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

We theoretically investigate the properties of a two-electron system confined in the three-dimensional potential of coupled quantum dots formed in a quantum wire. For this purpose, we implement a variational Heitler-London method that minimizes the system energies with respect to variational parameters in electron trial wave functions. We find that tunnel and exchange couplings rapidly decay with increasing interdot distance and interdot barrier height. In the quasi-one-dimensional limit achieved by reducing the wire diameter, we find that the overlap between the dots decreases, which results in a drop in the exchange coupling. We also discuss the validity of our variational Heitler-London method with respect to the model potential parameters; we find good agreement between our results and available experimental data.