Anomalous electronic properties of complex crystals: from cluster compounds to quasicrystals

Abstract

It has been reported recently that icosahedral (i-) crystals with perfect quasicrystalline order exhibit semimetallic conductivity that falls below Mott's minimum metallic conductivity. Moreover, their transport properties are anomalous in comparison with disordered systems with low metallic conductivity. Results obtained from these ordered phases based on good metals (Al, Cu) are presented. The anomalies in transport properties and their strong dependence on crystal chemistry have revealed a peculiar bandstructure effect induced by the Fermi-surface-Jones-zone-boundaries (FS-JZB) interaction in i-crystals. Central to the FS-JZB interaction criterion of phase stability is the existence of a pseudogap which is enhanced by the global icosahedral symmetry. Further understanding of the i-crystals has been advanced through studies of crystal analogs known as approximants. Several approximant structures are constructed from the b.c.c. packing of large icosahedral clusters. Bandstructure calculations for these cluster compounds are now available. Decagonal-crystal structures constructed from the periodic stacking of two-dimensional quasiperiodic layers known as decagonal crystals are also studied. Comparison between the approximant and amorphous phases has provided insight to the understanding of quasiperiodicity, randomness, and atomic-potential as well as dimensionality effects on electronic properties.