A perturbation theory study of electron vortices in electromagnetic fields: The case of infinitely long line charge and magnetic dipole

The novel discovery of electron vortices carrying quantized orbital angular momentum motivated intensive research of their basic properties as well as applications, e.g. structural characterization of magnetic materials. In this paper, the fundamental interactions of electron vortices within infinitely long atomic-column-like electromagnetic fields are studied based on the relativistically corrected Pauli-Schrödinger equation and the perturbation theory. The relative strengths of three fundamental interactions, i.e. the electron-electric potential interaction, the electron-magnetic potential/field interaction and the spin-orbit coupling are discussed. The results suggest that the perturbation energies of the last two interactions are in an order of 103-104 smaller than that of the first one for electron vortices. In addition, it is also found that the strengths of these interactions are strongly dependant on the spatial distributions of the electromagnetic field as well as the electron vortices.