Magnetic control of Weyl nodes and wave packets in three-dimensional warped semimetals

We investigate the topological phase transitions driven by band warping, $\lambda$, and a transverse magnetic field, $B$, for three-dimensional Weyl semimetals. First, we use the Chern number as a mathematical tool to derive the topological $\lambda \times B$ phase diagram. Next, we associate each of the topological sectors to a given angular momentum state of a rotating wave packet. Then we show how the position of the Weyl nodes can be manipulated by a transverse external magnetic field that ultimately quenches the wave packet rotation, first partially and then completely, thus resulting in a sequence of field-induced topological phase transitions. Finally, we calculate the current-induced magnetization and the anomalous Hall conductivity of a prototypical warped Weyl material. Both observables reflect the topological transitions associated with the wave packet rotation and can help to identify the elusive 3D quantum anomalous Hall effect in three-dimensional, warped Weyl materials.