Dimensionality efiects in vertical two-electron quantum dots in a perpendicular magnetic field

The efiect of third dimension on various physical properties of a two-electron vertical quantum dot is analysed. We show that at specific values the magnetic field gives rise to dynamical symmetries of the dot. A remarkable agreement between experimental data and calculations for the additional energy exhibits important role of the dot thickness for interpretation of ground state transitions in the magnetic field. We show that these transitions can be successfully reproduced as well in the two-dimensional approximation (only lateral confinement) but with the effective (screened) Coulomb interaction. We provide an analytical expression for the screening for the case of a parabolic vertical potential.