Spin oscillation and its reduction in a quantum dot

Exact spectra of two electrons in quantum dots (QD’s) with parabolic potentials in a magnetic field are obtained. The spectra are dramatically changed with the variation of the field and that the spin of the ground state oscillates with magnetic field. The reason is found by studying confinement dependence of the interaction energies in detail. The lowest singlet and triplet states of two electrons in disklike QD’s with fixed thickness and a positively charged ion in magnetic field are calculated by a variational method. It is found that the broken symmetry of a QD with an ion has an important effect on the spin oscillation. The ion reduces the oscillation, and the oscillation reduction and the binding energies are strongly dependent on the broken symmetry related to the dot-reflection symmetry and the ion position. The results predict a possibility to observe phenomena related to ion-electron and electron-electron interactions in broken symmetry QD’s.