Quantum-dot beryllium: A carbon-like atom in atwo-dimensional world

摘要

We report results of an exact-diagonalisation study of quantum-dot beryllium –a system of four Coulomb-interacting two-dimensional electrons in the harmonic-oscillatorpotential. We calculate the ground and excited state energies of the system in zero magneticfield as a function of Coulomb interaction, and study physical properties of the ground state(charge and spin densities, pair-correlation functions) at different interaction strengths. Theground state of quantum-dot beryllium is characterised by quantum numbers (L,S)=(0,1)(the total angular momentum and the total spin) and is three-fold degenerate with respect to theprojection of the total spin Sc We show that electron-electron correlations are qualitativelydifferent in the states with the total-spin projection Sc=0 and±1. As a result, formation ofWigner molecules with the growing interaction strength is going on in qualitatively differentways in these states. Conclusions of our work have a general character and are not restrictedby assumptions of the parabolic confinement or two-dimensional nature of the electrons.