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arXiv:0706.3354 · Physical Review B

Reliability of the Heitler-London approach for the exchange coupling between electrons in semiconductor nanostructures

André Saraiva, M. J. Calderón, Belita Koiller

Published Dec 21, 2007• 15 citations
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Abstract

We calculate the exchange coupling $J$ between electrons in a double-well potential in a two-dimensional semiconductor environment within the Heitler-London (HL) approach. Two functional forms are considered for the single-well potential. We show that by choosing an appropriate and relatively simple single-electron variational wave function it is possible, within the HL approach, to significantly improve the estimates for $J$. In all cases the present scheme overcomes the artifacts and limitations at short interdot distances, previously attributed to the HL method, where unphysical triplet ground states have been found, and leads to an overall agreement with analytic interpolated expressions for $J$ obtained for a donor-type model potential.

DOI
10.1103/physrevb.76.233302

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New Journal of Physics•Feb 21, 2006•37 citations
We calculate the exchange coupling JJJ between electrons in a double-well potential in a two-dimensional semiconductor environment within the Heitler-London (HL) approach. Two functional forms are considered for the single-well potential. We show that by choosing an appropriate and relatively simple single-electron variational wave function it is possible, within the HL approach, to significantly improve the estimates for JJJ. In all cases the present scheme overcomes the artifacts and limitations at short interdot distances, previously attributed to the HL method, where unphysical triplet ground states have been found, and leads to an overall agreement with analytic interpolated expressions for JJJ obtained for a donor-type model potential.
We calculate the exchange coupling J between electrons in a double-well potential in a two-dimensional semiconductor environment within the Heitler-London (HL) approach. Two functional forms are considered for the double-well potential. We show that by choosing an appropriate and relatively simple single-electron variational wave function it is possible, within the HL approach, to significantly improve the estimates for J. In all cases the present scheme overcomes the artifacts and limitations at short interdot distances, previously attributed to the HL method, where unphysical triplet ground states have been found, and leads to an overall agreement with analytic interpolated expressions for J obtained for a donor-type model potential.
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{\mathrm{H}}_{2}H2​ 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.
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.
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.
We report simple expressions for the exchange coupling in double quantum dots calculated within the Heitler-London and the Hund-Mulliken approximations using four different confining potentials. At large interdot distances and at large magnetic fields, the exchange coupling does not depend significantly on the details of the potentials. In contrast, at low fields and short distances, different behaviors of the exchange coupling can be attributed to particular features of the potentials. Our results may be useful as guidelines in numerical studies and in the modeling of experiments.
We report on our recent progress in applying semiconductor quantum dots for spin-based quantum computation, as proposed by Loss and DiVincenzo (1998 Phys. Rev. A 57 120). For the purpose of single-electron spin resonance, we study different types of single quantum dot devices that are designed for the generation of a local ac magnetic field in the vicinity of the dot. We observe photon-assisted tunnelling as well as pumping due to the ac voltage induced by the ac current driven through a wire in the vicinity of the dot, but no evidence for ESR so far. Analogue concepts for a double quantum dot and the hydrogen molecule are discussed in detail. Our experimental results in laterally coupled vertical double quantum dot device show that the Heitler–London model forms a good approximation of the two-electron wavefunction. The exchange coupling constant J is estimated. The relevance of this system for two-qubit gates, in particular the SWAP operation, is discussed. Density functional calculations reveal the importance of the gate electrode geometry in lateral quantum dots for the tunability of J in realistic two-qubit gates.