Finite-thickness effects in ground-state transitions of two-electron quantum dots

Using the exactly solvable excitation spectrum of two-electron quantum dots with parabolic potential, we show that the inclusion of the vertical extension of the quantum dot provides a consistent description of the experimental findings of Nishi [Phys. Rev. B 75, 121301(R) (2007)]. We found that the second singlet-triplet transition in the ground state is a vanishing function of the lateral confinement in the three-dimensional case, while it always persists in the two-dimensional case. We show that a slight decrease of the lateral confinement leads to a formation of the Wigner molecule at low magnetic fields.