### Abstract

We theoretically investigate the ground-state electronic structure and the spin polarization of four electrons confined in two-dimensional (2D) polygonal quantum dots. We employ standard mean-field theory approaches using unrestricted Hartree-Fock (UHF) and density functional theory (DFT) calculations. Resonant UHF configuration interaction (res-UHF CI) calculations were also performed to incorporate the electron correlation more intuitively. Odd polygons (trigons and pentagons) preferentially generate the ground-state triplet as predicted by Hund's rule, whereas even polygons (tetragons, hexagons, and octagons) promote ground-state instability in the spin multiplicity and tend to produce an anti-Hund state of the ground-state singlet with strengthening of the interelectron interaction. The circle, a limited polygon having an infinite number of apexes, divides these odd and even polygons, and the ground-state instability can be well classified by the area of the polygon apexes that protrudes from an equisized circle.

Original language | English |
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Article number | 155316 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 85 |

Issue number | 15 |

DOIs | |

Publication status | Published - 2012 Apr 18 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*85*(15), [155316]. https://doi.org/10.1103/PhysRevB.85.155316

**Shape of polygonal quantum dots and ground-state instability in the spin polarization.** / Ishizuki, Masamu; Takemiya, Hannyo; Okunishi, Takuma; Takeda, Kyozaburo; Kusakabe, Kouichi.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 85, no. 15, 155316. https://doi.org/10.1103/PhysRevB.85.155316

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TY - JOUR

T1 - Shape of polygonal quantum dots and ground-state instability in the spin polarization

AU - Ishizuki, Masamu

AU - Takemiya, Hannyo

AU - Okunishi, Takuma

AU - Takeda, Kyozaburo

AU - Kusakabe, Kouichi

PY - 2012/4/18

Y1 - 2012/4/18

N2 - We theoretically investigate the ground-state electronic structure and the spin polarization of four electrons confined in two-dimensional (2D) polygonal quantum dots. We employ standard mean-field theory approaches using unrestricted Hartree-Fock (UHF) and density functional theory (DFT) calculations. Resonant UHF configuration interaction (res-UHF CI) calculations were also performed to incorporate the electron correlation more intuitively. Odd polygons (trigons and pentagons) preferentially generate the ground-state triplet as predicted by Hund's rule, whereas even polygons (tetragons, hexagons, and octagons) promote ground-state instability in the spin multiplicity and tend to produce an anti-Hund state of the ground-state singlet with strengthening of the interelectron interaction. The circle, a limited polygon having an infinite number of apexes, divides these odd and even polygons, and the ground-state instability can be well classified by the area of the polygon apexes that protrudes from an equisized circle.

AB - We theoretically investigate the ground-state electronic structure and the spin polarization of four electrons confined in two-dimensional (2D) polygonal quantum dots. We employ standard mean-field theory approaches using unrestricted Hartree-Fock (UHF) and density functional theory (DFT) calculations. Resonant UHF configuration interaction (res-UHF CI) calculations were also performed to incorporate the electron correlation more intuitively. Odd polygons (trigons and pentagons) preferentially generate the ground-state triplet as predicted by Hund's rule, whereas even polygons (tetragons, hexagons, and octagons) promote ground-state instability in the spin multiplicity and tend to produce an anti-Hund state of the ground-state singlet with strengthening of the interelectron interaction. The circle, a limited polygon having an infinite number of apexes, divides these odd and even polygons, and the ground-state instability can be well classified by the area of the polygon apexes that protrudes from an equisized circle.

UR - http://www.scopus.com/inward/record.url?scp=84860249084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860249084&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.85.155316

DO - 10.1103/PhysRevB.85.155316

M3 - Article

AN - SCOPUS:84860249084

VL - 85

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 15

M1 - 155316

ER -