  The response of semiconductor materials to external magnetic fields is a
reliable approach to probe intrinsic electronic and spin-dependent properties.
In this study, we investigate the common Zeeman splitting features of novel
wurtzite materials, namely InP, InAs, and GaAs. We present values for the
effective g-factors of different energy bands and show that spin-orbit coupling
effects, responsible for the spin splittings, also have noticeable
contributions to the g-factors. Within the Landau level picture, we show that
the nonlinear Zeeman splitting recently explained in magneto photoluminescence
experiments for InP nanowires by Tedeschi et al. [Phys. Rev. B 99, 161204
(2019)] are also present in InAs, GaAs and even in the conventional GaN. Such
nonlinear features stem from the peculiar coupling of the A and B valence
bands, as a consequence of the interplay between the wurtzite crystal symmetry
and the breaking of time-reversal symmetry by the external magnetic field.
Moreover, we develop an analytical model to describe the experimental nonlinear
Zeeman splitting and apply it to InP and GaAs data. Extrapolating our fitted
results, we found that the Zeeman splitting of InP reaches a maximum value,
which is a prediction that could be probed at higher magnetic fields.
