Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2008-08-07
Phys. Rev. B 78 (2008) 205320
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
final version, to appear in Phys. Rev. B
Scientific paper
10.1103/PhysRevB.78.205320
In a two-dimensional parabolic quantum dot charged with $N$ electrons, Thomas-Fermi theory states that the ground-state energy satisfies the following non-trivial relation: $E_{gs}/(\hbar\omega)\approx N^{3/2} f_{gs}(N^{1/4}\beta)$, where the coupling constant, $\beta$, is the ratio between Coulomb and oscillator ($\hbar\omega$) characteristic energies, and $f_{gs}$ is a universal function. We perform extensive Configuration Interaction calculations in order to verify that the exact energies of relatively large quantum dots approximately satisfy the above relation. In addition, we show that the number of energy levels for intraband and interband (excitonic and biexcitonic) excitations of the dot follows a simple exponential dependence on the excitation energy, whose exponent, $1/\Theta$, satisfies also an approximate scaling relation {\it a la} Thomas-Fermi, $\Theta/(\hbar\omega)\approx N^{-\gamma} g(N^{1/4}\beta)$. We provide an analytic expression for $f_{gs}$, based on two-point Pad\'e approximants, and two-parameter fits for the $g$ functions.
Delgado Alain
Gonzalez Augusto
Odriazola Alexander
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