G -band Raman double resonance in twisted bilayer graphene: Evidence of band splitting and folding

The stacking faults (deviates from Bernal) will break the translational symmetry of multilayer graphenes and modify their electronic and optical behaviors to the extent depending on the interlayer coupling strength. This paper addresses the stacking-induced band splitting and folding effect on the electronic band structure of twisted bilayer graphene. Based on the first-principles density-functional theory study, we predict that the band folding effect of graphene layers may enable the G band Raman double resonance in the visible excitation range. Such prediction is confirmed experimentally with our Raman observation that the resonant energies of the resonant G mode are strongly dependent on the stacking geometry of graphene layers.