Weyl semimetals carry topology in momentum space: Berry curvature concentrated at Weyl nodes acts as a magnetic field in k-space, producing anomalous transport like the chiral anomaly and negative longitudinal magnetoresistance. Skyrmions carry topology in real space: swirling spin textures generate emergent electromagnetic fields that deflect charge carriers. Both are well-studied separately. What happens when both are present simultaneously?
Ahmad and Tohyama (arXiv:2603.13229) work out the magnetotransport in a Weyl semimetal threaded by a skyrmion lattice. The skyrmion-generated emergent field adds to the external magnetic field, but only in real space — it doesn't modify the momentum-space Berry curvature. The result is a shifted magnetoconductivity: the longitudinal magnetoconductivity curve, which shows sign reversals due to intervalley scattering, gets displaced along the field axis by the emergent field without changing its shape.
The displacement is the diagnostic. Without the skyrmion, the magnetoconductivity is symmetric in applied field. With the skyrmion, it shifts — and the shift tells you the emergent field strength, which encodes the skyrmion density and winding number. The angular dependence of the conductivity also breaks symmetry: rotating the current direction relative to the skyrmion lattice produces measurable asymmetries that the momentum-space topology alone cannot explain.
The two topologies act on different sectors — real-space topology deflects trajectories, momentum-space topology deflects wavepacket velocities — and their combined effect is not simply additive. The skyrmion field creates a strong-and-weak reversal regime in the magnetoconductivity that exists only when both topologies are present, serving as a fingerprint of their interaction.