One can create electron beams with well-defined orbital angular momentum. These have come to be known as electron vortex beams (EVB). The idea apparently goes back to Bliokh et al., who derived semiclassical solutions to the Schrödinger equation representing electron wave-packets freely propagating in three dimensions and carrying phase vortices. At the time, they also suggested some ways to create such electron beams by analogy with the optical counterparts.
Since then, several groups have investigated EVBs, for example [2-5]. An interesting advance, which disperses beams of differing angular momenta along the Z-axis, comes from Verbeeck et al. . It results from inserting a spiral aperture into the condensor plane of a STEM column. In previous work, the beams were dispersed in plane , so that they were all in focus simultaneously. With the spiral aperture in place, experiments can select beam angular momentum simply by changing focus.
Grillo et al.  have recently claimed to achieve 37% efficiency in converting Gaussian electron beams into Bessel (vortex) beams.
 Bliokh et al., PhysRevLett 99(2007)190404, doi: 10.1103/PhysRevLett.99.190404
 Uchida and Tonomura, Nature 464(2010)737, doi: 10.1038/nature08904
 McMorran et al., Science 331(2011)192, doi:10.1126/science.1198804
 Verbeeck et al., ApplPhysLett 99(2011)203109, doi: 10.1063/1.3662012
 Schattschneider, et al., PhysRevLett 109(2012)084081, doi: 10.1103/PhysRevLett.109.084801
 Saitoh et al., PhysRevLett 111(2013)074801, doi: 10.1103/PhysRevLett.111.074801; see also arXiv:1307.6304
 Verbeeck et al., arXiv:1405.7222
 Verbeeck et al., arXiv:1403.5457 and references therein
 Grillo et al., arXiv:1505.07815.