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

TL;DR

This paper evaluates the Heitler-London approximation for calculating exchange coupling in semiconductor nanostructures, identifying its limitations and conditions under which it provides reliable results, especially relevant for quantum computing applications.

Contribution

The study systematically analyzes the accuracy of the Heitler-London approach across different potentials and dimensions, highlighting its failures and ranges of validity in semiconductor double well systems.

Findings

HL fails at large interatomic distances for atomic potentials.

Inadequate electron-electron correlation modeling causes inaccuracies.

Validity improves with increased interdot distance and in certain dimensional models.

Abstract

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 H2 molecule, the most dramatic failure occurs at very large interatomic distances, where HL predicts a triplet ground state, both in 3D and in 2D, coming from the absence of electron-electron correlation effects in this approach. For a 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 and consequently an inadequate representation of the two-particle states written, within HL, in terms of the ground state orbital at each isolated well. We find that in the double dot case, the range of validity of HL is improved (restricted) in a related 3D (1D) model, and that results always tend to become more reliable as the interdot distance increases. Our calculated exchange coupling is of relevance to the exchange gate quantum computer architectures in semiconductors.