Interference effects in polarization controlled Rayleigh scattering in twisted bilayer graphene

We calculate the \tco{polarization}-controlled Rayleigh scattering response of twisted bilayer graphene (tBLG) based on the continuum electronic band model developed by Bistritzer and MacDonald while considering its refinements which address the effects of structural corrugation, doping-dependent Hartree interactions and particle-hole asymmetry. The dominant wave vectors for the Rayleigh scattering process emanate from various regions of the Moir\'e Brillouin zone (MBZ) in contrast to single-layer graphene (SLG) and AB-stacked bilayer graphene (AB-BLG), where the dominant contributions always stem from the vicinity of the $\bm{K}$ point for optical laser energies and below. Compared to SLG, the integrated Rayleigh intensity is strongly enhanced for small twist angles (\emph{e.g.}, at a twist angle $\theta = 1.2^{\circ}$, the integrated Rayleigh intensity at laser energy $E_l=2~\si{\electronvolt}$ enhances by a factor of $\sim$ 100 for the case of parallel \tco{polarization}). While for the case of cross-\tco{polarization}, it exhibits a markedly complex \tco{behavior} suggestive of strong interference effects mediated by the optical matrix elements. We find that at small twist angles, \emph{e.g.}, $\theta = 1.05^{\circ}$, the corrugation effects strongly enhances the ratio $\bm{R}_A = \frac{ \text{integrated Rayleigh intensity for parallel \tco{polarization}}}{\text{integrated Rayleigh intensity for cross-\tco{polarization}}}$ by $\sim$ $1300$ times \emph{viz a viz} SLG or AB-BLG.