Fig. 1. Schematic illustration of the wave reflection at a surface of black phosphorus in a Cartesian coordinate system. A black phosphorus sheet is placed on the top of a homogeneous and isotropic substrate. The photonic SHE occurs on the reflecting surface and exhibits in-plane and transverse spin Hall shifts.

Fig. 2. Real and imaginary parts of the conductivity of the 2D atomic crystal as a function of frequency. Parameters are set as η=0.01  eV, ωx=1  eV, and ωy=0.35  eV. The frequency of interband electron transitions is present at ωy=0.35  eV. (a), (b) The optical axis is chosen as ϕ=0°. (c), (d) The optical axis is chosen as ϕ=30°. The doping concentration of the 2D atomic crystal is n=5×1013  cm−2.

Fig. 3. (a) Real and (b) imaginary parts of the conductivity of the 2D atomic crystal as a function of optical axis angles. The parameters of the 2D atomic crystal are n=5×1013  cm−2 and ω=0.1  eV. (c) Real and (d) imaginary parts of the conductivity as a function of doping concentration. The optical axis is chosen as ϕ=30°. Other parameters are the same as in Fig. 2.

Fig. 4. (a) In-plane and (b) transverse spin-dependent shifts on the surface of anisotropic 2D atomic crystal as a function of optical axis angle and frequency. The incident light impinges on the substrate at θi=60°, the refractive index of the substrate is assumed as 2, and the doping concentration is n=10×1013  cm−2.

Fig. 5. (a) In-plane and (b) transverse spin Hall shifts on the anisotropic 2D atomic crystal as a function of the optical axis angle and doping concentration. The frequency ω=0.1  eV. Other parameters are the same as in Fig. 4.