Flat Thomas-Fermi artificial atoms

Ovchinnikov, Yu. N.; Halder, Avik; Kresin, Vladimir Z.

doi:10.1209/0295-5075/107/37001

Cited by 2 publications

(1 citation statement)

References 44 publications

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“…Treatments of the full TF equation incorporating edge effects for such systems as axially symmetric 2D quantum dots, planar metallic surfaces, metal clusters and 3D parabolically confined electrons can be found, e.g. in [6,[15][16][17][18].…”

Section: Semiclassical Theory and Its Classical Limitmentioning

confidence: 99%

Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots

Halder¹,

Kresin²

2016

J. Phys.: Condens. Matter

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We consider a droplet of electrons confined within an external harmonic potential well of elliptical or ellipsoidal shape, a geometry commonly encountered in work with semiconductor quantum dots and other nanoscale or mesoscale structures. For droplet sizes exceeding the effective Bohr radius, the dominant contribution to average system parameters in the Thomas-Fermi approximation comes from the potential energy terms, which allows us to derive expressions describing the electron droplet's shape and dimensions, its density, total and capacitive energy, and chemical potential. The analytical results are in very good agreement with experimental data and numerical calculations, and make it possible to follow the dependence of the properties of the system on its parameters (the total number of electrons, the axial ratios and curvatures of the confinement potential, and the dielectric constant of the material). An interesting feature is that the eccentricity of the electron droplet is not the same as that of its confining potential well.

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Section: Semiclassical Theory and Its Classical Limitmentioning

confidence: 99%

Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots

Halder¹,

Kresin²

2016

J. Phys.: Condens. Matter

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Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions

Le Doussal,

Smith,

Argaman

2024

SciPost Phys.

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We consider a system of NN spinless fermions, interacting with each other via a power-law interaction \epsilon/r^nϵ/rn, and trapped in an external harmonic potential V(r) = r^2/2V(r)=r2/2, in d=1,2,3d=1,2,3 dimensions. For any 0 < n < d+20<n<d+2, we obtain the ground-state energy E_NEN of the system perturbatively in \epsilonϵ, E_{N}=E_{N}^{≤ft(0)}+\epsilon E_{N}^{≤ft(1)}+O≤ft(\epsilon^{2})EN=EN≤ft(0)+ϵEN≤ft(1)+O≤ft(ϵ2). We calculate E_{N}^{≤ft(1)}EN≤ft(1) exactly, assuming that NN is such that the “outer shell” is filled. For the case of n=1n=1 (corresponding to a Coulomb interaction for d=3d=3), we extract the N \gg 1N≫1 behavior of E_{N}^{≤ft(1)}EN≤ft(1), focusing on the corrections to the exchange term with respect to the leading-order term that is predicted from the local density approximation applied to the Thomas-Fermi approximate density distribution. The leading correction contains a logarithmic divergence, and is of particular importance in the context of density functional theory. We also study the effect of the interactions on the fermions’ spatial density. Finally, we find that our result for E_{N}^{≤ft(1)}EN≤ft(1) significantly simplifies in the case where nn is even.

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Flat Thomas-Fermi artificial atoms

Cited by 2 publications

References 44 publications

Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots

Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots

Exact first-order effect of interactions on the ground-state energy of harmonically-confined fermions

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