Zone folding effect in Raman G -band intensity of twisted bilayer graphene

The G-band Raman intensity is calculated for twisted bilayer graphene as a function of laser excitation energy based on the extended tight binding method. Here we explicitly consider the electron-photon and electron-phonon matrix elements of twisted bilayer graphene to calculate the resonance Raman intensity. The G-band Raman intensity is sensitive to the laser excitation energy and the twisting angle between the layers as a result of folding the electronic energy band structure. The Van Hove energy singularity, which is an electron transition energy between the conduction and valence bands, depends on n-m of the twisting vector $(n,m)$. The relative intensity of the G band as a function of twisting vectors is presented, which should be useful for the experimental identification of the twisting angle.