Universal Properties in the Energy Spectrum of Semiconductor Quantum Dots

  • Alexander Odriazola Instituto Cibernética, Matemática y Física, Ciudad de La Habana
  • Alain Delgado Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear, Ciudad de la Habana
  • Augusto González Instituto Cibernética, Matemática y Física, Ciudad de La Habana

Abstract

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: Egs/(ℏω) ≈ N3/2fgsN1/4β, where the coupling constant, β , is the ratio between Coulomb and oscillator (ℏω) characteristic energies, and fgs 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/ϴ , satisfies also an approximate scaling relation a lá Thomas-Fermi, ϴ/ℏω ≈ Ng(N1/4β). We provide an analytic expression for fgs , based on two-point Padé approximants, and two-parameter fits for the g functions. The structure of the numerical library Libqdot, as well as the role of each Fortran 90 module is explained.

Published
Jun 15, 2009
How to Cite
ODRIAZOLA, Alexander; DELGADO, Alain; GONZÁLEZ, Augusto. Universal Properties in the Energy Spectrum of Semiconductor Quantum Dots. Revista Cubana de Física, [S.l.], v. 26, n. 1, p. 61-70, june 2009. ISSN 2224-7939. Available at: <https://revistacubanadefisica.org/index.php/rcf/article/view/RCF_26-1_61_2009>. Date accessed: 13 aug. 2022.
Section
Original Articles