Kondo holes in strongly correlated impurity arrays: RKKY driven Kondo screening and hole-hole interactions

TL;DR

This paper investigates how local magnetic moments induced by vacancies in strongly correlated systems are screened through various mechanisms, revealing complex low-temperature behaviors and phase transitions influenced by Coulomb interactions and RKKY coupling.

Contribution

It provides a comprehensive analysis of multiple screening mechanisms for local moments in impurity arrays, including a novel understanding of the Kondo scale and the role of RKKY interactions.

Findings

Local moments are screened by delocalization due to Coulomb interactions.

Identification of a Kosterlitz-Thouless transition with an exponential low-energy scale.

Discovery of a finite-energy Kondo hole orbital that quenches local moments.

Abstract

The emerging and screening of local magnetic moments in solids has been investigated for more than 60 years. Local vacancies as in graphene or in Heavy Fermions can induce decoupled bound states that lead to the formation of local moments. In this paper, we address the puzzling question how these local moments can be screened and what determines the additionally emerging low temperature scale. We review the initial problem for half-filled conduction bands from two complementary perspectives: By a single-particle supercell analysis in the uncorrelated limit and by the Lieb-Mathis theorem for systems with a large Coulomb interaction $U$. We proof that the stable local moments are subject to screening by three different mechanisms. Firstly the local moments are delocalized by a finite $U$ beyond the single-particle bound state. We find a Kosterlitz-Thouless type transition governed by an exponentially suppressed low energy scale of a counterintuitive Kondo form with $J_{\rm eff} \propto U^n$ for small $U$, where $n>1$ depends on the precise model. Secondly, we show that away from half-filling the local moment phase becomes unstable and is replaced by two types of singlet phases that are adiabatically connected. At a critical value for the band center, the physics is governed by an exponentially suppressed Kondo scale approaching the strong coupling phase that is replaced by an singlet formation via antiferromagnetic RKKY interaction for large deviation from the critical values. Thirdly, we show that the local magnetic moment can be screened by a Kondo hole orbital at finite energy, even though the orbital occupation is negligible: An additional low energy scale emerges below which the localized moment is quenched. Similarities to the experimental findings in Ce$_{1-x}$La$_x$Pd$_3$ are pointed out.