Origin of Hund’s multiplicity rule in quasi-two-dimensional two-electron quantum dots

Abstract

The origin of Hund's multiplicity rules has been studied for a system of two electrons confined by a quasi-two-dimensional harmonic-oscillator potential by relying on a full configuration interaction wave function and Cartesian anisotropic Gaussian basis sets. In terms of appropriate normal-mode coordinates the wave function factors into a product of the center-of-mass and the internal components. The ${}^{1}{\ensuremath{\Pi}}_{u}$ singlet state and the ${}^{3}{\ensuremath{\Pi}}_{u}$ triplet state represent the energetically lowest pair of states to which Hund's multiplicity rule applies. They are shown to involve excitations into different degrees of freedom, namely, into the center-of-mass angular mode and the internal angular mode for the singlet and triplet states, respectively. The presence of an angular nodal line in the internal space allows then the triplet state to avoid the singularity in the electron-electron interaction potential, leading to the energy lowering of the triplet state relative to its counterpart singlet state.