Recent experiments by two Japanese teams [1] on a quasiperiodic alloy, Au_{51}Al_{34}Yb_{15}, indicate that this may be the case. This perfect quasicrystal or QC-p (where "perfect" indicates little or no disorder) has icosahedral symmetry, with Yb atoms located at the vertices of icosahedra and the Au and Al atoms in the interior and exterior (Fig. b). The magnetic susceptibility diverges at low temperature and vanishing magnetic field: χ(T) ~ 1/√T. Measurements of the specific heat and the resistivity confirm that this compound does not behave like a normal Fermi liquid but rather like a system near a quantum critical point. Remarkably, this behavior is found with **no tuning of parameters**. Just as remarkable is the contrast with the closely related periodic compound Au_{51}Al_{35}Yb_{14}, termed QC-a (for approximant), which has the same icosahedral enviroments, but where the susceptibility tends to a finite value as T tends towards zero.

*a) Structure model of the AuAlYb quasicrystal, showing the positions of Yb atoms after projection onto a plane perpendicular to the 5-fold symmetry axis (Reproduced with permission from Deguchi et al [1]). b) Magnetic susceptibility versus temperature for small T and different values of Kondo coupling J, showing power law divergence for small J. Variables have been normalized with respect to their typical values. c) A different example of a QCP in physics.*

A team of theoreticians has provided a simple explanation for these observations [2] using the fact that, in a perfect quasicrystal, electronic wavefunctions have special properties – they are neither localized nor extended but "critical", with enormous amplitude fluctuations. When a magnetic impurity is placed in a quasiperiodic medium, one expects there to be a large variation of the Kondo temperature T_{K} (at which the local moment is "quenched" due to interactions with conduction electrons) depending on the local environment. Calculations show that, in the perfect QC, a finite fraction of moments remain active in the limit of vanishing T. These are responsible for the power law divergence of the susceptibility, as shown in Fig. c, for small values of the Kondo coupling J.

To summarize, critical states of the perfect quasicrystal are the reason why this alloy is automatically at its critical point without need for adjusting parameters: QC-p=QCP!

### References:

[1] K. Deguchi et al, *Nature Materials* **11**, 1013–1016 (2012); T. Watanuki et al, *Phys. Rev. B* **86** 094201 (2012).

[2] Non-Fermi-Liquid Behavior in Metallic Quasicrystals with Local Magnetic Moments

Eric C. Andrade et al.*Phys. Rev. Lett.* **115**, 036403 (2015).