Exchange coupling between two electrons in double quantum dot structures

General properties of the stability diagram and the exchange energy for a few-electron laterally coupled quantum dots in magnetic fields are investigated. The calculations are performed by numerically exact diagonalization of the Schrödinger equation. The behavior of the exchange energy extracted from the stability diagram obtained with the model potential is qualitatively consistent with a more comprehensive approach based on multiscale modeling of the whole quantum dot device interacting with its environment. In particular, the variation of the curvature and the double-triple point separation in the stability diagrams confirms the weakening of the inter-dot coupling with increasing magnetic fields. We also find that the exchange energy in experimental system shows profound variations as the confinement gate biases (effective barrier between the dots) are changed while the singlet-triplet transition is insensitive to the latter and remains fixed at about 1.5 T.