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In this paper, we propose a first principle calculation method for theeffective Zeeman's coupling based on the second perturbation theory and applyit to a few topological materials. For Bi and Bi$_2$Se$_3$, our numericalresults are in good accord with the experimental data; for Na$_3$Bi, TaN, andZrTe$_5$, the structure of the multi-bands Zeeman's couplings are discussed.Especially, we discuss the impact of Zeeman's coupling on the Fermi surface'stopology in Na$_3$Bi in detail.

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