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

We investigate the topological phase transitions driven by band warping, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>λ</a:mi></a:math>, and a transverse magnetic field, <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>B</b:mi></b:math>, for three-dimensional Weyl semimetals. First, we use the Chern number as a mathematical tool to derive the topological <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>λ</c:mi><c:mo>×</c:mo><c:mi>B</c:mi></c:mrow></c:math> 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.