

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Abstract
The electronic properties of a large number of icosahedral-crystal systems have been studied experimentally. These systems include alloys of the simple metals and those that contain transition metals. Some of the icosahedral phases (i-phases) are thermally stable while others are metastable; and their degree of structural order varies within each of the stability classes. The importance of sample quality to the exposition of intrinsic properties is emphasized, particularly for systems with high resistivities. As a result, experiments on single-phase samples from the diversity of systems studied have shed light on the physics of quasicrystalline alloys. Comparison made with the approximant and amorphous phases have provided important insights to the understanding of quasicrystallinity, randomness, and atomic-potential effects on electronic properties. Reduction in the electronic density of states (DOS) at the Fermi level relative to the free-electronic value is observed in the stable i-phase systems studied to date. Examples are the GaMgZn, AlCuLi, AlCuFe, and AlCuRu systems. Although the simple-metal i-alloys such as AlCu (Mg, Li) and (Al, Ga)MgZn within their metastable phase fields are found to have nearly free-electron DOS, the anomalies in their transport behaviour and compositional dependence of electronic properties have revealed the important role of the Fermi-surface-Jones-zone boundaries (FS-JZB) interaction in these measurements. Also, central to the FS-JZB interaction criterion of phase stability is the existence of a pseudogap in the DOS which is most evident in the stable i-phases. Unusual transport behaviour has been reported for the structurally ordered i-phases that contain transition metals. These materials exhibit semi-metallic transport behaviour characterized by a high resistivity (∼4000–30000 μΩcm), a large resistivity ratio ρ(4·2 K)/ρ(300 K) ranging from 1·5 to 4 as well as a low carrier concentration of 10−2 to 10−3 electron per atom. Adding to the anomalous electron transport are the strong temperature dependences of the Hall coefficient and thermopower leading to a change of sign. Further understanding of the ordered i-phases has been advanced through studies of amorphous phases and crystalline counterparts of i-phases known as rational approximants. Based on these studies, the key findings are reported: (i) even for simple-metal systems in the weak scattering regime, differences in the electronic properties between the structural phases begin to emerge as the FS-JZB interaction increases in strength, (ii) semi-metallic conductivity and other anomalous transport properties are also observed in the approximant-crystals that contain transition metals (e.g. AlMnSi, AlFeCu), (iii) on the other hand, disordered i-phases and amorphous phases containing transition metals are found to possess metallic-glass-like properties. Experimental results reported indicate that the electronic properties of an ordered icosahedral quasicrystal are similar to those of a crystal in the presence of a strong FS-JZB interaction. Quite surprisingly, the elastic scattering time of electrons in the sp-d band ordered phases is found to be much longer than that in the nearly-free-electron i-phases. The propensity towards electron localization is ascribed to the realization of a potentially strong FS-JZB interaction in an ordered structure, particularly that with the icosahedral point group symmetry. The data have also provided evidence for the existence of rapidly varying electronic structures within the pseudogap of a semi-metallic i-crystal and its crystal analogue, despite the short electronic mean free path. The electron transport at low temperature can be described by the weak localization and electron-electron interaction effects. Contact with theories on quasiperiodic systems is also made. Finally, results from the stable decagonal crystals are discussed.