Semiclassical analysis of a two - electron quantum dot in a magnetic field : dimensional phenomena

While the dynamics for three-dimensional axially symmetric two-electron quantum dots with parabolic confinement potentials is in general non-separable we have found an exact separability with three quantum numbers for specific values of the magnetic field. Furthermore, it is shown that the magnetic properties such as the magnetic moment and the susceptibility are sensitive to the presence and strength of a vertical confinement. Using a semiclassical approach the calculation of the eigenvalues reduces to simple quadratures providing a transparent and almost analytical quantization of the quantum dot energy levels which differ from the exact energies only by a few percent. Current nanofabrication technology allows one to control the size and shape of quantum dots [1–3]. Due to the confinement of the electrons in all three spatial directions the energy spectrum is quantized creating excellent experimental and theoretical opportunities to study controlled single-particle and collective dynamics at the atomic scale. For example, depending on the experimental setup, the spectrum of a quantum dot displays shell structure 1