Raman tensor for two-dimensional massive Dirac fermions

Raman spectroscopy is a valuable characterization tool for two-dimensional materials. Starting from model Hamiltonians for Chern insulators and magnetized monolayers of transition metal dichalcogenides, we theoretically predict two unconventional features of Raman spectroscopy. First, a selection rule emerges in the Raman tensor when the incident and scattered photons are circularly polarized. This rule generalizes the well-known valley selection rule of optical conductivity in Dirac insulators. Second, for an electronic model with single massive Dirac fermion, the phase difference between Raman tensor elements is quantized to $\pm\pi/2$ for any frequency of the incident light. The quantization is robust under perturbations and the sign of the phase difference is reversed when the mass term of the Hamiltonian is inverted.