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arXiv:cond-mat/0512321 · Physical Review B

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

M. J. Calderón, Belita Koiller, S. Das Sarma

Published Jul 17, 2006• 19 citations
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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 ${\mathrm{H}}_{2}$ 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.

DOI
10.1103/physrevb.74.045310

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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 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.
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 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 consider a quantum-gate mechanism based on electron spins in coupled semiconductor quantum dots. Such gates provide a general source of spin entanglement and can be used for quantum computers. We determine the exchange coupling JJJ in the effective Heisenberg model as a function of magnetic (B)(B)(B) and electric fields, and of the interdot distance aaa within the Heitler-London approximation of molecular physics. This result is refined by using sp\mathrm{sp}sp hybridization, and by the Hund-Mulliken molecular-orbit approach, which leads to an extended Hubbard description for the two-dot system that shows a remarkable dependence on BBB and aaa due to the long-range Coulomb interaction. We find that the exchange JJJ changes sign at a finite field (leading to a pronounced jump in the magnetization) and then decays exponentially. The magnetization and the spin susceptibilities of the coupled dots are calculated. We show that the dephasing due to nuclear spins in GaAs can be strongly suppressed by dynamical nuclear-spin polarization and/or by magnetic fields.
Exchange interaction has been studied for electrons in coupled quantum dots (QDs) by a configuration interaction method using confinement potentials with different profiles. The confinement potential has been parametrized by a two-centre power-exponential function, which allows us to investigate various types of QDs described by either soft or hard potentials of different ranges. For the soft (Gaussian) confinement potential the exchange energy decreases with increasing interdot distance due to the decreasing interdot tunnelling. For the hard (rectangular-like) confinement potential we have found a non-monotonic behaviour of the exchange interaction as a function of distance between the confinement potential centres. In this case, the exchange interaction energy exhibits a pronounced maximum for the confinement potential profile which corresponds to the nanostructure composed of the small inner QD with a deep potential well embedded in the large outer QD with a shallow potential well. This effect results from the strong localization of electrons in the inner QD, which leads to the large singlet–triplet splitting. Implications of this finding for quantum logic operations have been discussed.