Origin of Quantum Criticality in Yb-Al-Au Approximant Crystal and Quasicrystal

TL;DR

This paper investigates the mechanism behind unconventional quantum criticality in Yb-Al-Au quasicrystals by analyzing an approximant crystal model, revealing local Yb-valence fluctuations and small energy scales as key factors.

Contribution

The study introduces a minimal model showing how local Yb-valence fluctuations lead to quantum criticality, explaining phenomena in quasicrystals through approximant analysis.

Findings

Charge-transfer mode is enhanced with flat momentum dependence.

Magnetic and valence susceptibilities follow a T^{-0.5} scaling.

Quantum criticality arises from local Yb-valence fluctuations and small Brillouin zone.

Abstract

To get insight into the mechanism of emergence of unconventional quantum criticality observed in quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$, the approximant crystal Yb$_{14}$Al$_{35}$Au$_{51}$ is analyzed theoretically. By constructing a minimal model for the approximant crystal, the heavy quasiparticle band is shown to emerge near the Fermi level because of strong correlation of 4f electrons at Yb. We find that charge-transfer mode between 4f electron at Yb on the 3rd shell and 3p electron at Al on the 4th shell in Tsai-type cluster is considerably enhanced with almost flat momentum dependence. The mode-coupling theory shows that magnetic as well as valence susceptibility exhibits $\chi\sim T^{-0.5}$ for zero-field limit and is expressed as a single scaling function of the ratio of temperature to magnetic field $T/B$ over four decades even in the approximant crystal when some condition is satisfied by varying parameters, e.g., by applying pressure. The key origin is clarified to be due to the strong locality of the critical Yb-valence fluctuation and small Brillouin zone reflecting the large unit cell, giving rise to the extremely-small characteristic energy scale. This also gives a natural explanation for the quantum criticality in the quasicrystal corresponding to the infinite limit of the unit-cell size.