Charge occupancy of two interacting electrons on artificial molecules: Exact results

We present exact solutions for two interacting electrons on an artificial atom and on an artificial molecule made by one and two (single level) quantum dots connected by ideal leads. Specifically, we calculate the accumulated charge on the dots as function of the gate voltage ${\epsilon }_0,$ for various strengths of the electron-electron interaction U and of the hybridization between the dots and the (one-dimensional) leads $\gamma .$ For $\gamma <1\mathrm{}$ and $2\left(\gamma -1\right)\equiv {\epsilon }_{00}<{\epsilon }_0<0,$ there are no bound states. As ${\epsilon }_0$ decreases beyond ${\epsilon }_{00},$ the accumulated charge P in the two-electron ground state increases in gradual steps from 0 to 1 and then to 2. The values $P\sim 0$ represent an “insulating” state, where both electrons are bound to shallow states on the impurities. The value of $P\approx 1$ corresponds to a “metal,” with one electron localized on the dots and the other extended on the leads. The value of 2 corresponds to another “insulator,” with both electrons strongly localized. The width of the “metallic” regime diverges with U for the single dot, but remains very narrow for the double dot. These results are contrasted with the simple Coulomb blockade picture.