First principle calculation of the effective Zeeman's couplings in topological materials

In this paper, we propose a first principle calculation method for the effective Zeeman’s 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 Zeeman’s couplings are discussed. Especially, we discuss the impact of Zeeman’s coupling on the Fermi surface’s topology in Na${}_3$Bi in detail.