The violation of the Hund rule in semiconductor artificial atoms

Abstract

The unrestricted Pople-Nesbet approach for real atoms is adapted to quantum dots, the manmade artificial atoms, under applied magnetic field. Gaussian basis sets are used instead of the exact single-particle orbitals in the construction of the appropriated Slater determinants. Both system chemical potential and charging energy are calculated, as also the expected values for total and z-component in spin states. We have verified the validity of the energy shell structure as well as the Hund's rule state population at zero magnetic field. Above given fields, we have observed a violation of the Hund's rule by the suppression of triplets and quartets states at the 1p energy shell, taken as an example. We also compare our present results with those obtained using the LS-coupling scheme for low electronic occupations. We have focused our attention to ground-state properties for GaAs quantum dots populated up to forty electrons.

Few-electron semiconductor quantum dots with Gaussian confinement

“…We gave a systematic procedure for constructing the basis set for the self-consistent calculations with a given precision from the one-electron problem. The orbital energies provide an insight of the occupancy of the levels and show the fulfillment of the Hund rule in agreement with previous results obtained with other models [11,12].…”

“…More recently, a UHF calculation of ground state, chemical potential, and charging energies of electrons in an infinite spherical potential well, with and without magnetic field, has been reported [12]. However, the sharp discontinuity at the QD radius for such a potential well is not completely satisfactory both from a physical and a computational point of view, and some interpolating potentials [13] as well as smoothly varying potentials have been proposed [14][15][16][17][18].…”

A study of two-electron quantum dot spectrum using discrete variable representation method

“…Traditionally, the spatial confinement of a quantum system can be simulated by the imposition of the boundary conditions on the wave functions, [30][31][32][33][34] by changing the actual potential to a model one, 35 and by the introduction of a confinement potential; 36,37 some of these are employed to treat quantum dot systems. On the other hand, several geometric kinds are used as the confining potential in a quantum dot.…”

“…Various theoretical approaches have been used for this purpose. We can cite, among them, the Hartree approximation, 63,64 the Hartree-Fock procedure, 33,42,46,63,65,66 the configuration interaction ͑CI͒ method, 32,44,46,49 the density-functional theory, 45,50,58,65,67 the exact diagonalization, 51,68 the Green function, 69 the quantum Monte Carlo technique, 70,71 the analytical approaches, 56,72,73 the algebraic procedure, 74 the perturbation theory, 53 the WKB treatment, 75 and the randomphase approximation. 76 Most of these studies are limited to ground-state and few excited-state properties.…”

Hund and anti-Hund rules in circular molecules

“…Such a situation is known to exist, for example, in quantum dots, where the zero spin ground state is associated with a spin density wave [7], or in artificial molecules, when the increase of level splitting overcame the exchange energy gain by parallel spin alignment [9]. In semiconduc-tor artificial atoms under magnetic field, the Hund rule violation is noticed in connection with changes in the ground state symmetry [34], while in quadratically confining quantum dots is related to the modification of the localization properties of some singlet states [16].…”