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Two-dimensional (2D) atomic crystals have extraordinary electronic and photonic properties and hold great promise in the applications of photonic and optoelectronics. Here, we review some of our works about the spin-orbit interaction of light on the surface of 2D atomic crystals. First, we propose a general model to describe the spin-orbit interaction of light of the 2D free standing atomic crystal, and find that it is not necessary to involve the effective refractive index to describe the spin-orbit interaction. By developing the quantum weak measurements, we detect the spin-orbit interaction of light in 2D atomic crystals, which can act as a simple method for defining the layer numbers of graphene. Moreover, we find the transverse spin-dependent splitting in the photonic spin Hall effect exhibits a quantized behavior. Furthermore, the spin-orbit interaction of light for the case of air-topological insulator interface can be routed by adjusting the strength of the axion coupling. These basic finding may enhance the comprehension of the spin-orbit interaction, and find the important application in optoelectronic.
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