Elastic Softening in Quantum Critical Yb-Al-Au Approximant Crystal and Quasicrystal

TL;DR

This paper theoretically investigates elastic softening in quantum critical Yb-Al-Au quasicrystals and their approximant crystals, revealing significant elastic constant softening near the quantum critical point due to valence fluctuations.

Contribution

It introduces a realistic effective model for the approximant crystal and demonstrates elastic constant softening linked to quantum criticality in Yb-based quasicrystals.

Findings

Elastic softening occurs in bulk modulus and longitudinal modes at low temperatures.

The model predicts a quantum critical point driven by Yb-valence transition.

Results suggest relevance to experimental observations in quasicrystals and approximants.

Abstract

The elastic property of quantum critical quasicrystal (QC) Yb$_{15}$Al$_{34}$Au$_{51}$ is analyzed theoretically on the basis of the approximant crystal (AC) Yb$_{14}$Al$_{35}$Au$_{51}$. By constructing the realistic effective model in the AC, we evaluate the 4f-5d Coulomb repulsion at Yb as $U_{fd}\approx 1.46$ eV realizing the quantum critical point (QCP) of the Yb-valence transition. The RPA analysis of the QCP shows that softening in elastic constants occurs remarkably for bulk modulus and longitudinal mode at low temperatures. Possible relevance of these results to the QC as well as the pressure-tuned AC is discussed.