Failure of standard approximations of the exchange coupling in nanostructures

Pedersen, Jesper Goor; Flindt, Christian; Mortensen, N. Asger; Jauho, Antti–Pekka

doi:10.1103/physrevb.76.125323

Cited by 33 publications

(75 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…10,11,12,13,14,15,16,17,18 We show here that the limitations of previous studies are mainly due to the choice of the single-particle wave functions rather than being intrinsic to the HL method.…”

Section: 9mentioning

confidence: 68%

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

2007

View full text Add to dashboard Cite

We calculate the exchange coupling J between electrons in a double-well potential in a twodimensional 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.PACS numbers: 03.67. Lx, 73.20.Hb, 85.35.Gv, For quantum computer architectures based on electron spins, 1,2,3,4,5 two-qubit logical gates can be implemented by entangling electrons bound to neighboring potential wells through a transient exchange coupling.1 Accurate evaluation of this coupling-namely, the difference in energy between triplet and singlet two-electron ground-state configurations-requires numerically intensive calculations which are highly dependent on the physical parameters of the system. Such parameters are in general not precisely known, and for this reason the Heitler-London (HL) method 6,7 is of special interest in providing intuitive insight and computational simplicity for prospective estimations of the exchange coupling strength over a wide range of potential-related parameters. This is particularly important for gated quantum dots in which the exact form of the potentials, produced by electrodes over a two-dimensional electron gas (2DEG), has to be modeled. Also, within the HL approach, it is in principle possible to explore the exchange energy at large interwell distances, which would require great computational effort in more accurate methods.Prospective model calculations based on the HL method have led to an inaccurate exchange coupling asymptotic (large interdot distances) decay and to unphysical artifacts such as predicting a triplet ground state at short interwell distances (negative-J anomaly). 8,9It is usually argued that these problems are due to limitations in the HL approach, 8,9 and it has been suggested that they could only be overcome within more complex quantum chemistry or numerical methods. 10,11,12,13,14,15,16,17,18 We show here that the limitations of previous studies are mainly due to the choice of the single-particle wave functions rather than being intrinsic to the HL method.Within the single-valley effective mass approximation, the Hamiltonian for an electron trapped in a single cylindrically symmetric well potential in a 2D semiconductor environment is given by h(ρ) = − ∂ 2 ∂ρ 2 + V (ρ), where ρ = x 2 + y 2 is the distance from the well minimum, and the energies and distances are given in atomic units Ry * = m ⊥ e 4 /2h 2 ε 2 and a * =h 2 ε/m ⊥ e 2 , respectively. Here the semiconductor is characterized by m ⊥ , the transverse eff...

show abstract

Section: 9mentioning

confidence: 68%

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

2007

View full text Add to dashboard Cite

show abstract

“…consists of the biquadratic confinement 51,72 and the external electric field. For E = 0, the potential is minimal at ±d.…”

Section: Modelmentioning

confidence: 99%

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

2012

View full text Add to dashboard Cite

Highly accurate numerical results of phonon-induced two-electron spin relaxation in silicon double quantum dots are presented. The relaxation, enabled by spin-orbit coupling and the nuclei of 29 Si (natural or purified abundance), is investigated for experimentally relevant parameters, the interdot coupling, the magnetic field magnitude and orientation, and the detuning. We calculate relaxation rates for zero and finite temperatures (100 mK), concluding that our findings for zero temperature remain qualitatively valid also for 100 mK. We confirm the same anisotropic switch of the axis of prolonged spin lifetime with varying detuning as recently predicted in GaAs. Conditions for possibly hyperfine-dominated relaxation are much more stringent in Si than in GaAs. For experimentally relevant regimes, the spin-orbit coupling, although weak, is the dominant contribution, yielding anisotropic relaxation rates of at least two orders of magnitude lower than in GaAs.

show abstract

“…This behavior is well known for the Heitler-London approximation. 11,13 Eventually, the Heitler-London approximation also breaks down for the potential V q and predicts a negative exchange coupling, however, only at lower confinement energies ͑not shown͒. At large confinement energies, the potentials V min and V q Ј give nonnegative, finite values of the exchange coupling at short distances.…”

Section: Resultsmentioning

confidence: 99%

“…The first three potentials have previously been considered in the literature. 2,5,[7][8][9][10][11][12][13] The following approximations take as starting point the uncoupled dots at large distances, d ӷ r 0 . For the left or right dot centered at r L/R = ͑ϯd ,0͒, the ground state can be written 14 as …”

Section: Modelmentioning

confidence: 99%

See 1 more Smart Citation

Influence of confining potentials on the exchange coupling in double quantum dots

et al. 2010

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Failure of standard approximations of the exchange coupling in nanostructures

Cited by 33 publications

References 22 publications

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

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

Theory of spin relaxation in two-electron laterally coupled Si/SiGe quantum dots

Influence of confining potentials on the exchange coupling in double quantum dots

Contact Info

Product

Resources

About