Dimensionality effects in the two-electron system in circular and elliptic quantum dots

The properties of a two-electron system confined in single vertical quantum dots with circular and rectangular mesa structure geometries were studied by the direct diagonalization of the many particle Schrodinger equation for which confinement potentials are obtained from multiscale modeling performed for the whole three-dimensional layered mesa structure. We found that with increasing electron population the confinement strength of the circular dot decreases monotonically in good agreement with experimental data, while in the rectangular mesa dot it exhibts an oscillatory behavior reminiscent of the shell structure. We also showed that the singlet-triplet energy separation (exchange energy) computed for two- and three-dimensional (2D and 3D) confinement potentials at zero magnetic field in the rectangular mesa quantum dot is significantly smaller than in the circular one; however, the magnetic fields at which singlet-triplet transition occur have close values for both structures. For 3D potentials, we observed a suppression of the electron localization in the rectangular mesa dot when compared with the results of 2D simulations.