Landau quantisation of photonic spin Hall effect in monolayer black phosphorus

The photonic spin Hall effect (PSHE) is a promising candidate for controlling the spin states of photons and exploiting next-generation photonic devices based on spinoptics. Herein, the influences of a perpendicular magnetic field on the PSHE appearing on the surface of monolayer black phosphorus (BP) are investigated. Results reveal that both the in-plane and transverse spin-dependent shifts are quantised and show an oscillating pattern due to the splitting of Landau levels (LLs) induced by the external magnetic field B. And the oscillation period of spin Hall shifts gradually increases with strengthening B because of the increase of LL spacings. By contrast, for a fixed magnetic field, as the LL spacings become smaller and smaller with increasing the LL index, the oscillation period of spin Hall shifts gradually decreases as the photonic energy increases. Moreover, it is possibly due to the synergistic role of intrinsic anisotropy, high crystallinity, and quantisation-incurred localised decreases in beating-like complex conductivities of the BP film, giant spin Hall shifts, hundreds of times of the incident wavelength, are obtained in both transverse and in-plane directions. These unambiguously confirm the strong impact of the external magnetic field on the PSHE and shed important insights into understanding the rich magneto-optical transport properties in anisotropic two-dimensional atomic crystals.