Resonance effects on the Raman spectra of graphene superlattices

In this work, a study of resonance effects in the Raman spectra of twisted bilayer graphene (tBLG) is presented. The analysis takes into account the effect of the mismatch angle $\ensuremath{\theta}$ between the two layers, and also of the excitation laser energy on the frequency, linewidth, and intensity of the main Raman features, namely the rotationally induced $R$ band, the $G$ band, and the second-order ${G}^{\ensuremath{'}}$ (or $2D$) band. The resonance effects are explained based on the $\ensuremath{\theta}$ dependence of the tBLG electronic structure, as calculated by ab initio methodologies. The twist angle $\ensuremath{\theta}$ also defines the observation of a ``$D$-like'' band which obeys the double-resonance process, but relies on the superlattice along with long-range defects in order to fulfill momentum conservation. The study was possible due to the development of a route to produce and identify rotationally stacked bilayer graphene by means of atomic force microscopy (AFM).