Quasicrystals are metallic alloys that possess long-range, aperiodic structures with diffraction symmetries forbidden to conventional crystals. Since the discovery of quasicrystals by Schechtman et al. in 1984, there has been considerable progress in resolving their geometric structure. For example, it is well known that the golden ratio of mathematics and art occurs over and over again in their crystal structure. However, the characteristic properties of the electronic states--whether they are extended as in periodic crystals or localized as in amorphous materials--are still unresolved. Here we report the first observation of quantum (T = 0) critical phenomena of the Au-Al-Yb quasicrystal--the magnetic susceptibility and the electronic specific heat coefficient arising from strongly correlated 4f electrons of the Yb atoms diverge as T→0. Furthermore, we observe that this quantum critical phenomenon is robust against hydrostatic pressure. By contrast, there is no such divergence in a crystalline approximant, a phase whose composition is close to that of the quasicrystal and whose unit cell has atomic decorations (that is, icosahedral clusters of atoms) that look like the quasicrystal. These results clearly indicate that the quantum criticality is associated with the unique electronic state of the quasicrystal, that is, a spatially confined critical state. Finally we discuss the possibility that there is a general law underlying the conventional crystals and the quasicrystals.

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A P-type icosahedral quasicrystal is formed in Au-Al-Yb alloy of which 6-dimensional lattice parameter a 6D = 7.448 Å. The composition of the quasicrystal was analyzed to be Au 51 Al 34 Yb 15 . This quasicrystal is formed in as-cast alloys, and is regarded as metastable because of decomposition into other crystalline phases by annealing at 700 ºC. Among Tsai-type quasicrystals, this quasicrystal is situated just between Zn-Sc group with smaller a 6D and larger Cd-Yb group. Intermediate valence of Yb recently observed in this quasicrystal may be due to this unique situation, namely smaller major component Au-Al than in Cd-Yb.The predominant phase in the annealed specimen is a 1/1 cubic approximant with lattice parameter a = 14.500 Å belonging to the space group Im ! 3. This phase is stable at the composition Au 51 Al 35 Yb 14 at 700 ºC. Rietveld structural analysis indicated that the crystal structure is understood as periodic arrangement of Tsai-type clusters each

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Superconductivity is ubiquitous as evidenced by the observation in many crystals including carrier-doped oxides and diamond. Amorphous solids are no exception. However, it remains to be discovered in quasicrystals, in which atoms are ordered over long distances but not in a periodically repeating arrangement. Here we report electrical resistivity, magnetization, and specific-heat measurements of Al–Zn–Mg quasicrystal, presenting convincing evidence for the emergence of bulk superconductivity at a very low transition temperature of K. We also find superconductivity in its approximant crystals, structures that are periodic, but that are very similar to quasicrystals. These observations demonstrate that the effective interaction between electrons remains attractive under variation of the atomic arrangement from periodic to quasiperiodic one. The discovery of the superconducting quasicrystal, in which the fractal geometry interplays with superconductivity, opens the door to a new type of superconductivity, fractal superconductivity.