Electronic structure calculation for N-electron quantum dots

McCarthy, Shane P.; Wang, Jingbo; Abbott, Paul

doi:10.1016/s0010-4655(01)00401-5

Cited by 11 publications

(7 citation statements)

References 17 publications

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“…Yannouleas and Landman 2, 3 also studied circularly symmetric quantum dots, using an unrestricted spin‐space Hartree–Fock approach, however, as the authors mentioned, it was unclear whether the symmetry breaking shown in their result was real or an artifact of the mean‐field approximation. McCarthy et al 4 developed a Hartree–Fock Mathematica package, which provided similar results as the earlier studies.…”

Section: Introductionsupporting

confidence: 52%

Spin‐adapted states: A basis for quantum dot structure calculation

Muhandiramge

Wang

2005

Int J of Quantum Chemistry

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ABSTRACT:The exact diagonalization method using a spin-adapted basis is employed to calculate the electronic structure of a multi-electron quantum dot. By isolating spin and orbital angular momentum eigenstates, we have significantly reduced the size of the matrices required in comparison with the standard configuration interaction method. A novel approach to the simplification of the interaction integrals that arise in the calculation is also presented, which allows exact evaluation of the Hamiltonian matrix required in the calculations. This Mathematica package permits accurate calculation of energy levels and wave functions for both ground and excited states of multiple electrons confined in a circular quantum dot.

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Section: Introductionsupporting

confidence: 52%

Spin‐adapted states: A basis for quantum dot structure calculation

Muhandiramge

Wang

2005

Int J of Quantum Chemistry

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“…McCarthy, Wang, and Abbott studied quantum dots 212—electrons trapped between two layers of semiconductor that display many properties of 2‐D atoms that make them potential components of efficient and precise lasers, nanodevices, and quantum computers 306. They described HF SCF calculations of the electronic states of N ‐electron quantum dots using MATHEMATICA 212.…”

Section: Lasers and Electronic Behavior Of Nanosystemsmentioning

confidence: 99%

Symbolic calculation in chemistry: Selected examples

Barnett

Capitani

Gathen

et al. 2004

Int J of Quantum Chemistry

247

174

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“…Both X H1L and X H2L are antisymmetric under permutation P 1, 2 , but X H1L is antisymmetric under permutation P 3, 4 , while X H2L is symmetric under permutation P 3,4 . This means A F X H2L vanishes but A F X H1L is nonzero.…”

Section: · the Antisymmetry And Representation Matricesmentioning

confidence: 99%

“…Examples of self-consistent field approaches in the literature include Yannouleas and Landman [2,3], who studied circularly symmetric quantum dots using an unrestricted spin-space Hartree-Fock approach, and McCarthy et al [4], who developed a Hartree-Fock Mathematica package. Macucci et al [5] studied quantum dots with up to 24 electrons using a mean-field local-density-functional approach, in which the spin exchange-correlation potential was approximated by an empirical polynomial expression.…”

Section: ‡ Introductionmentioning

confidence: 99%

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Electronic Structure of Multi-Electron Quantum Dots

Muhandiramge¹,

Wang²

2006

TMJ

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This article describes the use of the SACI package-a package for calculating the energy levels and wavefunctions of a multi-electron quantum dot modelled as a 2D harmonic well with electrons interacting through a Coulomb potential and under the influence of a perpendicular magnetic field. ‡ Introduction Quantum dots are artificially fabricated atoms, in which charge carriers are confined in all three dimensions just like electrons in real atoms. Consequently, they exhibit properties normally associated with real atoms such as quantised energy levels and shell structures. These properties are described by the electron wavefunctions whose evolution is governed by the Schrödinger equation and the Pauli exclusion principle.There are many methods available to solve the Schrödinger equation for multiple electrons. They roughly fall into the categories of the diagonalisation method, mean-field density-functional theory, and the self-consistent field approach. One of the first theoretical studies of quantum dots was by Pfannkuche et al. [1], who compared the results of Hartree-Fock self-consistent calculations and exact diagonalisation of the Hamiltonian for two electrons in a circularly symmetric parabolic potential. They found good agreement between the two methods for the triplet state but marked differences for the singlet state, indicating important spin correlations were not included properly in their HartreeFock model. This suggests that the proper treatment of electron spins is crucial for correctly obtaining the electronic structures in quantum dots.Examples of self-consistent field approaches in the literature include Yannouleas and Landman [2,3], who studied circularly symmetric quantum dots using an unrestricted spin-space Hartree-Fock approach, and McCarthy et al. [4], who developed a Hartree-Fock Mathematica package. Macucci et al. [5] studied quantum dots with up to 24 electrons using a mean-field local-density-functionalThe Mathematica Journal 10:2

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Electronic structure calculation for N-electron quantum dots

Cited by 11 publications

References 17 publications

Spin‐adapted states: A basis for quantum dot structure calculation

Spin‐adapted states: A basis for quantum dot structure calculation

Symbolic calculation in chemistry: Selected examples

Electronic Structure of Multi-Electron Quantum Dots

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