Interference effects in polarization-controlled Rayleigh scattering in twisted bilayer graphene

We calculate the 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 moire 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 K point for optical laser energies and below. Compared to SLG, the integrated Rayleigh intensity is strongly enhanced for small twist angles (e.g., at a twist angle 0 = 1.2 degrees, the integrated Rayleigh intensity at laser energy El = 2 eV enhances by a factor of similar to 100 for the case of parallel polarization). While for the case of cross-polarization, it exhibits a markedly complex behavior suggestive of strong interference effects mediated by the optical matrix elements. We find that at small twist angles, e.g., 0 = 1.05 degrees, the corrugation effects strongly enhances the ratio RA = integrated Rayleigh intensity for parallel polarization integrated Rayleigh intensity for cross-polarization by similar to 1300 times viz-a-viz SLG or AB-BLG. Measured as a function of the incoming laser energy El, RA exhibits a characteristic evolution as the twist angle reduces, thus providing a unique fingerprint of the prevailing twist angle of the tBLG sample under study, which would be interesting to verify experimentally.