1 Large Wigner Molecules and Quantum 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 diagonalisation. 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. The quasi-crystalline structure found in large dots suggests that the low energy states of the system may be mapped to an effective charge-spin lattice model, as was recently proposed in Ref.1, and the effectiveness of this procedure is investigated by comparison with the results from exact diagonalisation. It is found that the effective model predicts the correct ordering of energy levels, and gives a reasonable first approximation to the size of the energy spacings. The model can be further refined to account for the detailed behaviour of the low energy levels by including spin-flip processes previously neglected in the derivation of the effective model. We conclude that this approach is a useful method to obtain the low energy spectrum of few-electron quantum dots.