Incommensurately Stacked Graphene Bi-Layer: A Raman Scattering Study

We report results of Raman scattering studies of two novel graphene systems based on incommensurate stacking of sp$^{2}$ carbon: (1) an incommensurate bi-layer (IBL) formed by folding a graphene sheet onto itself; (2) a graphene scroll formed by rolling up a graphene sheet via a shearing motion between scotch tape and substrate during the micro-mechanical cleaving process . In (1), we have a flat bi-layer system; in (2) it is a gently curved multilayer system -- both should be incommensurate. Interestingly, although no significant D-band is observed in the parent graphene system, the incommensurate contact of the graphene sheet in (1) and (2) leads to strong D-band scattering near 1350 cm$^{-1}$ using 514.5 nm excitation. The dispersion of the D-bands in (1) and (2) is significantly different: scroll ($\sim $38 cm$^{-1}$/eV) and IBL ($\sim $50 cm$^{-1}$/eV). A second Raman band is observed nearby at $\sim $1384 cm$^{-1}$ in both the IBL and the scroll. However, the $\sim $1384 cm$^{-1}$ band is non-dispersive in both cases and is much sharper in the IBL than in the scroll. Our data will be compared to theoretical calculations based on double-resonant (DR) scattering and the electronic states of an IBL.