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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."
This book presents the wide range of topics in two-dimensional
physics of quantum Hall systems, especially fractional quantum Hall
states. It covers the fundamental problems of two-dimensional
quantum statistics in terms of topology and the corresponding braid
group formalism for composite fernions, and the main formalism used
in many-body quantum Hall theories, the Chern-Simons theory.
Numerical studies are introduced for spherical systems and the
composite fermion theory is tested. The book introduces the concept
of the hierarchy of condensed states, the BCS paired Hall state,
and multi-component quantum Hall systems and spin quantum Hall
systems.
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