This book reflects the current status of theoretical and experimental research of graphene based nanostructures, in particular quantum dots, at a level accessible to young researchers, graduate students, experimentalists and theorists. It presents the current state of research of graphene quantum dots, a single or few monolayer thick islands of graphene. It introduces the reader to the electronic and optical properties of graphite, intercalated graphite and graphene, including Dirac fermions, Berry's phase associated with sublattices and valley degeneracy, covers single particle properties of graphene quantum dots, electron-electron interaction, magnetic properties and optical properties of gated graphene nanostructures. The electronic, optical and magnetic properties of the graphene quantum dots as a function of size, shape, type of edge and carrier density are considered. Special attention is paid to the understanding of edges and the emergence of edge states for zigzag edges. Atomistic tight binding and effective mass approaches to single particle calculations are performed. Furthermore, the theoretical and numerical treatment of electron-electron interactions at the mean-field, HF, DFT and configuration-interaction level is described in detail.

This book reflects the current status of theoretical and experimental research of graphene based nanostructures, in particular quantum dots, at a level accessible to young researchers, graduate students, experimentalists and theorists. It presents the current state of research of graphene quantum dots, a single or few monolayer thick islands of graphene. It introduces the reader to the electronic and optical properties of graphite, intercalated graphite and graphene, including Dirac fermions, Berry's phase associated with sublattices and valley degeneracy, covers single particle properties of graphene quantum dots, electron-electron interaction, magnetic properties and optical properties of gated graphene nanostructures. The electronic, optical and magnetic properties of the graphene quantum dots as a function of size, shape, type of edge and carrier density are considered. Special attention is paid to the understanding of edges and the emergence of edge states for zigzag edges. Atomistic tight binding and effective mass approaches to single particle calculations are performed. Furthermore, the theoretical and numerical treatment of electron-electron interactions at the mean-field, HF, DFT and configuration-interaction level is described in detail.

We present an overview of the theoretical background and experimental re sults in the rapidly developing field of semiconductor quantum dots - systems 8 6 of dimensions as small as 10- -10- m (quasi-zero-dimensional) that contain a small and controllable number (1-1000) of electrons. The electronic structure of quantum dots, including the energy quan tization of the single-particle states (due to spatial confinement) and the evolution of these (Fock-Darwin) states in an increasing external magnetic field, is described. The properties of many-electron systems confined in a dot are also studied. This includes the separation of the center-of-mass mo tion for the parabolic confining potential (and hence the insensitivity of the transitions under far infrared radiation to the Coulomb interactions and the number of particles - the generalized Kohn theorem) and the effects due to Coulomb interactions (formation of the incompressible magic states at high magnetic fields and their relation to composite jermions), and finally the spin-orbit interactions. In addition, the excitonic properties of quantum dots are discussed, including the energy levels and the spectral function of a single exciton, the relaxation of confined carriers, the metastable states and their effect on the photoluminescence spectrum, the interaction of an exciton with carriers, and exciton condensation. The theoretical part of this work, which is based largely on original re sults obtained by the authors, has been supplemented with descriptions of various methods of creating quantum-dot structures."