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We demonstrate theoretically and experimentally an electromagnetic lensing concept using the magnetic vector potential—in a region free of classical electromagnetic fields—via the Aharonov–Bohm (AB) 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 field-free lens combines the advantages of traditional electromagnetic and electrostatic field-based lenses and opens up additional possibilities for the optical design of charged-particle systems. More generally, these results demonstrate that the AB effect can shape charged particle wavefronts beyond simple step shifts if topologies beyond simple flux lines are considered and further supports the physical significance of the magnetic vector potential.