### Abstract

We theoretically studied the validity of Hund's first and second rules in the three-dimensionally spherically parabolic quantum dot (3D-SPQD). We extended the unrestricted Hartree-Fock (exUHF) approach in order to determine the ground state while conserving the expectation values of the total orbital angular momentum 〈L̂^{2}〉 and its z component 〈L̂_{z}〉 during the scf procedure. We applied this exUHF method to a GaAs 3D-SPQD and obtained the ground-state energy spectra. Our calculation reveals that, among those states having the largest spin multiplicities, the state giving the largest value of 〈L̂ ^{2}〉 is energetically more stable than the others having a smaller value of 〈L̂^{2}〉; that is the spin filling in the 3D-SPQD obeys Hund's first and second rules.

Original language | English |
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Pages (from-to) | 4424-4433 |

Number of pages | 10 |

Journal | Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers |

Volume | 43 |

Issue number | 7 A |

DOIs | |

Publication status | Published - 2004 Jul 1 |

### Keywords

- Hund's rule
- Quantum dot orbitals
- Spherical quantum dot
- Spin-filling
- Total orbital angular momentum
- Unrestricted Hartree-Fock method

### ASJC Scopus subject areas

- Engineering(all)
- Physics and Astronomy(all)