Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots

Puente, A.; Serra, Llorenç; Nazmitdinov, R. G.

doi:10.1103/physrevb.69.125315

Cited by 46 publications

(39 citation statements)

References 30 publications

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“…We hope that these variational functions will also be useful in developing methods of isolating spins of individual electrons and coupling them in a controllable manner in lateral quantum dots, as well as in other areas of research, e.g. to study with analytical expressions the formation of Wigner molecules 29,30 . We add two remark of a technical nature: First, in the case of a double quantum dot we were using the parameters β optimized in a single circular dot.…”

Section: Discussionmentioning

confidence: 99%

“…The mean field approaches were applied to the two-electron system also in the context of symmetry breaking they may induce and subsequent symmetry restoration by RPA 27 and projection techniques 28 . This theoretical problem, as well as the exact and numerical solutions mentioned above, proved relevant for a description of a Wigner molecule consisting of two electrons in a quantum dot 29,30 . 28,36,37 .…”

Section: Introductionmentioning

confidence: 99%

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Two electrons in a strongly coupled double quantum dot: From an artificial helium atom to a hydrogen molecule

Dybalski

Hawrylak

2005

Phys. Rev. B

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We study the formation of molecular states in a two-electron quantum dot as a function of the barrier potential dividing the dot. The increasing barrier potential drives the two electron system from an artificial helium atom to an artificial hydrogen molecule. To study this strongly coupled regime, we introduce variational wavefunctions which describe accurately two electrons in a single dot, and then study their mixing induced by the barrier. The evolution of the singlet-triplet gap with the barrier potential and with an external magnetic field is analyzed.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two electrons in a strongly coupled double quantum dot: From an artificial helium atom to a hydrogen molecule

Dybalski

Hawrylak

2005

Phys. Rev. B

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“…Indeed, later calculations confirmed that these effects are largely artifacts of the approximations used. 23,25,26,27,28,29,30 Projection methods were then used to restore symmetries as a second stage of the UHF calculations. 31,32,33,34,35 DFT has been pushed toward the large r s limit through the average spin density approximation.…”

Section: Introductionmentioning

confidence: 99%

Incipient Wigner localization in circular quantum dots

et al. 2007

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We study the development of electron-electron correlations in circular quantum dots as the density is decreased. We consider a wide range of both electron number, N ≤ 20, and electron gas parameter, rs < ∼ 18, using the diffusion quantum Monte Carlo technique. Features associated with correlation appear to develop very differently in quantum dots than in bulk. The main reason is that translational symmetry is necessarily broken in a dot, leading to density modulation and inhomogeneity. Electron-electron interactions act to enhance this modulation ultimately leading to localization. This process appears to be completely smooth and occurs over a wide range of density. Thus there is a broad regime of "incipient" Wigner crystallization in these quantum dots. Our specific conclusions are: (i) The density develops sharp rings while the pair density shows both radial and angular inhomogeneity. (ii) The spin of the ground state is consistent with Hund's (first) rule throughout our entire range of rs for all 4 ≤ N ≤ 20. (iii) The addition energy curve first becomes smoother as interactions strengthen -the mesoscopic fluctuations are damped by correlation -and then starts to show features characteristic of the classical addition energy. (iv) Localization effects are stronger for a smaller number of electrons. (v) Finally, the gap to certain spin excitations becomes small at the strong interaction (large rs) side of our regime.

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“…Evidently, the effective confinement (Ω) increases with the magnetic field, and the contribution of the constant electron-electron interaction becomes weaker. Formally, if we introduce the characteristic length of the effective confinement ℓ Ω = /m * Ω, the parameter λ Ω = ℓ Ω /a * (R W at B = 0) determines the relative strength of the Coulomb interaction at a given ef- fective confinement [43]. This parameter decreases with an increase of the magnetic field strength.…”

Section: The Dependence Of the Measure E On The Magnetic Field Strmentioning

confidence: 99%

Magnetic alteration of entanglement in two-electron quantum dots

Simonović

Nazmitdinov

2015

Phys. Rev. A

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Quantum entanglement is analyzed thoroughly in the case of the ground and lowest states of two-electron axially symmetric quantum dots under a perpendicular magnetic field. The individualparticle and the center-of-mass representations are used to study the entanglement variation at the transition from interacting to noninteracting particle regimes. The mechanism of symmetry breaking due to the interaction, that results in the states with symmetries related to the later representation only, being entangled even at the vanishing interaction, is discussed. The analytical expression for the entanglement measure based on the linear entropy is derived in the limit of noninteracting electrons. It reproduces remarkably well the numerical results for the lowest states with the magnetic quantum number M ≥ 2 in the interacting regime. It is found that the entanglement of the ground state is a discontinuous function of the field strength. A method to estimate the entanglement of the ground state, characterized by the quantum number M , with the aid of the magnetic field dependence of the addition energy is proposed.

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Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots

Cited by 46 publications

References 30 publications

Two electrons in a strongly coupled double quantum dot: From an artificial helium atom to a hydrogen molecule

Two electrons in a strongly coupled double quantum dot: From an artificial helium atom to a hydrogen molecule

Incipient Wigner localization in circular quantum dots

Magnetic alteration of entanglement in two-electron quantum dots

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