First principle calculation of the effective Zeemans couplings in topological materials

In this paper, we propose a first principle calculation method for the effective Zeemans coupling based on the second perturbation theory and apply it to a few topological materials. For Bi and Bi$_2$Se$_3$, our numerical results are in good accord with the experimental data; for Na$_3$Bi, TaN, and ZrTe$_5$, the structure of the multi-bands Zeemans couplings are discussed. Especially, we discuss the impact of Zeemans coupling on the Fermi surfaces topology in Na$_3$Bi in detail.