Abstract:
Pinning of magnetic-field induced Wigner molecules (WMs) confined in parabolic two-dimensional quantum dots by a charged defect is studied by an exact diagonalization approach. We found a re-entrant pinning of the WMs as function of the magnetic field, a magnetic field induced re-orientation of the WMs and a qualitatively different pinning behaviour in the presence of a positive and negative Coulomb impurity.

Abstract:
The magneto-conductivity of a single graphene layer where the electrons are described by the Dirac Hamiltonian weakly modulated by a periodic potential is calculated. It is shown that Weiss oscillations periodic in the inverse magnetic field appear, that are more pronounced and less damped with the increment of temperature as compared with the same oscillations in a typical two-dimensional electron system with a standard parabolic energy spectrum.

Abstract:
The phase diagram of quantum electron bilayers in zero magnetic field is obtained using density functional theory. For large electron densities the system is in the liquid phase, while for smaller densities the liquid may freeze (Wigner crystallization) into four different crystalline phases; the lattice symmetry and the critical density depend on the the inter-layer distance. The phase boundaries between different Wigner crystals consist of both first and second order transitions, depending on the phases involved, and join the freezing curve at three different triple points.

Abstract:
The ring configurations for classical two-dimensional atoms are calculated within the Thomson model and compared with the results from `exact' numerical simulations. The influence of the functional form of the confinement potential and the repulsive interaction potential between the particles on the configurations is investigated. We also give exact results on those eigenmodes of the system whose frequency does not depend on the number of particles in the system.

Abstract:
Dirac fermions interacting with a cylindrically symmetric quantum dot potential created in single and bilayer graphene are not confined but form quasi-bound states. The broadening of these quasi-bound states (i. e. the inverse of their lifetimes) decreases (increases) with the orbital momentum of the electron in the case of graphene (bilayer). Quasi-bound states with energy below (above) the barrier height are dominantly electron(hole)-like. A remarkable decrease of the energy level broadening is predicted for electron energies close to the barrier height, which are a consequence of the total internal reflection of the electronic wave at the dot edge.

Abstract:
We investigate the stability, the dynamical properties and melting of a two-dimensional (2D) Wigner crystal (WC) of classical Coulombic particles in a bi-layer structure. Compared to the single-layer WC, this system shows a rich phase diagram. Five different crystalline phases are stable; the energetically favoured structure can be tuned by changing either the inter-layer distance or the particle density. Phase boundaries consist of both continuous and discontinuous transitions. We calculated the phonon excitations of the system within the harmonic approximation and we evaluated the melting temperature of the bi-layer WC by use of a modified Lindemann criterion, appropriate to 2D systems. We minimized the harmonic free-energy of the system with respect to the lattice geometry at different values of temperature/inter-layer distance and we found no temperature-induced structural phase transition.

Abstract:
By applying an electric field perpendicular to a semiconductor quantum ring we show that it is possible to modify the single particle wave function between quantum dot (QD)-like to ring-like. The constraints on the geometrical parameters of the quantum ring to realize such a transition are derived. With such a perpendicular electric field we are able to tune the Aharanov-Bohm (AB) effect for both single particles and for excitons. The tunability is in both the strength of the AB-effect as well as in its periodicity. We also investigate the strain induce potential inside the self assembled quantum ring and the effect of the strain on the AB effect.

Abstract:
We present a theoretical study of the spectrum of electrons confined in triple concentric rings. An unusual ordering and rich variety of angular momentum transitions are found that depend on the coupling between the rings and the confinement potential of the rings. Using the Configuration Interaction (CI) method, we calculated the two electron energy spectrum. Spin singlet to spin triplet transitions of the electron ground state are predicted and a fractional Aharonov-Bohm effect is found. We show that both the period and amplitude of the spin singlet - triplet energy gap depend strongly on the confinement potential and the external magnetic field. The spin singlet - triplet transition is found to depend on the spin Zeeman energy, especially for rings with weak confinement and in the presence of large magnetic field. The amplitude of the spin singlet - triplet energy gap depends on the Land\'{e} $g$-factor but the period of the transitions is independent of $g$.

Abstract:
We investigate the ground and excited states of a bipolar artificial molecule composed of two vertically coupled quantum dots containing different type of carriers -- electrons and holes -- in equilibrium. The approach based on exact diagonalization is used and reveals an intricate pattern of ground-state angular momentum switching and a rearrangement of approximate single-particle levels as a function of the inter-dot coupling strength.

Abstract:
We calculate the equilibrium properties and the dynamic response of two vertically coupled circular quantum dots populated by particles of different electrical charge sign, i.e. electrons and holes. The equilibrium density profiles are obtained and used to compute the frequencies and oscillator strengths of magnetoplasma excitations. We find a strong coupling between the modes derived from the center-of-mass modes of the individual dots which leads to an anticrossing with a pronounced oscillator strength transfer from the ``acoustic'' to the ``optical'' branch. Also, due to breaking of the generalized Kohn theorem a number of other than center-of-mass modes are excited whose oscillator strengths, however, are rather weak.