Molecule-type phases and Hund's rule in vertically coupled quantum dots

We study the ground state of two vertically coupled quantum dots as a function of the interdot distance within the spin density functional theory. The tunneling between the dots is included. For small and large interdot distances the atomic phases are recovered. For intermediate distances new molecule-type phases are predicted which can be observed experimentally in the addition energies. The results are interpreted in terms of an effective single particle picture and we find that Hund's rule breaks down for 11 and 12 electrons. The results are summarized in a phase diagram in which spin and isospin blockade regions are also found.