Electronic struture and quantum transport in systems of quantum dots exposed to magnetic fields

The present thesis is about artificial nanostructures in which the electronic motion is restricted in all spatial dimensions precisely in the regime where quantum effects dominate. These structures which are called quantum dots can be prepared in the laboratory and offer a high degree of access to their electronic and transport properties thereby naturally being established as a prominent candidate for future nanoelectronics. In the present thesis a theoretical investigation of the electronic structure and quantum transport properties of quantum dots has been performed. In addition to the research performed, the theoretical framework for investigating transport through open and almost isolated quantum dots are reviewed. Thereby it is natural to divide the present contribution in two parts. In the first part, which deals with transport in open quantum dot systems, we will contribute a parallel algorithm solving for the Green’s function which goes beyond the trivial parallelization with regard to the external parameters of the transport problem, such as Fermi energy or magnetic field strength. Combining techniques of parallel linear algebra and cyclic reduction algorithms, the algorithm proceeds with the parallel treatment of the decomposed scattering region, thereby giving significant flexibility regarding the handling of highly demanding numerical problems as those encountered in materials with complex electronic structure (thereby requiring n-band effective mass models and atomistic Hamiltonians in order to be described). Further on, we apply our formalism to linear artificial crystals which are formed by quantum dots of various geometries. We review their properties from the perspective of building novel electronic devices based on quantum features and how they could operate at large temperatures. In the second part of the thesis, we review the physics of almost isolated dots, whose transport properties are determined solely by their electronic structure. The effects of electronelectron interactions, anisotropy in the confinement and magnetic field on the electronic structure of two-electron quantum dots are calculated via a configuration interaction approach, i.e., exact diagonalization of the two-body Hamiltonian matrix. Additionally, we introduce a stable numerical method for the evaluation of matrix elements containing integrals due to electron-electron (e-e) interactions. In this respect we have employed a combination of Gauss-Hermite and Gauss-Kronrod quadratures, that has allowed for the efficient and direct evaluation of the e-e matrix elements with large basis sets. Contrary to previous works, we were able to calculate several hundreds of excited states. Subsequently those were analysed statistically making it possible to trace the quantum chaotic patterns in the dot-spectrum, which determine the fluctuations of electron transport coefficients and other spectroscopic and thermodynamic properties. As a supplementary tool for our investigations, classical dynamics have been studied in the corresponding classical phase space. Regarding the application of a magnetic field we introduced new maps of the low-lying excitation pro- file of the spectrum that allow the interpretation of experiments in few-electron quantum dots in a simple and straightforward manner. The experimental parameters are the strength of a homogeneous magnetic field applied vertically to the plane of the dot and the anisotropic shape of the dot. Many-body features due to strong e-e correlations can be easily identified by measurements

Magnetically controlled current flow in coupled-dot arrays

Quantum transport through an open periodic array of up to five dots is investigated in the presence of a magnetic field. The device spectrum exhibits clear features of the band structure of the corresponding one-dimensional artificial crystal which evolves with varying field. A significant magnetically controlled current flow is induced with changes up to many orders of magnitude depending on temperature and material parameters. Our results put forward a simple design for measuring with current technology the magnetic subband formation of quasi one-dimensional Bloch electrons.Comment: 9 pages, 5 figure