Flexural phonon modes and structural stability of graphene nanoribbons

PABLO SCURACCHIO; SEBASTIÁN COSTAMAGNA; ARIEL DOBRY

niteroi

Workshop; CIAM Worshop; 2013

We analyze the out of plane phonon modes and the height -height correlation functions of a narrow graphene nanoribbon. Starting from a continuum membranelike model in the harmonic approximation, we study two different boundary conditions: fixed and free edges. For the first case, there are not acoustic modes and all the phonon branches have a gap. Thermal fluctuations produce only local perturbations of the flat situation. However, the long range crystalline order is not distorted. For free edges the situation changes because low energy phonons are gapless. These modes decouple into a bulk and an edge excitation. The bulk excitation tends to destabilize the crystalline order toward a crumpling instability. Then, we consider a lattice dynamic model based in a fifth-nearest-neighbor force constant model. We obtain the phononic dispersion of the nanoribbons with different conditions at the edges and compare the low energy branches with the prediction of the continuum model.