Classical understanding of the electron vortex beams in a uniform   magnetic field
  Recently interesting observations on electron vortex beams, which have angular momentum about the center of the vortex beams, have been made. We have shown that the basic features of the electron vortex beams in a uniform magnetic field are understandable by using the classical motions of electrons. We have constructed a classical vortex-like motion by the collective motion of individual electrons in their cyclotron motions with a constant canonical angular momentum in the symmetric gauge, which models electron vortex beams, in a uniform magnetic field. With this model the various properties of circulating currents and the relation between energy and kinetic angular momentum in the electron vortex beams are well explained. We have also shown that the mismatch between the centers of the electron vortex beam and the classical cyclotron orbits naturally induces the parallel axis theorem and also the time-varying kinetic angular momentum of the electron vortex beam for certain distributions of classical electrons. 
Yeong Deok Han and Taeseung Choi
quant-ph