  We demonstrate theoretically and experimentally a new electromagnetic lensing
concept using the magnetic vector potential - in a region free of classical
electromagnetic fields - via the Aharonov-Bohm effect. This toroid-shaped lens
with poloidal current flow allows for electromagnetic lensing which can be
tuned to be convex or concave with a spherical aberration coefficient of
opposite polarity to its focal length. This new lens combines the advantages of
traditional electromagnetic and electrostatic field-based lenses and opens up
new possibilities for the optical design of charged-particle systems. More
generally, these results demonstrate that the Aharonov-Bohm effect can shape
charged particle wavefronts beyond simple step shifts if topologies beyond
simple flux lines are considered and supports the physical significance of the
magnetic vector potential.
