### Abstract

We present a theoretical study of the ground state electronic structure and the spin polarization for four electrons confined in two-dimensional (2D) square quantum dots (SQDs). We employ standard mean field theory (MFT) approaches using the unrestricted Hartree-Fock (UHF) and density functional theory calculations. The resonant UHF configuration interaction (res-UHF CI) calculation was also performed in order to incorporate the electron correlation more intuitively. The MFT ground state is expected to be spin-polarized when SQDs have a small confinement length L or aspect ratio δ = L _{x}/L_{y} = 1, in agreement with Hund's rule. In contrast, the spin-unpolarized ground state singlet is expected in all in other SQDs. Thus, the MFT calculations produce the anti-Hund state, where the spin-density wave forms having the zero of the total spin, even though the SQD has the point group symmetry D_{4h}. However, the res-UHF CI calculation restores the geometrical symmetry in the resulting ground state when the Coulomb interaction is strengthened. Nevertheless, the res-UHF CI ground state maintains the zero total spin. Thus, ground state instability is expected in the spin-polarization of the SQD system, which eventually violates Hund's rule in accordance with the Coulomb interaction.

Original language | English |
---|---|

Article number | 085001 |

Journal | Japanese Journal of Applied Physics |

Volume | 50 |

Issue number | 8 PART 1 |

DOIs | |

Publication status | Published - 2011 Aug |

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### ASJC Scopus subject areas

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

### Cite this

*Japanese Journal of Applied Physics*,

*50*(8 PART 1), [085001]. https://doi.org/10.1143/JJAP.50.085001

**Ground state instability in spin polarization for electrons confined in two-dimensional square quantum dots.** / Negishi, Yhuki; Ishizuki, Masamu; Okunishi, Takuma; Takeda, Kyozaburo.

Research output: Contribution to journal › Article

*Japanese Journal of Applied Physics*, vol. 50, no. 8 PART 1, 085001. https://doi.org/10.1143/JJAP.50.085001

}

TY - JOUR

T1 - Ground state instability in spin polarization for electrons confined in two-dimensional square quantum dots

AU - Negishi, Yhuki

AU - Ishizuki, Masamu

AU - Okunishi, Takuma

AU - Takeda, Kyozaburo

PY - 2011/8

Y1 - 2011/8

N2 - We present a theoretical study of the ground state electronic structure and the spin polarization for four electrons confined in two-dimensional (2D) square quantum dots (SQDs). We employ standard mean field theory (MFT) approaches using the unrestricted Hartree-Fock (UHF) and density functional theory calculations. The resonant UHF configuration interaction (res-UHF CI) calculation was also performed in order to incorporate the electron correlation more intuitively. The MFT ground state is expected to be spin-polarized when SQDs have a small confinement length L or aspect ratio δ = L x/Ly = 1, in agreement with Hund's rule. In contrast, the spin-unpolarized ground state singlet is expected in all in other SQDs. Thus, the MFT calculations produce the anti-Hund state, where the spin-density wave forms having the zero of the total spin, even though the SQD has the point group symmetry D4h. However, the res-UHF CI calculation restores the geometrical symmetry in the resulting ground state when the Coulomb interaction is strengthened. Nevertheless, the res-UHF CI ground state maintains the zero total spin. Thus, ground state instability is expected in the spin-polarization of the SQD system, which eventually violates Hund's rule in accordance with the Coulomb interaction.

AB - We present a theoretical study of the ground state electronic structure and the spin polarization for four electrons confined in two-dimensional (2D) square quantum dots (SQDs). We employ standard mean field theory (MFT) approaches using the unrestricted Hartree-Fock (UHF) and density functional theory calculations. The resonant UHF configuration interaction (res-UHF CI) calculation was also performed in order to incorporate the electron correlation more intuitively. The MFT ground state is expected to be spin-polarized when SQDs have a small confinement length L or aspect ratio δ = L x/Ly = 1, in agreement with Hund's rule. In contrast, the spin-unpolarized ground state singlet is expected in all in other SQDs. Thus, the MFT calculations produce the anti-Hund state, where the spin-density wave forms having the zero of the total spin, even though the SQD has the point group symmetry D4h. However, the res-UHF CI calculation restores the geometrical symmetry in the resulting ground state when the Coulomb interaction is strengthened. Nevertheless, the res-UHF CI ground state maintains the zero total spin. Thus, ground state instability is expected in the spin-polarization of the SQD system, which eventually violates Hund's rule in accordance with the Coulomb interaction.

UR - http://www.scopus.com/inward/record.url?scp=80052017580&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052017580&partnerID=8YFLogxK

U2 - 10.1143/JJAP.50.085001

DO - 10.1143/JJAP.50.085001

M3 - Article

AN - SCOPUS:80052017580

VL - 50

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 - 8 PART 1

M1 - 085001

ER -