Electron vortex beams in a magnetic field and spin filter

We investigate the propagation of electron vortex beams in a magnetic field. It is pointed out that when electron vortex beams carrying orbital angular momentum propagate in a magnetic field, the Berry curvature associated with the scalar electron moving in a cyclic path around the vortex line is modified from that in free space. This alters the spin-orbit interaction, which affects the propagation of nonparaxial beams. The electron vortex beams with tilted vortices lead to a spin Hall effect in free space. In the presence of a magnetic field in time-space we have spin filtering such that either positive or negative spin states emerge in spin Hall currents with clustering of spin 12 states.