Artificial molecules: A theoretical study of electron correlations in two vertically coupled quantum dots

The effects of electron correlations in artificial molecules consisting of two vertically coupled quantum dots were investigated. The quantum dots considered in this thesis are small electron islands made by laterally confining a two-dimensional electron gas in a semiconductor heterostructure. The lateral confinement potential is taken parabolic which is a realistic and at the same time computationally convenient approximation. The number of electrons in a quantum dot can range from zero to several thousand. Like natural atoms, these small electronic systems contain a discrete number of electrons and have a discrete spectrum. Therefore, they are called artificial atoms. It is shown that these artificial atoms exhibit new Physics which have no analogue in real atoms due to the increased importance of electron correlations. Because the size, the geometry and the number of electrons of artificial atoms can be changed arbitrarily, they can be considered as tiny laboratories in which quantum mechanics and the effects of electron-electron interactions can be studied. The interest in the study of vertically coupled quantum dots is motivated by the fact that now also the interdot coupling can be tuned by varying the interdot distance. This leads to a competition between intradot and interdot electron interactions, resulting in an extra degree of freedom to explore electron correlations. We considered in each chapter of this thesis a different experimental situation and consequently applied a different theoretical technique.; The first two chapters deal with two coupled classical dots. First in chapter 2 the classical system is considered and the electrons are treated as classical point-like particles. The ground state configuration and the eigenmodes were calculated for two dots having the same parabolic confinement strength as a function of the interdot distance. In chapter 3 the many electron classical limit is considered and the electrons are treated as a liquid. This classical hydrodynamic approximation can be used if one is not interested in the exact Wigner configuration but in the total energy or the excitation spectrum. We used this classical hydrodynamic approach to calculate the equilibrium density profiles and the magnetoplasma excitations.; The connection between classical and quantum systems of coupled dots is made in chapter 4. It is shown that the classical artificial molecule, with in each dot one electron, can also exhibit a second order transition.; Chapter 5 and 6 deal with the quantum system of two vertically coupled quantum dots. The ground state is studied as a function of the interdot distance within the spin density functional theory formalism in chapter 5. As this is a quantum system, the tunneling of an electron between the dots is taken into account. The results of chapter 5 are extended in chapter 6 to the experimental important case in which a perpendicular magnetic field is present. Therefore we made use of current spin density functional theory for non-zero magnetic fields. (Abstract shortened by UMI.)...