Numerical analysis on vacancy induced vibrational properties of graphene nanoribbons

The effect of vacancy-type defects on the vibrational properties of graphene nanoribbons has been discussed numerically. We have computed the phonon density of states and mode pattern over a broad range of vacancies using the forced vibrational method which is based on the mechanical response to extract the pure vibrational eigenmodes by numerical simulation. We find that the armchair-edge and the vacancy-type defects break down the phonon degeneracy at the Г point of the LO and TO mode, distort and shift down the phonon density of states significantly. The phonon density of states in the armchair graphene nanoribbons with vacancy-type defects show the remarkable increase in the low frequency region induced by their defect formations. The mode patterns obtained by our numerical experiments reveal that the in-plane optical phonon modes in the K point are localized near the armchair-edges which are in good agreement with the high intensity D peak in the Raman spectra originate from the armchair-edge. The simulation results also demonstrate that the lattice vibrations in the defective graphene nanoribbons show the remarkably different properties such as spatial localizations of lattice vibrations due to their random structures from those in the perfect graphene nanoribbons. These differences manifest themselves in the predicted temperature behavior of the constant-volume specific heat capacity of both structures.