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

An exact method is proposed to diagonalize the Hamiltonian of a double-laye r 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 appl ied magnetic field. As a result of the electron-electron interaction, compl ete sets of "magic numbers" are found to characterize the total orbital ang ular momentum of the N-electron dot in the ground state for both the polari zed and unpolarized spins. It is shown that discrete transitions of the gro und state between magic numbers takes place when the external magnetic fiel d changes. The origin of the magic numbers is completely explained in terms of the underlying symmetry.