  The photonic spin Hall effect of light beams reflected from the surfaces of
various two-dimensional hexagonal crystalline structures, considering their
associated time-reversal $\mathcal{T}$ and inversion $\mathcal{I}$ symmetries,
is investigated. Employing the Haldane model with tunable parameters as a
generic model, we examine the longitudinal and transverse spin-separations of
the reflected beam in both topological non-trivial and trivial systems. The
study reveals that the sign switching of the PSHE in these materials is
attributed to the non-trivial and trivial topology. By manipulating the
interplay between spin-orbit coupling and external electric fields, we
demonstrate topological phase transitions in buckled Xene monolayer materials
through the photonic spin Hall effect. Different behaviors of the photonic spin
Hall effect are observed in various topological phases within these materials.
Additionally, we explore the reflected spin and valley-polarized spatial shifts
in monolayer transition metal dichalcogenides. The photonic spin Hall effect in
buckled Xene monolayer materials and transition metal dichalcogenides is highly
influenced by the spin and valley degrees of freedom of charge carriers,
offering a promising avenue to explore spintronics and valleytronics in these
hexagonal materials. We propose that the photonic spin Hall effect in Haldane
materials can serve as a metrological tool for optical parameter
characterization and as a promising method for determining Chern numbers and
topological phase transitions through direct optical weak measurement
techniques.
