Recently, two unusual features were theoretically predicted for the Raman response of out-of-plane phonons in magnetic two-dimensional materials hosting massive Dirac fermions. First, the phase difference between certain Raman tensor elements was found to be quantized to $\pm \pi /2$, sensitive only to the sign of the Dirac fermion mass. Second, a selection rule was identified in the Raman intensity under circularly polarized light, which generalizes the well-known optical valley selection rule. These predictions were based on a low-energy effective model in the continuum approximation. Here, we test the robustness of those results for more realistic theoretical approaches. First, we calculate the Raman tensor for an electronic tight-binding model on a honeycomb lattice with broken time-reversal and inversion symmetries. Second, we compute the Raman tensor from density-functional theory for a monolayer of ferromagnetic $2\mathrm{H}\text{−}{\mathrm{RuCl}}_2$. Both calculations corroborate the analytical results found in the continuum model, thereby theoretically confirming the peculiar behavior of the Raman tensor for two-dimensional massive Dirac fermion systems.

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• Dirac fermions
• Electron-phonon coupling
• Optical phonons
• 2-dimensional systems
• Dirac semimetal
• Transition metal dichalcogenides
• First-principles calculations
• Inelastic light scattering
• Raman spectroscopy