Exchange coupling in semiconductor nanostructures:: Validity and limitations of the Heitler-London approach

The exchange coupling of the spins of two electrons in double-well potentials in a semiconductor background is calculated within the Heitler-London (HL) approximation. Atomic and quantum dot types of confining potentials are considered, and a systematic analysis for the source of inaccuracies in the HL approach is presented. For the strongly confining Coulombic atomic potentials in the H-2 molecule, the most dramatic failure occurs at very large interatomic distances, where the HL approximation predicts a triplet ground state, in both three and two dimensions, coming from the absence of electron-electron correlation effects in this approach. For a two-dimensional (2D) double-well potential, failures are identified at relatively smaller interdot distances, and may be attributed to the less confining nature of the potential, leading to larger overlap. We find that in the double-dot case, the range of validity of the HL approximation is improved (restricted) in a related 3D (1D) model, and that results always tend to become more reliable as the interdot distance increases. Our analysis of the exchange coupling is of relevance to the exchange-gate quantum computer architectures in semiconductors.