Non-Divergent Grüneisen Parameter in Quantum Critical Quasicrystal Yb${}_{15}$Al${}_{34}$Au${}_{51}$: Reflection of Robustness of Quantum Criticality under Pressure

Abstract

The mechanism of not diverging Grüneisen parameter in the quantum critical heavy-fermion quasicrystal (QC) Yb${}_{15}$Al${}_{34}$Au${}_{51}$ is analyzed. We construct the formalism for calculating the specific heat $C_V(T)$, the thermal-expansion coefficient $\alpha (T)$, and the Grüneisen parameter $\Gamma (T)$ near the quantum critical point of the Yb valence transition. By applying the framework to the QC, we calculate $C_V(T)$, $\alpha (T)$, and $\Gamma (T)$, which explains the measurements. Not diverging $\Gamma (T)$ is attributed to the robustness of the quantum criticality in the QC under pressure. The difference in $\Gamma (T)$ at the lowest temperature between the QC and approximant crystal is shown to reflect the difference in the volume derivative of characteristic energy scales of the critical Yb-valence fluctuation and the Kondo temperature. Possible implications of our theory to future experiments are also discussed.

13 pages, 5 figures

References in corpus (4)

• Quantum critical state in a magnetic quasicrystal
• Quantum Valence Criticality as Origin of Unconventional Critical Phenomena
• Grüneisen parameter studies on heavy fermion quantum criticality
• Grüneisen Parameter and Thermal Expansion near Magnetic Quantum Critical Points in Itinerant Electron Systems

Cited by in corpus (2)

• Crystalline Electronic Field in Rare-Earth Based Quasicrystal and Approximant: Analysis of Quantum Critical Au-Al-Yb Quasicrystal and Approximant
• Elastic Softening in Quantum Critical Yb-Al-Au Approximant Crystal and Quasicrystal