Abstract: We study theoretically the simultaneous effect of regular and random pinning potentials on the vortex lattice structure at filling factor of 1. This structure is determined by a competition between the square symmetry of regular pinning array, by the intervortex interaction favoring a triangular symmetry, and by the randomness trying to depin vortices from their regular positions. Both analytical and molecular-dynamics approaches are used. We construct a phase diagram of the system in the plane of regular and random pinning strengths and determine typical vortex lattice defects appearing in the system due to the disorder. We find that the total disordering of the vortex lattice can occur either in one step or in two steps. For instance, in the limit of weak pinning, a square lattice of pinned vortices is destroyed in two steps. First, elastic chains of depinned vortices appear in the film; but the vortex lattice as a whole remains still pinned by the underlying square array of regular pinning sites. These chains are composed into fractal-like structures. In a second step, domains of totally depinned vortices are generated and the vortex lattice depins from regular array.

Abstract: The persistent current in two vertically coupled quantum rings containing few electrons is studied. We find that the Coulomb interaction between the rings in the absence of tunneling affects the persistent current in each ring and the ground-state configurations. Quantum tunneling between the rings alters significantly the ground state and the persistent current in the system.

Abstract: The energy spectrum of a one-electron quantum dot doped with a single magnetic ion is studied in the presence of an external magnetic field. The allowed cyclotron resonance (CR) transitions are obtained together with their oscillator strength as a function of the magnetic field, the position of the magnetic ion, and the quantum dot confinement strength. With increasing magnetic field a ferromagnetic-antiferromagnetic transition is found, which results in clear signatures in the CR absorption. It leads to discontinuities in the transition energies and the oscillator strengths and to an increase in the number of allowed transitions.

Abstract: On the basis of the momentum-balance equation derived from the Boltzmann equation in which electron interactions with impurities and acoustic and optic phonons are included, we examine the dependence of the resistivity in graphene on temperature and electron density. Simple analytical expressions for the different contributions to the resistivity are obtained. Our results reproduce recent experimental findings and we are able to understand the different temperature dependence of the resistivity for low and high density samples.