Few-electron double-layer quantum dots in magnetic fields: Energy spectrum of an artificial molecule

An exact method is proposed to diagonalize the Hamiltonian of a double-layer quantum dot containing N electrons in arbitrary magnetic fields. For N = 3 and 4, energy spectra of the dot are calculated as a function of the applied magnetic field. As a result of the electron-electron interaction, complete sets of "magic numbers" are found to characterize the total orbital angular momentum of the N-electron dot in the ground state for both the polarized and unpolarized spins. It is shown that discrete transitions of the ground state between magic numbers takes place when the external magnetic field changes. The origin of the magic numbers is completely explained in terms of the underlying symmetry.