Selection Rules for Two Channel Kondo Models of U and Ce ions in Metals

TL;DR

This paper develops symmetry-based selection rules to determine when two-channel Kondo interactions can occur for U$^{4+}$ and Ce$^{3+}$ ions in metals, highlighting the conditions under which quadrupolar and magnetic Kondo effects are possible.

Contribution

It introduces minimal symmetry-based criteria and a dynamic rule for the existence of two-channel Kondo effects in U$^{4+}$ and Ce$^{3+}$ ions, clarifying their dependence on crystal symmetry.

Findings

Two-channel quadrupolar Kondo effect occurs for U$^{4+}$ in certain symmetries.

The effect is restricted to specific ionic ground states for Ce$^{3+}$.

Yb$^{3+}$ ions are unlikely to exhibit two-channel Kondo behavior.

Abstract

Symmetry based selection rules are developed providing minimal criteria for the existence of two-channel Kondo interactions between conduction electrons and the low energy degrees of freedom on U$^{4+}$ and Ce$^{3+}$ in a metal host, assuming that the underlying microscopics are regulated by the Anderson Hamiltonian. An additional dynamic selection rule is imposed on Ce$^{3+}$ ions. The selection rules restrict the two-channel quadrupolar Kondo effect to U$^{4+}$ ions in cubic, tetragonal, and hexagonal symmetry. For hexagonal and tetragonal symmetry, the Kondo effect for a U$^{4+}$ ion will always be quadrupolar. The selection rules for Ce$^{3+}$ ions restrict the two-channel magnetic Kondo effect to one of three possible doublet ionic ground states in hexagonal symmetry and the lone doublet ionic ground state in cubic symmetry. The dynamical selection rule apparently excludes two-channel Kondo behavior for Yb$^{3+}$ ions.