Spin-density-functional theory of circular and elliptical quantum dots

Using spin-density-functional theory, we study the electronic states of a two-dimensional parabolic quantum dot with up to $N=58$ electrons. We observe a shell structure for the filling of the dot with electrons. Hund's rule determines the spin configuration of the ground state, but only up to 22 electrons. At specific N, the ground state is degenerate, and a small elliptical deformation of the external potential induces a rotational charge-density-wave state. Previously identified spin-density-wave states are shown to be artifacts of broken spin symmetry in density-functional theory.