Tight-binding and density-functional study of the Raman tensor in two-dimensional massive Dirac fermion systems

TL;DR

This study confirms that the unique Raman response features predicted for massive Dirac fermions in 2D materials are robust, using tight-binding and density-functional calculations to validate earlier continuum model predictions.

Contribution

The paper demonstrates the robustness of predicted Raman tensor features in 2D massive Dirac systems through realistic tight-binding and DFT calculations, extending previous continuum model results.

Findings

Quantized phase difference in Raman tensor elements depends on Dirac mass sign

Selection rule for Raman intensity under circular polarization is confirmed

Results are consistent across continuum, tight-binding, and DFT models

Abstract

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 2H-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.