The nature of the Zeeman effect and field-induced topological semimetals*

In the present talk, I will propose a new way to classify centrosymmetric metals by studying the
Zeeman effect caused by an external magnetic field described by the momentum dependent g-factor
tensor on the Fermi surfaces. Nontrivial U(1) Berry's phase and curvature can be generated once the
otherwise degenerate Fermi surfaces are split by the Zeeman effect, which will be determined by
both the intrinsic band structure and the structure of g-factor tensor on the manifold of the Fermi
surfaces. Such Zeeman effect generated Berry's phase and curvature can lead to three important
experimental effects, modification of spin-zero effect, Zeeman effect induced Fermi surface Chern
number, and the in-plane anomalous Hall effect. By first-principle calculations, we study all these
effects on two typical material, ZrTe5 and TaAs2, and the results are in good agreement with the
existing experiments.