### 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 |
---|---|

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 |

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### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

**Hund's first and second rules in spherical quantum dots (I) in the zero-magnetic field.** / Asari, Yusuke; Takeda, Kyozaburo; Tamura, Hiroyuki.

Research output: Contribution to journal › Article

*Japanese Journal of Applied Physics, Part 1: Regular Papers and Short Notes and Review Papers*, vol. 43, no. 7 A, pp. 4424-4433. https://doi.org/10.1143/JJAP.43.4424

}

TY - JOUR

T1 - Hund's first and second rules in spherical quantum dots (I) in the zero-magnetic field

AU - Asari, Yusuke

AU - Takeda, Kyozaburo

AU - Tamura, Hiroyuki

PY - 2004/7

Y1 - 2004/7

N2 - 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 〈L̂2〉 and its z component 〈L̂z〉 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 〈L̂2〉; that is the spin filling in the 3D-SPQD obeys Hund's first and second rules.

AB - 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 〈L̂2〉 and its z component 〈L̂z〉 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 〈L̂2〉; that is the spin filling in the 3D-SPQD obeys Hund's first and second rules.

KW - Hund's rule

KW - Quantum dot orbitals

KW - Spherical quantum dot

KW - Spin-filling

KW - Total orbital angular momentum

KW - Unrestricted Hartree-Fock method

UR - http://www.scopus.com/inward/record.url?scp=4644317057&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4644317057&partnerID=8YFLogxK

U2 - 10.1143/JJAP.43.4424

DO - 10.1143/JJAP.43.4424

M3 - Article

VL - 43

SP - 4424

EP - 4433

JO - Japanese Journal of Applied Physics, Part 1: Regular Papers & Short Notes

JF - Japanese Journal of Applied Physics, Part 1: Regular Papers & Short Notes

SN - 0021-4922

IS - 7 A

ER -