  The ground states of artificial molecules made of two vertically coupled
quantum rings are studied within the spin density functional theory for systems
containing up to 13 electrons. Quantum tunneling effects on the electronic
structure of the coupled rings are analyzed. For small ring radius, our results
recover those of coupled quantum dots. For intermediate and large ring radius,
new phases are found showing the formation of new diatomic artificial ring
molecules. Our results also show that the tunneling induced phase transitions
in the coupled rings occur at much smaller tunneling energy as compared to
those for coupled quantum dot systems.
