Magnetic field effects on anisotropic parabolic quantum dots

The many-electron ground states of cylindrical parabolic quantum dots in magnetic fields parallel to the cylindrical axis are investigated by means of an unrestricted Hartree-Fock method. The many-electron eigenstates are assigned by two quantum numbers, L-z and S-z, the z-components of the total orbital angular momentum and the total spin, respectively. As the strength of the magnetic field increases, the spin state of the ground state changes from the paramagnetic to the ferromagnetic state according to Hund's rule. \L-z\ of the ground state increases monotonically with magnetic field strength. In the extremely high-field region of complete spin polarization, \L-z\ increases the electron number N by N. From the total energy of the ground state, the chemical potential and the magnetic susceptibility of quantum dots are calculated as functions of electron number up to 12. Magnetic field dependence of the chemical potential exhibits many cusps, caused by the transitions of many-electron ground states. The chemical potential depends on the vertical extent of a quasi-two-dimensional dot only in weak and intermediate fields where the spin polarization is incomplete, and it depends only slightly on the spin Zeeman term for GaAs dots. The magnetic susceptibility for an array of dots consists of two parts, paramagnetic and diamagnetic, and shows oscillation with electron number at low temperatures.