Tunable photonic spin Hall effect on a hyperbolic crystal coated with graphene monolayer

In this article, we theoretically explore the photonic spin Hall effect (PSHE) observed in a light beam upon reflections from a graphene-based uniaxial hyperbolic crystal geometry. By applying appropriate boundary conditions to both the incident and reflected light beams, we derive expressions for the Fresnel’s coefficients of reflection for the $s$- and $p$-light beams. The presence of graphene introduces an additional degree of tunability, allowing precise control over the PSHE through its chemical potential and temperature, while the hyperbolic crystal allows modulation via the $c$-axis orientation and reststrahlen band selection. Consequently, the transverse spin-dependent shift can be dynamically tuned by varying the chemical potential. Additionally, we reveal that the Brewster angle of the system is tunable via the orientation of the c-axis, with larger orientation angles leading to a reduction in spin-dependent splitting. The amplitude of the PSHE is significantly enhanced in the second reststrahlen band compared to the first reststrahlen band. Finally, we find that temperature effect has a strong influence on the PSHE, with the spin shift being markedly larger at zero temperature. These results suggest that graphene-integrated hyperbolic materials could enable advanced terahertz modulators and spin-based photonic devices.