In this study, we present a complete experimental and theoretical investigation of the fundamental exciton Zeeman splitting in wurtzite InP nanowires. We determined the exciton gyromagnetic factor, $g_{exc}$, by magneto-photoluminescence spectroscopy using magnetic fields up to 29 T. We found that $g_{exc}$ is strongly anisotropic with values differing in excess of 50% between the magnetic field oriented parallel and perpendicular to the nanowire long axis. Furthermore, for magnetic fields oriented along the nanowire axis, $g_{exc}$ is nearly three times larger than in bulk zincblende InP and it shows a marked sublinear dependence on the magnetic field, a common feature to other non-nitride III-V wurtzite nanowires but not properly understood. Remarkably, this nonlinearity originates from only one Zeeman branch characterized by a specific type of light polarization. All the experimental findings are modeled theoretically by a robust approach combining the $k cdot p$ method with the envelope function approximation and including the electron-hole interaction. We revealed that the nonlinear features arise due to the coupling between Landau levels pertaining to the A (heavy-hole like) and B (light-hole like) valence bands of the wurtzite crystal structure. This general behavior is particularly relevant for the understanding of the spin properties of several wurtzite nanowires that host the set for the observation of topological phases potentially at the base of quantum computing platforms.
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