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.
as written by the authors arXiv:2608.12285v1
Strong coupling to a magnetic texture makes an electron propagate through an emergent curved space. We show that an elementary vortex realizes the exterior spatial geometry of an Ellis wormhole: an ultrastatic throat with radius fixed by the topological charge and Hund exchange, cut off at short distances by the microscopic core. Two separable signatures follow directly: the electron deflection collapses onto a single Ellis curve governed by the vortex winding and exchange coupling, while the spin Berry phase produces a half-flux Aharonov--Bohm response switched on and off by winding parity. The same metric can be emulated in a designer honeycomb lattice, where the valley-symmetrized wave-packet response follows the predicted exterior geodesic. These signatures are accessible through real-space electron deflection and scattering, providing experimentally distinct probes of the emergent geometry and Berry flux. The magnetic vortex thus turns a topological defect into a tunable curved-space lens for electrons in quantum materials and designer lattices.
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.