Vortex structures in few-electron quantum dots with spin degree of freedom

The vortex structures and formations of the few-electron states in quantum dots without the Zeeman splitting are investigated. With spin degree of freedom, it is noticed that both the choices of probe electron and the ways to fix the other electrons in conditional single-particle wave functions affect the display of the vortex structures and behaviors. Then the vortex transitions in magnetic fields for the lowest states with different spins are studied. When the field is not very strong, with the increase of the field, the vortex number is monotone non-decreasing, and there are absent states although their angular momenta are in accordance with transition rules given by the theory of electron molecules. Different behaviors of the vortices with the change of interaction range reveal the respective analogies to the vortices of electrons and quasi-particles in fractional quantum Hall system. The separated vortices keep apart from the electrons even when the interaction is screened and such behavior can give an understanding of the absences of the angular momenta in the transition sequences.