Correlated electronic states in quasicrystals

Abstract

Strong correlations in quasiperiodic systems have attracted much interest since the recent observation of quantum critical behavior in the Tsai-type quasicrystal compound Au51Al34Yb15. Possible long-range electronic orders in such systems have also been widely debated. This chapter reviews our theoretical investigations on correlation effects in the quasiperiodic system, such as the Mott transition, valence transition, and superconductivity. In the metallic state close to the Mott transition point, the quasiparticle weight strongly depends on the site and its geometry while the Mott transition occurs simultaneously and is not suppressed by the quasiperiodicity. On the other hand, the valence transition is suppressed by the quasiperiodicity, where the Kondo and valence-fluctuating states appear depending on the site. For superconductivity, we found unconventional weak-coupling superconductivity formed by the Cooper pairs deviating from those of Bardeen-Cooper-Schrieffer superconductivity in periodic systems. This deviation can be seen in the real-space distribution of the superconducting order parameter, jump of specific heat, and current-voltage characteristic curve. These results indicate that superconductivity in quasiperiodic systems is qualitatively different from that in periodic and random systems. In particular, the results are consistent with the superconductivity recently discovered in an Al-Mg-Zn quasicrystal and provide a clue to understanding its mechanism and property.