2006/11/03 by Anuradha Jagannathan, A. Jagannathan, Frédéric Piéchon +1
Materials Science · Physics and Astronomy · #Condensed matter physics #Density of states #Exponent #Materials science #Physics #Quasicrystal #Quasicrystal Structures and Properties #Quasiperiodic function #Statistical physics #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.1080/14786430701196990
15 pages including 19 figures. Review article, submitted to Phil. Mag
arxiv created 2006/11/03 · openalex publication_date 2007/05/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quasicrystals can be considered, from the point of view of their electronic properties, as being intermediate between metals and insulators. For example, experiments show that quasicrystalline alloys such as AlCuFe or AlPdMn have conductivities far smaller than those of the metals that these alloys are composed from. Wavefunctions in a quasicrystal are typically intermediate in character between the extended states of a crystal and the exponentially localized states in the insulating phase, and this is also reflected in the energy spectrum and the density of states. In the theoretical studies we consider in this review, the quasicrystals are described by a pure hopping tight binding model on simple tilings. We focus on spectral properties, which we compare with those of other complex systems, in particular, the Anderson model of a disordered metal. We discuss ‘strong‘ and ‘weak’ quasicrystals, which are described by different universal laws. We find similarities and universal behaviour, but also significant differences between quasiperiodic models and models with disorder. Like weakly disordered metals, the quasicrystal can be described by the universal level statistics that can be derived from random matrix theory. These level statistics are only one aspect of the energy spectrum, whose very large fluctuations can also be described by a level spacing distribution that is log-normal. An analysis of spectral rigidity shows that electrons diffuse with a bigger exponent (super-diffusion) than in a disordered metal. Adding disorder attenuates the singular properties of the perfect quasicrystal, and leads to improved transport. Spectral properties are also used in computing conductances of such systems, and to attempt to resolve the experimental enigmas such as whether quasicrystals are intrinsically conductors, and if so, how conductances depend on the structure.