We consider a model of hydrogen-like artificial molecule formed by two vertically coupled quantum dots in the shape of axially symmetrical thin layers with on-axis single donor impurity in each of them and with the magnetic field directed along the symmetry axis. We present numerical results for energies of some low-lying levels as functions of the magnetic field applied along the symmetry axis for different quantum dot heights, radii, and separations between them. The evolution of the Aharonov-Bohm oscillations of the energy levels with the increase of the separation between dots is analyzed.

The electronic states of a singly ionized on-axis double-donor complex (D2+) confined in two identical vertically coupled, axially symmetrical quantum dots in a threading magnetic field are calculated. The solutions of the Schrödinger equation are obtained by a variational separation of variables in the adiabatic limit. Numerical results are shown for bonding and antibonding lowest-lying artificial molecule states corresponding to different quantum dot morphologies, dimensions, separation between them, thicknesses of the wetting layers, and magnetic field strength.