Bending mode fluctuations and structural stability of graphene nanoribbons

We analyze the thermal fluctuations of a narrow graphene nanoribbon. Using a continuum membranelike model in the harmonic approximation, we study the height-height correlation functions and the destabilization modes corresponding to two different boundary conditions: fixed and free edges. For the first case, the thermal spectrum has a gap and the correlations along the ribbon decay exponentially. 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 as thermal excitations are gapless. The low energy spectrum decouples into a bulk and an edge excitation. The bulk excitation tends to destabilize the crystalline order producing a homogeneous rippling. Furthermore, we can relate the edge mode to a precluding perturbation leading to scrolled edges, as seen in suspended graphene samples. We also analyze the implications of our results in the thermal conductivity of graphene nanoribbons. DOI: 10.1103/PhysRevB.87.165411