The violation of the Hund's rule in semiconductor artificial atoms

TL;DR

This paper investigates the violation of Hund's rule in semiconductor quantum dots under magnetic fields, revealing suppression of certain spin states and comparing different coupling schemes for electrons.

Contribution

It adapts the unrestricted Pople-Nesbet approach with Gaussian basis sets to quantum dots, analyzing Hund's rule violations and spin state behaviors under magnetic fields.

Findings

Hund's rule is violated at high magnetic fields in quantum dots.

Suppression of triplet and quartet states at the 1p shell observed.

Comparison with LS-coupling scheme for low electron numbers.

Abstract

The unrestricted Pople-Nesbet approach for real atoms is adapted to quantum dots, the man-made 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.