Three-Channel Kondo Effect Emerging from Ho Ions

TL;DR

This paper demonstrates the theoretical emergence of the three-channel Kondo effect in a Ho ion model, revealing a residual entropy linked to the golden ratio and exploring quantum criticality, with implications for experimental observation.

Contribution

It introduces a seven-orbital impurity Anderson model for Ho ions and uses NRG to show the three-channel Kondo effect with a residual entropy of log(phi).

Findings

Residual entropy of log(phi) indicating three-channel Kondo effect

Identification of quantum critical point between Kondo and Fermi-liquid phases

Potential experimental realization in cubic Ho compounds

Abstract

We illustrate the emergence of the three-channel Kondo effect in a seven-orbital impurity Anderson model hybridized with $\Gamma_7$ and $\Gamma_8$ conduction electron bands employing a numerical renormalization group method. In particular, we focus on the case with ten local $f$ electrons corresponding to a Ho$^{3+}$ ion. By investigating the dependence of the low-temperature behavior of the $f$-electron entropy on the crystalline electric field potential and hybridization, we found a residual entropy of $\log \phi$ with the golden ratio $\phi=(1+\sqrt{5})/2$, characteristic of the three-channel Kondo effect, for the wide range of parameters of the local $\Gamma_5$ triplet ground state. To improve our insight of local impurity spin, we explored a quantum critical point between three-channel Kondo and Fermi-liquid phases. Finally, we briefly discussed the cubic Ho compound as a candidate to observe experimentally the three-channel Kondo effect.