Electronic Structure of Quasicrystals

Pierangelo Gröning, Swiss Federal Laboratories for Materials Testing and Research (EMPA)

Since their first public report by the end of 1984 [1], quasicrystals (QCs) have attracted a lot of scientific interest due to their extraordinary crystal structure and their unusual physical properties. QCs are characterized by the absence of translational symmetry, however in combination with a well defined atomic arrangement and rotational symmetry, which situates this class of materials between crystalline and disordered solids. QCs exhibit very particular mechanical, magnetic, electronic transport and surface properties, which have been partly associated whit the aperiodic atomic structure. The aperiodicity of QCs has triggered particular interest with regard to the valence electronic structure as the Bloch Theorem, fundamental to the electron band picture of classical crystalline solids, cannot be applied anymore and the concept of a well defined Brillouin zone and associated zone-folding breaks down. It has been suggested by theory that the valence electron states of QC should exhibit, due to the absence of translational symmetry, a new character lying in between the extended states of a classical periodic crystal and the localized states of a random atomic arrangement [2]. These new class of states was denoted as “critical states”, neither being extended nor localized. Associated with these critical states a so-called “spiky” density of states (DOS) was postulated showing a fractal-like appearance of peaks and pseudo gaps. However this spiky DOS could not be corroborated by experiments.