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The ratio of the Zeeman splitting to the cyclotron energy ($M=\Delta E_Z /\hbar \omega_c$), which characterizes the relative strength of the spin-orbitinteraction in crystals, is examined for the narrow gap IV-VI semiconductorsPbTe, SnTe, and their alloy Pb$_{1-x}$Sn$_x$Te on the basis of the multiband$k\cdot p$ theory. The inverse mass $\alpha$, the g-factor $g$, and $M$ arecalculated numerically by employing the relativistic empirical tight-bindingband calculation. On the other hand, a simple but exact formula of $M$ isobtained for the six-band model based on the group theoretical analysis. It isshown that $M<1$ for PbTe and $M>1$ for SnTe, which are interpreted in terms ofthe relevance of the interband couplings due to the crystalline spin-orbitinteraction. It is clarified both analytically and numerically that $M=1$ justat the band inversion point, where the transition from trivial to nontrivialtopological crystalline insulator occurs. By using this property, one candetect the transition point only with the bulk measurements. It is alsoproposed that $M$ is useful to evaluate quantitatively a degree of the Diracelectrons in solids.

Crystalline spin-orbit interaction and the Zeeman splitting in Pb$_{1-x}$Sn$_x$Te