Electronic properties of non-circular quantum dots

Abstract

Quantum dots are nanoscale electronic objects, typically fabricated using two-dimensional semiconductor heterostructures or three-dimensional atomic clusters. In addition to promising technological applications, quantum dots represent excellent sources of interesting many-electron quantum physics.

This thesis deals with the theoretical modeling of two-dimensional quantum dots consisting of less than twenty electrons. The aim is to clarify how the geometry of the confining potential affects the ground-state structure of the system with and without the presence of an external magnetic field. The question is of a great importance in understanding and predicting the basic electronic properties of actual quantum-dot devices.

The calculations are based on the density-functional theory applied within a real-space multigrid approach, which is shown to be a powerful method for the systems considered in this thesis. The accuracy of the method is, however, highly dependent on the local spin-density approximation used. Hence, different parametrizations for the exchange-correlation energy are compared. Furthermore, the problem of the density-functional theory as a mean-field approach using a single-configuration wave function is analyzed in this thesis.

Quantum dots of various shapes are investigated, beginning with polygonal systems to determine the critical densities for the Wigner crystallization. Rectangular dots are shown to be particularly sensitive to the geometry, but a qualitative agreement is obtained with the experimental addition energy spectra. The lack of circular symmetry does not prevent the maximum-density-droplet formation when an external magnetic field is applied, and the high-field limit may be characterized by remarkably regular state oscillations. The symmetry can also be distorted by an external impurity, for which a realistic model is obtained with a comparison to experimental data. Presumably, some of the rich variety of phenomena identified in this thesis for non-circular quantum dots will have a realization in the future nanoelectronics.