A vortex beam is a pure quantum mechanics object as it is a non-trivial superposition of semi-classical free space trajectories and an eigenstate of orbital angular momentum. Since its introduction, it has changed the microscopist approach to the electron beams. At the same time, the advent of vortex beams marked the introduction of electron synthetic holograms and custom beam shaping.

However after 5-6 years for their introduction microscopists are still trying to find the real strong application in material science, in spite of an over whelming quantity of theoretical proposals.

Potential applications go from magnetic measurements to spin-orbit effects and coupling with electromagnetic radiation. Some the most appealing applications regards the case of very large vortex with a winding number of even 1000 that we are realizing by a strong improvement of nanofabrication.

The first part of the seminar will examine the basic concepts of electron vortex beams and clarify the intuitive picture about it with reference to both quantum and semi-classical effects.

The second part will make an overview on the possible applications and the way we can couple to EM-field, large Landau states, magnetic field measurement and to spin manipulation. Some of the more immediate prospective will be analyzed in some detail.