A quasicrystal is an ordered but nonperiodic structure understood as a projection from a higher-dimensional periodic structure. Some physical properties of quasicrystals are different from those of conventional solids. An anomalous increase in heat capacity at high temperatures has been discussed for over two decades as a manifestation of a hidden high dimensionality of quasicrystals. A plausible candidate for this origin has been the phason, which has excitation modes originating from the additional atomic rearrangements introduced by the quasiperiodic order, which can be understood in terms of shifting a higher-dimensional lattice. However, most theoretical studies of phasons have used toy models. A theoretical study of the heat capacity of realistic quasicrystals or their approximants has yet to be conducted because of the huge computational complexity. To bridge this gap between experiment and theory, we show experiments and molecular simulations on the same material, an Al-Pd-Ru quasicrystal, and its approximants. We show that at high temperatures, aluminum atoms diffuse with discontinuouslike jumps, and the diffusion paths of the aluminum can be understood in terms of jumps corresponding to hyperatomic-fluctuations-associated atomic rearrangements of the phason degrees of freedom. It is concluded that the anomaly in the heat capacity of quasicrystals arises from the hyperatomic fluctuations that play a role in diffusive Nambu-Goldstone modes.

• Received 28 May 2023
• Revised 29 January 2024
• Accepted 28 March 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.196301