The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
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Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Engineering Physics and Mathematics for public examination and debate in Auditorium E at Helsinki University of Technology (Espoo, Finland) on the 10th of October, 2003, at 12 o'clock noon.
Overview in PDF format (ISBN 951-22-6709-8) [713 KB]
Dissertation is also available in print (ISBN 951-22-6708-X)
Quantum dots are man-made nanoscale structures. As they show typical atomic properties they are often referred to as artificial atoms. The wave functions, shell structure, and energy levels are usually reminiscent of real atomic systems. A wide variety of geometries is possible by choosing appropriate materials and external confinement: one-dimensional rods, two-dimensional pancakes, or three-dimensional spheres. Since quantum dots are nanoscale systems, quantum mechanics is required for their accurate description. However, the electronic structure of these systems is very hard or even impossible to solve exactly even in the case of a few electrons, and approximations must be used.
This thesis concentrates on electronic structure calculations of two-dimensional quantum dot systems, using the density-functional approach. The spin-density-functional theory (SDFT) and the current-spin-density-functional theory (CSDFT) are applied to study the ground-state properties of quantum dot systems in zero and finite magnetic fields. Especially the effects of complex electron-electron interactions are studied.
Emphasis has also been set on developing and testing various methods and approximations. This is done by comparing the ground-state energy and other observables to those obtained using the variational quantum Monte Carlo method. The Kohn-Sham equations of the density-functional theories are solved in real-space by using the Rayleigh quotient multigrid method. This approach is compared to the traditional plane-wave solving methods.
The systems under consideration in this work include single quantum dots with different confining potentials, double quantum dot 'hydrogen' molecule, and a superconductor-normal quantum dot-superconductor (SNS) structure. Symmetry-breaking solutions emerge in these calculations. These include spin-density-wave-like solutions, charge-density-wave-like solutions, Wigner molecule formation, and solutions with vortex structures. The structure and properties of these solutions have been calculated and the interpretation of the broken symmetry is discussed.
This thesis consists of an overview and of the following 7 publications:
Keywords: spin-density-functional theory, current-spin-density-functional theory, density-functional approach, quantum dot
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© 2003 Helsinki University of Technology