Abstract: A quasiclassical theory of few-electron quantum dots in a strong magnetic field is developed. The ground state energy and the corresponding many-electron wave function are obtained and used to derive a universal relation of critical magnetic fields and calculate the currents and the density-current correlation function.

Abstract: The technique of beam optics is applied to the description of the wave function of Dirac electrons. This approach is illustrated by considering electron transmission through simple nonhomogeneous structures, such as flat and bent p-n junctions and superlattices. We found that a convex p-n junction compresses the beam waist, while a concave interface widens it without loosing its focusing properties. At a flat p-n junction the waist of the transmitted Gaussian beam can be narrowed or widened, depending on the angle of incidence. A general condition is derived for the occurrence of beam collimation in a superlattice which is less stringent than previous discussed.

Abstract: The properties of a two-dimensional electron are investigated in the presence of a circular step magnetic-field profile. Both electrons with parabolic dispersion as well as Dirac electrons with linear dispersion are studied. We found that in such a magnetic quantum dot no electrons can be confined. Nevertheless close to the Landau levels quasibound states can exist with a rather long lifetime.

Abstract: A comparative study is made of the propagation of wave packets and fronts in three different meta-media, i.e. graphene, left-handed media (LHM) and transmission lines, using one-dimensional models. It is shown that a potential step in graphene influences only the frequency of the electronic wave, i.e., the particular spectrum branch (electron or hole) to which the wave belongs to, while the envelop function (the wave front or packet form) remains unchanged. Although the model for a vacuum and LHM interface is similar to that of the potential step in graphene, the solutions are quite different due to differences in the chirality of the waves. Comparing the propagation of wave fronts and packets in a standard transmission line and its meta-analog we demonstrate that the propagating packets in the meta-line are much more deformed as compared to the standard one, including broadening, asymmetry and even the appearance of fast moving precursors. This influence is seen not only in the case of packets with steep fronts but in soft Gaussian packets as well.

Abstract: We show how snake-orbit states which run along a magnetic edge can be confined electrically. We consider a two-dimensional electron gas (2DEG) confined into a quantum wire, subjected to a strong perpendicular and steplike magnetic field B/ − B. Close to this magnetic step, new, spatially confined bound states arise as a result of the lateral confinement and the magnetic-field step. The number of states, with energy below the first Landau level, increases as B becomes stronger or as the wire width becomes larger. These bound states can be understood as an interference between two counter-propagating one-dimensional snake-orbit states.