Theory of One-Channel vs. Multi-Channel Kondo Effects for Ce$^{3+}$ Impurities

TL;DR

This paper models Ce$^{3+}$ impurities in cubic metals, exploring the competition between single-channel and multi-channel Kondo effects, and identifies potential non-Fermi-liquid behavior with implications for interpreting experimental alloys.

Contribution

It introduces a new model capturing the competition between different Kondo fixed points and predicts a three-channel Kondo effect in certain parameter regimes.

Findings

Possible three-channel Kondo effect identified.

Thermopower sign as a fixed point diagnostic.

Results likely robust with additional f^2 and conduction states.

Abstract

We introduce a model for Ce$^{3+}$ impurities in cubic metals which exhibits competition between the Fermi-liquid fixed point of the single channel Kondo model and the non-Fermi-liquid fixed point of the two- and three-channel Kondo models. Using the non-crossing approximation and scaling theory, we find: (i) A possible three-channel Kondo effect between the one- and two-channel regimes in parameter space. (ii) The sign of the thermopower is a fixed point diagnostic. (iii) Our results will likely survive the introduction of additional $f^2$ and conduction states. We apply this model to interpret the non-Fermi liquid alloy La$_{1-x}$Ce$_x$Cu$_{2.2}$Si$_2$.