We show that weak measurements can be used to measure the tiny signature of topological phase transitions. The signature is an in-plane photonic spin Hall effect, which can be described as a consequence of a Berry phase. It is also parallel to the propagation direction of a light beam. The imaginary part of the weak value can be used to analyze ultrasmall longitudinal phase shifts in different topological phases. These optical signatures are related to the Chern number and bandgaps; we also use a preselection and postselection technique on the spin state to enhance the original signature. The weak amplification technique offers a potential way to determine the spin and valley properties of charge carriers, Chern numbers, and topological phases by direct optical measurement.

We examine the spin-orbit interaction of light and photonic spin Hall effect on the surface of anisotropic two-dimensional atomic crystals. As an example, the photonic spin Hall effect on the surface of black phosphorus is investigated. The photonic spin Hall effect manifests itself as the spin-dependent beam shifts in both transverse and in-plane directions. We demonstrate that the spin-dependent shifts are sensitive to the orientation of the optical axis, doping concentration, and interband transitions. These results can be extensively extended to other anisotropic two-dimensional atomic crystals. By incorporating the quantum weak measurement techniques, the photonic spin Hall effect holds great promise for detecting the parameters of anisotropic two-dimensional atomic crystals.