Non-Divergent Grüneisen Parameter in Quantum Critical Quasicrystal Yb15Al34Au51: Reflection of Robustness of Quantum Criticality under Pressure

The mechanism of not diverging Grüneisen parameter in the quantum critical heavy-fermion quasicrystal (QC) Yb15Al34Au51 is analyzed. We construct the formalism for calculating the specific heat CV(T), the thermal-expansion coefficient α(T), and the Grüneisen parameter Γ(T) near the quantum critical point of the Yb valence transition. By applying the framework to the QC, we calculate CV(T), α(T), and Γ(T), which explains the measurements. Not diverging Γ(T) is attributed to the robustness of the quantum criticality in the QC under pressure. The difference in Γ(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