Quantum Valence Criticality in Heavy Fermions on Periodic and Aperiodic Crystals

TL;DR

This paper reviews recent experimental and theoretical advances in understanding quantum valence criticality in heavy fermion systems, highlighting evidence of valence quantum critical points in specific periodic and aperiodic crystals and explaining observed scaling behaviors.

Contribution

It provides a unified theoretical framework for quantum valence criticality applicable to both periodic and aperiodic heavy fermion materials, supported by recent experimental findings.

Findings

Evidence of valence quantum critical points in $eta$-YbAlB$_4$ and quasicrystals.

Observation of $T/B$ scaling in magnetization consistent with valence fluctuation theory.

Theoretical explanation of critical behaviors in diverse heavy fermion systems.

Abstract

Progress of theories and experiments of the quantum valence criticality is overviewed focusing on recent discoveries of direct evidence of quantum critical point of valence transitions in periodic crystal $\alpha$-YbAl$_{1-x}$Fe$_x$B$_4$ at $x=0.014$ and quasicrystal Yb$_{15}$(Al$_{1-x} $Ga$_{x}$)$_{34}$(Au$_{1-y}$Cu$_{y}$)$_{51}$ at $x=y=0$. The common quantum criticality as well as $T/B$ scaling behavior in the magnetization observed in the periodic crystal $\beta$-YbAlB$_4$ and quasicrystal Yb$_{15}$Al$_{34}$Au$_{51}$ is shown to be explained from the theory of critical Yb-valence fluctuations starting from the Hamiltonians for describing the low-energy electronic states in both systems.