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The quantized photonic spin Hall effect (PSHE) in the strained graphene-substrate system is predicted under a sub-Tesla external magnetic field, which is two orders of magnitude smaller than required to produce the quantized effect in the conventional graphene-substrate system. It is found that in-plane and transverse spin-dependent splittings in the PSHE, exhibit different quantized behaviors and are closely related to the reflection coefficients. Unlike the quantized PSHE in the conventional graphene-substrate system formed by the splitting of real Landau levels, the quantized PSHE in the strained graphene-substrate system is attributed to the splitting of pseudo-Landau levels caused by the pseudo-magnetic field and the lifting of valley degeneracy of the n ≠ 0 pseudo-Landau levels induced by the sub-Tesla external magnetic field. At the same time, the pseudo-Brewster angles of the system are also quantized with the change of Fermi energy. The sub-Tesla external magnetic field and the PSHE appear as quantized peak values near these angles. The giant quantized PSHE is expected to be used for direct optical measurements of the quantized conductivities and pseudo-Landau levels in the monolayer strained graphene.

We systematically study the lattice-dependent spin Hall effect of light (SHEL) in a Weyl semimetal (WSM) by considering left-handed polarization of the incident beam, and propose a new simple method to sense the lattice spacing precisely. It is revealed that the lattice spacing plays as essential a role as the Weyl points separation in the influences on the SHEL, and the variations of SHEL shifts are closely related to the real part of Hall conductivity. Specifically, the SHEL shifts increase to the peak values first and then decrease gradually with the increase of lattice spacing, and a quantitative relationship between the SHEL and the lattice spacing is established. By simulating weak measurement experiments, the lattice-dependent SHEL shifts are amplified and measured in desirable accuracies. Subsequently, we propose a method of precisely sensing the lattice spacing based on the amplified SHEL shifts. These researches provide theoretical basis for manipulating the SHEL in WSMs, and may open the possibility of fabricating the WSM parameter sensors.