Interacting electrons in polygonal quantum dots

TL;DR

This paper investigates the low-energy states of two electrons in polygonal quantum dots, exploring the transition from weak to strong correlations and evaluating an effective charge-spin model for larger dots.

Contribution

It introduces an exact diagonalization approach for polygonal quantum dots and assesses a charge-spin model for describing electron correlations.

Findings

Transition from charge distribution to Wigner molecule with increasing dot size

Effective charge-spin model accurately predicts energy level ordering

Model provides good approximation for level spacings in large dots

Abstract

The low-lying eigenstates of a system of two electrons confined within a two-dimensional quantum dot with a hard polygonal boundary are obtained by means of exact diagonalization. The transition from a weakly correlated charge distribution for small dots to a strongly correlated "Wigner molecule" for large dots is studied, and the behaviour at the crossover is determined. In sufficiently large dots, a recently proposed mapping to an effective charge-spin model is investigated, and is found to produce the correct ordering of the energy levels and to give a good first approximation to the size of the level spacings. We conclude that this approach is a valuable method to obtain the low energy spectrum of few-electron quantum dots.