Phase transitions of a few-electron system in a spherical quantum dot

Sundqvist, P. A.; Volkov, S. Yu.; Lozovik, Yu. E.; Willander, Magnus

doi:10.1103/physrevb.66.075335

Cited by 15 publications

(19 citation statements)

References 22 publications

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“…For example, using Table I and Eq. (7), the CF magic numbers in the interval 15 ≤ L ≤ 45 (m = 1) are found to be the following nine, 67 15, 21,25,27,30,33,35,39,45.…”

Section: A Predictions Of Magic Angular Momentamentioning

confidence: 97%

Two-dimensional quantum dots in high magnetic fields: Rotating-electron-molecule versus composite-fermion approach

Yannouleas

Landman

2003

Phys. Rev. B

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Exact diagonalization results are reported for the lowest rotational band of N = 6 electrons in strong magnetic fields in the range of high angular momenta 70 ≤ L ≤ 140 (covering the corresponding range of fractional filling factors 1/5 ≥ ν ≥ 1/9). A detailed comparison of energetic, spectral, and transport properties (specifically, magic angular momenta, radial electron densities, occupation number distributions, overlaps and total energies, and exponents of current-voltage power law) shows that the recently discovered rotating-electron-molecule wave functions [Phys. Rev. B 66, 115315 (2002)] provide a superior description compared to the composite-fermion/Jastrow-Laughlin ones.

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“…For example, using Table I and Eq. (7), the CF magic numbers in the interval 15 ≤ L ≤ 45 (m = 1) are found to be the following nine, 67 15, 21,25,27,30,33,35,39,45.…”

Section: A Predictions Of Magic Angular Momentamentioning

confidence: 97%

Two-dimensional quantum dots in high magnetic fields: Rotating-electron-molecule versus composite-fermion approach

Yannouleas

Landman

2003

Phys. Rev. B

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“…4,6 Numerical computations of the ground-and excited-state energies of the three-electron harmonium atom have also been carried out, involving methods ranging from the HartreeFock approximation 21 and low-level electron-correlation approaches 22 to Monte Carlo calculations 23 and the full configuration interaction (FCI) employed in conjunction with extrapolation to the complete basis set (CBS). 24 The FCI/CBS study, in which approximate energies of the 2 P − and 4 P + states have been computed for 12 values of ω between 0.1 and 1000.0, has uncovered both advantages and disadvantages of using uncorrelated Gaussian basis sets in electronic structure calculations on harmonium atoms.…”

Section: Introductionmentioning

confidence: 99%

The three-electron harmonium atom: The lowest-energy doublet and quadruplet states

Ciosłowski

Strasburger

Matito

2012

The Journal of Chemical Physics

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Calculations of sub-μhartree accuracy employing explicitly correlated Gaussian lobe functions produce comprehensive data on the energy E(ω), its components, and the one-electron properties of the two lowest-energy states of the three-electron harmonium atom. The energy computations at 19 values of the confinement strength ω ranging from 0.001 to 1000.0, used in conjunction with a recently proposed robust interpolation scheme, yield explicit approximants capable of estimating E(ω) and the potential energy of the harmonic confinement within a few tenths of μhartree for any ω ≥ 0.001, the respective errors for the kinetic energy and the potential energy of the electronelectron repulsion not exceeding 2 μhartrees. Thanks to the correct ω → 0 asymptotics incorporated into the approximants, comparable accuracy is expected for values of ω smaller than 0.001. Occupation numbers of the dominant natural spinorbitals and two different measures of electron correlation are also computed.

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“…Notice, however, that Ref. 51 obtained an incomplete wave function, since the companion step of restoration of the rotational symmetry was not considered (see section VI below).…”

Section: 49mentioning

confidence: 99%

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

2003

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We present a group theoretical study of the symmetrybroken unrestricted Hartree-Fock orbitals and electron densities in the case of a two-dimensional N -electron single quantum dot (with and without an external magnetic field). The breaking of rotational symmetry results in canonical orbitals that (1) are associated with the eigenvectors of a Hückel hamiltonian having sites at the positions determined by the equilibrium molecular configuration of the classical N -electron problem, and (2) transform according to the irreducible representations of the point group specified by the discrete symmetries of this classical molecular configuration. Through restoration of the total-spin and rotational symmetries via post-Hartree-Fock projection techniques, we show that the point-group discrete symmetry of the unrestricted Hartree-Fock wave function underlies the appearance of magic angular momenta (familiar from exact-diagonalization studies) in the excitation spectra of the quantum dot. Furthermore, this two-step symmetrybreaking/symmetry-restoration method accurately describes the energy spectra associated with the magic angular momenta.

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Phase transitions of a few-electron system in a spherical quantum dot

Cited by 15 publications

References 22 publications

Two-dimensional quantum dots in high magnetic fields: Rotating-electron-molecule versus composite-fermion approach

Two-dimensional quantum dots in high magnetic fields: Rotating-electron-molecule versus composite-fermion approach

The three-electron harmonium atom: The lowest-energy doublet and quadruplet states

Group theoretical analysis of symmetry breaking in two-dimensional quantum dots

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