Energy spectra of two electrons in a harmonic quantum dot

Merkt, U.; Huser, J.; Wagner, Mathias

doi:10.1103/physrevb.43.7320

Cited by 425 publications

(288 citation statements)

References 13 publications

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“…This can be understood as follows. 95 On the one hand, a stronger confinement increases the Coulomb strength due to smaller effective particle distances |r 1 − r 2 | in H C . This is an effect somewhat linear in l −1 0 .…”

Section: Results: Biased Double Dotmentioning

confidence: 99%

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

2012

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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.

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Section: Results: Biased Double Dotmentioning

confidence: 99%

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

2012

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“…Because of this property quantum dots are regarded as potential sources for lasers [12,13] and quantum computers [14,15]. Indeed, it has been demonstrated computationally that the energy-level structure of quantum dots changes strongly for different strength of confinement [4,[16][17][18][19][20]. For the strong limit the confining potential dominates the energy spectrum and the electron-electron interaction plays only a minor role.…”

Section: Introductionmentioning

confidence: 99%

“…This model allows the wave functions of the electrons to be visualized in a two-dimensional plane and permits a detailed analysis of the correlation of the confined electrons. A Gaussian potential has been chosen as confining potential that is approximated in the low energy region by a harmonic-oscillator potential typically used for modeling semiconductor quantum dots [4,17,24]. Introducing anharmonicity into the confining potential is important for simulating realistic confining potentials [25] as well as for studying the breakdown of the generalized Kohn theorem [24,[26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Spectra and correlated wave functions of two electrons confined in a quasi-one-dimensional nanostructure

Sako

Diercksen

2007

Phys. Rev. B

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The energy spectra and wave functions of two electrons confined by a quasi-one-dimensional Gaussian potential have been calculated for different strength of confinement ω z and anharmonicity by using the quantum chemical full configuration interaction method employing a Cartesian anisotropic Gaussian basis set. The energy spectra for a nearly harmonic Gaussian potential have been studied and analyzed in three regimes of ωz, namely, large (ωz = 5.0) medium (ωz = 1.0), and small (ωz = 0.1). For large and medium ω z the energy spectrum shows a band structure which is characterized by the polyad quantum number v p while for small ω z it is characterized by the extended polyad quantum number v * p . The energy levels for small ω z form doublet pairs each of which consists of a pair of singlet and triplet states. The nodal pattern of their wave functions are almost identical to each other except for their phases. The energy spectra for the strongly anharmonic Gaussian potential look quite similar to those of the nearly harmonic case except that an irregular level structure appears in the high energy region for ω z = 0.1. The wave functions of the states in this high energy region have curved nodal lines which align along a pair of bent nodal coordinates. Two types of pairs of bent nodal coordinates have been identified, namely, those passing through the valley of the confining potential and the others passing on the hillside. It is shown that the wave functions with these nodal coordinates correspond to new types of classical local -mode motions of electrons.

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“…The spectral properties of harmonic-oscillator quantum dots or parabolic quantum dots [6,7] are exotic as compared to those of atoms in that the oscillator strengths are concentrated only in one dipole-allowed transition. This property of harmonicoscillator quantum dots is a direct consequence of the generalized Kohn theorem [6,[8][9][10][11][12][13] and is independent of the number of electrons, the strength of the confinement and the form of the electron-electron interaction potential.…”

Section: Introductionmentioning

confidence: 99%

Distribution of oscillator strength in Gaussian quantum dots: An energy flow from center-of-mass mode to internal modes

2006

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The energy spectra and oscillator strengths of two, three and four electrons confined by a quasitwo-dimensional attractive Gaussian-type potential have been calculated for different strength of confinement ω and potential depth D by using the quantum chemical configuration interaction (CI) method employing a Cartesian anisotropic Gaussian basis set. A substantial red shift has been observed for the transitions corresponding to the excitation into the center-of-mass mode (CM). The oscillator strengths, concentrated exclusively in the center-of-mass excitation in the harmonic limit, are distributed among the near-lying transitions as a result of the breakdown of the generalized Kohn theorem. The distribution of the oscillator strengths is limited to the transitions located in the lower-energy region when ω is large but it extends towards the higher-energy region when ω becomes small. The analysis of the CI wavefunctions shows that all states in the energy range covered by the present study can be classified according the polyad quantum number vp. It is shown that the distribution of the oscillator strengths for large ω occurs among transitions involving excited states with the same value of vp as the center-of-mass excited state, vp,cm, while it occurs among transitions involving the excited states with vp = vp,cm and vp = vp,cm + 2 for small ω.

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Energy spectra of two electrons in a harmonic quantum dot

Cited by 425 publications

References 13 publications

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

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

Spectra and correlated wave functions of two electrons confined in a quasi-one-dimensional nanostructure

Distribution of oscillator strength in Gaussian quantum dots: An energy flow from center-of-mass mode to internal modes

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