Wormhole Geometry from a Magnetic Vortex

Abstract

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.