The energy levels of laterally coupled parabolic double quantum dots are calculated for varying interdot distances. Electron-electron interaction is shown to dominate the spectra: In the diatomic molecule limit of large interdot separation, the two nearly degenerate singlet and triplet ground states are followed by a narrow band of four singlet and four triplet states. The energy spacing between the ground state and the first band of excited states scales directly with the confinement strength of the quantum wells. Similar level separation and band structure are found when the double dot is exposed to a perpendicular magnetic field. Conversely, an electric field parallel to the interdot direction results in a strong level mixing and a narrow transition from a localized state to a covalent diatomic molecular state.
The possibility to use perturbation theory to systematically improve calculations on circular quantum dots is investigated. A few different starting points, including Hartree-Fock, are tested and the importance of correlation is discussed. Quantum dots with up to 12 electrons are treated and the effects of an external magnetic field are examined. The sums over excited states are carried out with a complete finite radial basis set obtained through the use of B splines. The calculated addition energy spectra are compared with experiments and the implications for the filling sequence of the third shell are discussed in detail.
An implementation of the coupled-cluster single and double excitations (CCSD) method on two-dimensional quantum dots is presented. Advantages and limitations are studied through comparison with other high accuracy approaches, including another CCSD implementation, for up to twelve confined electrons. The possibility to effectively use a very large basis set is found to be an important advantage compared to full configuration interaction implementations. The error in the ground-state energy introduced by truncating at triple excitations is shown to be comparable to the difference between the results from the variation and diffusion Monte Carlo methods. Convergence of the iterative solution of the coupled cluster equations is found for surprisingly weak confinement strengths even when the full electron-electron interaction is treated as a perturbation. The relevance of the omitted excitations is investigated through comparison with full configuration interaction results.
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