Wigner molecules in polygonal quantum dots:  A density-functional study

We investigate the properties of many-electron systems in two-dimensional polygonal (triangle, square, pentagon, hexagon) potential wells by using the density-functional theory. The development of the ground-state electronic structure as a function of the dot size is of particular interest. First, we show that in the case of two electrons, the Wigner molecule formation agrees with previous exact diagonalization studies. Then we present in detail how the spin symmetry breaks in polygonal geometries as the spin density-functional theory is applied. In several cases with more than two electrons, we find a transition to the crystallized state, yielding coincidence with the number of density maxima and the electron number. We show that this transition density, which agrees reasonably well with previous estimations, is rather insensitive to both the shape of the dot and the electron number.