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We theoretically investigate the properties of a two-electron system confinedin the three-dimensional potential of coupled quantum dots formed in a quantumwire. For this purpose, we implement a variational Heitler-London method thatminimize the system energies with respect to variational parameters in electrontrial wavefunctions. We find that tunneling and exchange couplingsexponentially decay with increasing inter-dot distance and inter-dot barrierheight. In the quasi-one-dimensional limit achieved by reducing the wirediameter, we find that the overlap between the dots decreases, which results ina drop of the exchange coupling. We also discuss the validity of ourvariational Heitler-London method with respect to the model potentialparameters, and compare our results with available experimental data to findgood agreement between the two approaches.

Size effects in the exchange coupling between two electrons in quantum wire quantum dots