Local moment formation and Kondo screening in impurity trimers

TL;DR

This paper investigates the complex interplay of local moment formation, frustration, and Kondo screening in a triangular impurity cluster, revealing rich quantum phase transitions and mechanisms relevant for quantum dot systems.

Contribution

It introduces a detailed theoretical analysis of a triangular impurity cluster, highlighting novel quantum phase transitions influenced by frustration and symmetry, using analytical and numerical methods.

Findings

Identification of a quantum phase transition driven by local frustration.

Discovery of unique mechanisms for local moment formation and Kondo screening.

Relevance of results for triple quantum dot devices.

Abstract

We study theoretically a triangular cluster of three magnetic impurities, hybridizing locally with conduction electrons of a metallic host. Such a cluster is the simplest to exhibit frustration - an important generic feature of many complex molecular systems in which different interactions compete. Here, low-energy doublet states of the trimer are favored by effective exchange interactions produced by strong electronic repulsion in localized impurity orbitals. Parity symmetry protects a level-crossing of such states on tuning microscopic parameters, while an avoided crossing arises in the general distorted case. On coupling to a metallic host, the behavior is shown to be immensely rich, since collective quantum many-body effects now also compete. In particular, impurity degrees of freedom are totally screened at low temperatures in a Kondo-screened Fermi liquid phase, while degenerate ground states persist in a local moment phase. Local frustration drives the quantum phase transition between the two, which may be first order or of Kosterlitz-Thouless type, depending on symmetries. Unusual mechanisms for local moment formation and Kondo screening are found, due to the orbital structure of the impurity trimer. Our results are of relevance for triple quantum dot devices. The problem is studied by a combination of analytical arguments and the numerical renormalization group.