Crystalline spin–orbit interaction and the Zeeman splitting in Pb1−xSnxTe

Abstract

The ratio of the Zeeman splitting to the cyclotron energy (), which characterizes the relative strength of the spin–orbit interaction in crystals, is examined for the narrow gap IV–VI semiconductors PbTe, SnTe, and their alloy Pb1−xSnxTe on the basis of the multiband theory. The inverse mass α, the g-factor g, and M are calculated numerically by employing the relativistic empirical tight-binding band calculation. On the other hand, a simple but exact formula of M is obtained for the six-band model based on the group theoretical analysis. It is shown that M < 1 for PbTe and M > 1 for SnTe, which are interpreted in terms of the relevance of the interband couplings due to the crystalline spin–orbit interaction. It is clarified both analytically and numerically that M is not a quantized value but a continuous one, and M = 1 is obtained just at the band inversion point, where the transition from trivial to nontrivial topological crystalline insulator occurs. By using this property, one can detect the transition point only with the bulk measurements. It is also proposed that M is useful to evaluate quantitatively a degree of the Dirac electrons in solids.