Two-electron quantum dot in a magnetic field: Analytical results

Dineykhan, M.; Nazmitdinov, R. G.

doi:10.1103/physrevb.55.13707

Cited by 159 publications

(111 citation statements)

References 13 publications

(23 reference statements)

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“…First, we calculate the many-body states of a few electrons confined in V e (r) and show the formation of Wigner molecules owing to the strong correlation effect. [26][27][28][29][30] In the Wigner molecules of N electrons, the electrons behave as a single particle whose mass and charge are N times of those of an electron. In consequence, the energy of the ground state oscillates with Φ by the period of h/(N e), the so-called frac-tional AB effect.…”

Section: 25mentioning

confidence: 99%

Optical Aharonov-Bohm effect on Wigner molecules in type-II semiconductor quantum dots

2011

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We theoretically examine the magnetoluminescence from a trion and a biexciton in a type-II semiconductor quantum dot, in which holes are confined inside the quantum dot and electrons are in a ring-shaped region surrounding the quantum dot. First, we show that two electrons in the trion and biexciton are strongly correlated to each other, forming a Wigner molecule: Since the relative motion of electrons is frozen, they behave as a composite particle whose mass and charge are twice those of a single electron. As a result, the energy of the trion and biexciton oscillates as a function of magnetic field with half the period of the single-electron Aharonov-Bohm oscillation. Next, we evaluate the photoluminescence. Both the peak position and peak height change discontinuously at the transition of the many-body ground state, implying a possible observation of the Wigner molecule by the optical experiment.

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Section: 25mentioning

confidence: 99%

Optical Aharonov-Bohm effect on Wigner molecules in type-II semiconductor quantum dots

2011

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“…One of us has used the so-called oscillator representation method, perturbatively treating the residual interaction, to derive analytical expressions for the energy levels. 20 The paper is organized as follows. Section II introduces the magneto-parabolic units that allow one to trace the evolution of ground and excited states of artificial atoms at various conditions.…”

Section: Introductionmentioning

confidence: 99%

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

2004

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We provide a quantitative determination of the crystallization onset for two electrons in a parabolic two-dimensional confinement. This system is shown to be well described by a roto-vibrational model, Wigner crystallization occurring when the rotational motion gets decoupled from the vibrational one. The Wigner molecule thus formed is characterized by its moment of inertia and by the corresponding sequence of rotational excited states. The role of a vertical magnetic field is also considered. Additional support to the analysis is given by the Hartree-Fock phase diagram for the ground state and by the random-phase approximation for the moment of inertia and vibron excitations.

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“…The problem of two interacting electrons in a parabolic potential also admits exact solutions, but only for specific values of the oscillator frequency, as was shown by Taut 18,19,20 . The general case was treated analytically by the oscillator representation method 21 and variational calculations 22 , and studied numerically by the following approaches: 'exact' diagonalization using Fock-Darwin states 23,24 , integration of the radial motion Schroedinger equation after separating the center of mass motion 25 and a combination of both 26 . The results were compared with experimental data 24,26 and with the Hartree and HartreeFock methods 23 .…”

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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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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Two-electron quantum dot in a magnetic field: Analytical results

Cited by 159 publications

References 13 publications

Optical Aharonov-Bohm effect on Wigner molecules in type-II semiconductor quantum dots

Optical Aharonov-Bohm effect on Wigner molecules in type-II semiconductor quantum dots

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

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

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