Electron Correlations in an Excited State of a Quantum Dot in a Uniform Magnetic Field

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Electron correlations in a two-electron two-dimensional ‘artificial atom’ or quantum dot (with harmonic confining potential) in the presence of a uniform magnetic field in an excited singlet state are studied via quantal density functional theory (QDFT). QDFT allows for the separation of the electron correlations due to the Pauli exclusion principle and Coulomb repulsion, as well as the determination of the contribution of these correlations to the kinetic energy. The QDFT mapping is from the excited state of the quantum dot to one of noninteracting fermions in their ground state possessing the same basic variables of the density and physical current density, and the same orbital and spin angular momentum. A detailed analysis of these correlations in terms of their quantal sources, the corresponding ‘classical’ fields, and resulting potentials and energies is presented. The key conclusions are that as in natural atoms, the contributions of the Pauli and Coulomb correlations relative to the total energy for the excited state, are less than but of the same order of magnitude as those for the ground state of a quantum dot. However, in contrast, the correlation-kinetic contributions are an order of magnitude greater than those for a quantum dot in its ground state. These correlations constitute nearly 75% of the kinetic and 25% of the total energy. This result is consistent with prior work on low electron density Wigner systems in three-dimensions in which correlation-kinetic effects too play a significant role. The significance of these correlations to traditional excited state density functional theory is noted.