Theory of free electron vortices

The recent creation of electron vortex beams and their first practical application motivates a better understanding of their properties. Here, we develop the theory of free electron vortices with quantized angular momentum, based on solutions of the Schrödinger equation for cylindrical boundary conditions. The principle of transformation of a plane wave into vortices with quantized angular momentum, their paraxial propagation through round magnetic lenses, and the effect of partial coherence are discussed. ► Theory of vortex electrons. ► Proof that free electrons can carry quantized orbital momentum. ► Proof that electron vortices are stable and robust under spherical aberration. ► Demonstration of the strong influence of partial coherence.