Many-electron ground states in anisotropic parabolic quantum dots

The many-electron ground states in anisotropic parabolic quantum dots with the cylindrical symmetry are investigated by means of an unrestricted Hartree-Fock method. The calculated ground state of a large quantum dot is completely spin polarized up to 12 electrons, while the spin configuration of a small quantum dot obeys the Hund rule. The chemical potential and the differential capacitance of quantum dots are calculated as well. The capacitance shows the characteristic oscillation with an electron number caused by the shell structures of single-electron energy levels which are determined self-consistently with the spin configuration of the many-electron ground state. On the differential capacitance, the effect of the vertical extent of a dot is also studied. It becomes larger as the lateral extent of a quantum dot decreases, maintaining the same ratio to the vertical extent. Further, the effect in a small dot becomes especially enhanced at the special number of electrons, N=2,5,10,17,..., due to the shell structure. The excited states, which have different quantum numbers from the ground state, are also studied. © 1996 The American Physical Society.