Electron correlation in metal clusters, quantum dots and quantum rings

TL;DR

This review discusses how strong electron correlations influence the structure and behavior of finite electron systems like metal clusters, quantum dots, and rings, highlighting phenomena such as Wigner molecules and quantum Hall states.

Contribution

It provides a comparative analysis of electron correlation effects across different finite systems, emphasizing the role of correlations in determining their properties.

Findings

Electron correlations determine stability and shape of metal clusters.

Formation of Wigner molecules in low-density quantum dots and rings.

Vortex localization in high rotational states and quantum Hall liquids.

Abstract

This short review presents a few case studies of finite electron systems for which strong correlations play a dominant role. In simple metal clusters, the valence electrons determine stability and shape of the clusters. The ionic skeleton of alkali metals is soft, and cluster geometries are often solely determined by electron correlations. In quantum dots and rings, the electrons may be confined by an external electrostatic potential, formed by a gated heterostructure. In the low density limit, the electrons may form so-called Wigner molecules, for which the many-body quantum spectra reveal the classical vibration modes. High rotational states increase the tendency for the electrons to localize. At low angular momenta, the electrons may form a quantum Hall liquid with vortices. In this case, the vortices act as quasi-particles with long-range effective interactions that localize in a vortex molecule, in much analogy to the electron localization at strong rotation.