Few-electron artificial molecules formed by laterally coupled quantum rings

We study artificial molecular states formed in laterally coupled double semiconductor nanorings by one, two, and three electrons. An interplay of the interring tunneling and the electron-electron interaction is described, as well as its consequences for the magnetization and charging properties of the system. It is shown that both the magnetic dipole moment generated by the double-ring structure and the chemical potential of the system as function of the external magnetic field strongly depend on the number of electrons and the interring barrier thickness. Both the magnetization and chemical potentials exhibit cusps at the magnetic fields inducing ground-state parity and/or spin transformations. The symmetry transformations are discussed for various tunnel coupling strengths, from rings coupled only electrostatically to the limit of coalesced rings. We find that in the ground states for rings of different radii the magnetic field transfers the electron charge from one ring to the other. The calculations are performed with the configuration-interaction method based on an approach of Gaussian functions centered on a rectangular array of points covering the studied structure. Electron-electron correlation is also discussed.