  We examine the photonic spin Hall effect (SHE) in a graphene-substrate system
with the presence of external magnetic field. In the quantum Hall regime, we
demonstrate that the in-plane and transverse spin-dependent splittings in
photonic SHE exhibit different quantized behaviors. The quantized SHE can be
described as a consequence of a quantized geometric phase (Berry phase), which
corresponds to the quantized spin-orbit interaction. Furthermore, an
experimental scheme based on quantum weak value amplification is proposed to
detect the quantized SHE in terahertz frequency regime. By incorporating the
quantum weak measurement techniques, the quantized photonic SHE holds great
promise for detecting quantized Hall conductivity and Berry phase. These
results may bridge the gap between the electronic SHE and photonic SHE in
graphene.
