Engineering Exchange Interaction in Coupled Elongated Quantum Dots

Coupled elongated quantum dots containing up to two electrons are studied with a model potential in magnetic fields. Single and two particle Schrödinger equations are solved using numerical exact diagonolization to obtain the exchange energy and chemical potentials. Special emphasis is placed on the variation of the exchange interaction between the two electrons as the dot shape is modified. As the aspect ratio between the directions perpendicular and parallel to the coupling direction of the double dots increases, the exchange energy at zero magnetic field increases, while the magnetic field at the singlet-triplet transition decreases. By investigating the charge stability diagram, we obtain the inter-dot coupling strength for various configurations. We also show the onset of electron localization into one dot due to inter-dot detuning and increasing magnetic fields.