Probing crystallinity of graphene samples via the vibrational density of states

The purity of graphene samples is of crucial importance for their experimental and practical use. In this regard, the detection of the defects is of direct relevance. Here, we show that structural defects in graphene samples give rise to clear signals in the vibrational density of states (VDOS) at the specific peaks at high and low frequencies.These can be used as an independent probe of the defect density. In particular, we consider grain boundaries made of pentagon-heptagon pairs, and show that they lead to a shift of the characteristic vibrational D mode towards higher frequency; this distinguishes these line defects from the Stone-Wales point defects, which do not lead to such a shift. Our findings may be instrumental for the detection of structural lattice defects using experimental techniques that can directly measure VDOS, such as inelastic electron tunneling and inelastic neutron spectroscopy.