Near tunneling structures are proposed consisting of magnetic barriers that can be created by lithographic patterning of ferromagnetic or superconducting Slms. The form of the equivalent potential for such a barrier depends on the vive vector of the incident electron. This renders the transmission through such structures an inherently 20 process since the tunneling probability depends not only on the electron's momentum perpendicular to the tunnehng barrier but also on its momentum parallel to the barrier. Pronounced resonances are obtaitted for the tunneling probability and the conductance of a resonant tunneling device consisting of such magnetic barriers.

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 quasibound 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.

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.