  Inspired by recent experimental sub-atomic measurements using analytical
aberration-corrected scanning transmission electron microscopes (STEMs), we
studied electron probe propagation in crystalline SrTiO$_3$ at the sub-atomic
length scale. Here, we report the existence of sub-atomic channeling and the
formation of a vortex beam at this scale. The results of beam propagation
simulations, which are performed at various crystal temperatures and STEM probe
convergence angles (10 to 50 mrad) and beam energies (80 to 300 keV), showed
that reducing the ambient temperature can enhance the sub-atomic channeling and
that STEM probe parameters can be used to control the vortex beams and adjust
their intensity, speed, and area.
