Engineering topological phenomena via field-driven Weyl motion

We illustrate the field-driven anomalous Hall engineering via the momentum-space motion of Weyl nodes using pyrochlore iridates under a [111] magnetic field as an example. We model the system with a well-established microscopic Hamiltonian and the field effect with the spin rotation from the all-in-all-out to the ferromagnetic state. Tracking the position of Weyl nodes during the spin rotation, we demonstrate macroscopic anomalous Hall conductivity variations are fundamentally driven by Weyl node motions by comparing the full multi-band Kubo formula with the geometric Weyl node separation. The discrepancy occurs only near a critical spin rotation angle, where several Weyl nodes come into close proximity. We reveal that the evolution of anomalous Hall conductivity under the magnetic field agrees with reported experiments in an order-of-magnitude and non-monotonicity. These results elucidate the field-driven dynamics of momentum-space monopoles and provide a framework for understanding transport in strongly correlated topological materials.