Unusual spin properties of InP wurtzite nanowires revealed by Zeeman splitting spectroscopy

The knowledge of the value and anisotropy of the gyromagnetic factor in semiconducting nanowires (NWs) is crucial for their potential applications in several fields, such as spintronics and topological quantum computation. Here, we present a complete experimental and theoretical investigation of the Zeeman splitting of the fundamental exciton transition in an important material system: wurtzite (WZ) InP NWs. The excitonic $g$ factors are derived by the Zeeman splitting of the spin levels observed by photoluminescence measurements under magnetic fields $\stackrel{P\vec}{B}$ up to 29 T. In addition to being about three times greater than in zincblende InP, the $g$ factor in the WZ phase is strongly anisotropic (50%) upon variation of the direction of $\stackrel{P\vec}{B}$ from parallel to perpendicular to the NW axis. Moreover, it exhibits a marked sublinear dependence on $\stackrel{P\vec}{B}$ whenever $\stackrel{P\vec}{B}$ points along the NW axis, a feature common to other non-nitride III-V WZ NWs but never properly understood. All these features are well accounted for by a realistic $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ modeling of the Landau levels in WZ InP with the envelope function approximation including excitonic effects. The nonlinearity is spin dependent and due to the coupling between the heavy-hole- and light-hole-like Landau levels. This is indeed a general signature of the bulk WZ structure not requiring quantum confinement nor NW geometry, and is demonstrated to hold also for GaAs, InAs and GaN WZ crystals as reported by Faria Junior et al. [Phys. Rev. B, present issue]. Our study solves the outstanding puzzle of the nonlinear Zeeman splitting found in several III-V WZ NWs.