Electronic and magnetic properties of a two-electron Gaussian GaAs quantum dot with spin-Zeeman term: A study by numerical diagonalization

The problem of two interacting electrons moving in a two-dimensional semiconductor quantum dot with Gaussian confining potential under the influence of an external magnetic field is studied by numerical diagonalization of the Hamiltonian matrix. The energy spectrum, the magnetic moment and the susceptibility are calculated as a function of the magnetic field and the quantum dot parameters. The magnetic moment and the magnetic susceptibility are shown to have zero-temperature diamagnetic peaks due to the exchange-induced singlet-triplet oscillations. The position and the number of these peaks depend on the size of the quantum dot and also the strength of the electron-electron interaction. The addition energies of the two low-lying states are also obtained by directly calculating the chemical potential. Besides, the electric capacitance is calculated as well. The theory is applied to a GaAs quantum dot.