Spectral properties of two electrons vertically coupled in toroidal quantum rings

The energy spectrum of two electrons spatially separated in two toroidal and vertically stacked narrow nanorings with different radii has been analyzed by using a very simple model based on the adiabatic approximation. The low-lying energy levels are found to be a function of the ratio between the ring centreline radii and the magnetic field. Our results coincide with the exact solution previously obtained for the limiting case in which two electrons are constrained to move in a one-dimensional quantum ring.