Kondo volume collapse, Kondo breakdown, and Fermi surface transitions in heavy-fermion metals

TL;DR

This paper explores the interplay of Kondo volume collapse, Kondo breakdown, and Fermi surface transitions in heavy-fermion metals, revealing how lattice coupling influences the nature of quantum phase transitions and their experimental signatures.

Contribution

It introduces a model coupling electronic and lattice degrees of freedom, showing how different transitions merge or change order, and analyzes critical behavior at the zero-temperature endpoint.

Findings

Lifshitz transition merges with Kondo volume collapse, becoming first order.

Kondo breakdown remains second order except in very soft lattices.

At the endpoint, two continuous quantum phase transitions coincide without fine tuning.

Abstract

The unconventional critical behavior near magnetic quantum phase transitions in various heavy-fermion metals, apparently inconsistent with the standard spin-density-wave scenario, has triggered proposals on the breakdown of the Kondo effect at the critical point. Here we investigate, within one specific scenario, the fate of such a zero-temperature transition upon coupling of the electronic to lattice degrees of freedom. We study a Kondo-Heisenberg model with volume-dependent Kondo coupling -- this model displays both Kondo volume collapse and Kondo-breakdown transitions, as well as Lifshitz transitions associated with a change of the Fermi-surface topology. Within a large-N treatment, we find that the Lifshitz transition tends to merge with the Kondo volume collapse and hence becomes first order, whereas the Kondo breakdown transition remains of second order except for very soft lattices. Interesting physics emerges at the zero-temperature endpoint of the Kondo volume collapse: For electrons in two space dimensions, this endpoint is located at the Lifshitz line for a large range of parameters, thus two continuous quantum phase transitions coincide without fine tuning. We analyze the effective Landau theory for such a situation and discuss critical exponents. Finally, we relate our findings to current heavy-fermion experiments.