Raman tensor for two-dimensional massive Dirac fermions

TL;DR

This paper predicts novel features in Raman spectroscopy of two-dimensional massive Dirac fermions, including a polarization-dependent selection rule and a robust, quantized phase difference in the Raman tensor.

Contribution

It introduces a new polarization selection rule and phase quantization in Raman tensors for 2D massive Dirac fermions, extending understanding of their optical properties.

Findings

A polarization selection rule in Raman tensor for circularly polarized light.

Quantized phase difference of ±π/2 in Raman tensor elements.

Robustness of phase quantization under perturbations.

Abstract

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.