Wigner Molecules in Nanostructures

TL;DR

This paper investigates how electron arrangements in quantum dots transition from uniform to Wigner molecules due to Coulomb interactions, highlighting the effects of interaction range on electron localization.

Contribution

It provides a numerical analysis of electron densities in quantum dots, exploring the impact of Coulomb interaction range on Wigner molecule formation.

Findings

Wigner molecules form in quantum dots with long-range Coulomb interactions.

Cutting off the Coulomb interaction destroys Wigner crystallization.

Charge density waves emerge when interactions are exponentially suppressed.

Abstract

The one-- and two-- particle densities of up to four interacting electrons with spin, confined within a quasi one--dimensional ``quantum dot'' are calculated by numerical diagonalization. The transition from a dense homogeneous charge distribution to a dilute localized Wigner--type electron arrangement is investigated. The influence of the long range part of the Coulomb interaction is studied. When the interaction is exponentially cut off the ``crystallized'' Wigner molecule is destroyed in favor of an inhomogeneous charge distribution similar to a charge density wave .