A vortex in a magnetic material is like a whirlpool, but instead of water, the directions of magnetization twist. An electron flying through such a vortex feels not just a magnetic field, but a curvature of space: its path bends as if it were rolling down a funnel with a narrow neck. This neck is an analog of a 'wormhole': its radius is set by the vortex charge and the strength of the exchange interaction, and at short distances the funnel is cut off by the vortex core.
The electron's deflection follows a single curve that depends only on the vortex twist and the coupling strength. The same geometry can be created in a honeycomb lattice of atoms, where electrons behave just as in a real vortex. Then the electron's path can be bent on demand, like a lens for light.
The Aharonov–Bohm effect shows that an electron is affected by a magnetic field even where its strength is zero: what matters is not the field's intensity, but its 'flux' through a loop.