Electron Beams with Orbital Angular Momentum

Electron vortex beams are beams of freely propagating electrons that possess orbital angular momentum. Recently predicted and experimentally verified, electron vortices are hoped to lead to new developments in several areas, in particular electron microscopy, as well as other areas as diverse as spintronics and quantum information. This thesis introduces and examines key concepts relating to electron vortices, and as an introduction, the major developments relating to electron vortices over the past few years are outlined and discussed. The Bessel beam is derived as a suitable solution to the Schrodinger equation for an electron beam carrying orbital angular momentum. The linear and orbital angular momenta of such a beam are discussed alongside the use of electron vortices in manipulation of nanoparticles. Being a charged particle the electron vortex carries electromagnetic fields; the magnetic field is found to have an axial component, unique to the vortex beam. Coupling between the spin and orbital angular momentum of the electron propagating within its own field is found to be negligible in typical electron microscope contexts. Electron vortices are found to have a similar form as the more widely known optical vortices, but key differences between electrons and photons lead to fundamentally different behaviour in many circumstances. The main differences between electron and optical vortices are outlined throughout this thesis. Interactions between the electron and optical vortices and matter, in the form of a hydrogenic atom, are considered. In contrast to the optical vortex, interactions between atomic matter and the electron vortex are found to lead to transfer of orbital angular momentum, opening the possibility of using electron vortices in the electron microscope to probe magnetism at nano- or atomic-scales. The premise and requirements of such experiments are discussed.