Frustration and the Kondo effect in heavy fermion materials

TL;DR

This paper explores how frustration influences the Kondo effect in heavy fermion materials, proposing a combined phase diagram with Kondo and frustration axes, and analyzing models like the Shastry--Sutherland Kondo lattice to understand phase transitions.

Contribution

It introduces a combined Kondo-frustration phase diagram for heavy fermion systems and analyzes the frustrated Kondo lattice models, especially the Shastry--Sutherland model, using strong coupling and large-N methods.

Findings

Identification of a QK phase diagram for heavy fermion materials.

Characterization of the f-electron localization transition.

Qualitative phase diagram for the Shastry--Sutherland Kondo lattice.

Abstract

The observation of a separation between the antiferromagnetic phase boundary and the small-large Fermi surface transition in recent experiments has led to the proposal that frustration is an important additional tuning parameter in the Kondo lattice model of heavy fermion materials. The introduction of a Kondo (K) and a frustration (Q) axis into the phase diagram permits us to discuss the physics of heavy fermion materials in a broader perspective. The current experimental situation is analysed in the context of this combined "QK" phase diagram. We discuss various theoretical models for the frustrated Kondo lattice, using general arguments to characterize the nature of the $f$-electron localization transition that occurs between the spin liquid and heavy Fermi liquid ground-states. We concentrate in particular on the Shastry--Sutherland Kondo lattice model, for which we establish the qualitative phase diagram using strong coupling arguments and the large-$N$ expansion. The paper closes with some brief remarks on promising future theoretical directions.