Effect of the magnetic field on electron density distributions in two-electron quantum dots

We present a thorough analysis of the electron density distribution (shape) of two electrons, confined in the three-dimensional harmonic oscillator potential, as a function of the perpendicular magnetic field. We found that the interplay of the classical and quantum properties lead to a quantum shape transition from a lateral to a vertical localization of electrons in low-lying excited states at relatively strong Coulomb interaction with alteration of the magnetic field. While at this regime in the ground states, the electrons always form a ring-type distribution in the lateral plane.