Discrete breather on the edge of the graphene sheet with the armchair orientation

Linear and nonlinear vibrations of a graphene nanoribbon with free armchair edges subjected to tensile deformation have been studied by atomistic simulation methods. It has been shown that the phonon modes are split into two subsets. Atoms in some ($XY$) modes vibrate in the nanoribbon plane and in other ($Z$) modes vibrate along the normal to this plane. The possibility of the excitation of a gap discrete breather in an extended nanoribbon in the spectrum of the $Z$ modes, the frequency of which lies in the gap of the spectrum of the $XY$ modes, has been demonstrated. This breather is a large-amplitude vibrational mode in the $XY$ plane localized on the four atoms on the nanoribbon edge. The breather is unstable with respect to small perturbations in the form of displacements of atoms out of the nanoribbon plane. Nevertheless, the discrete breather decays slowly owing to its weak interaction with the Z modes, so that its lifetime can be on the order of $10^3$ vibrational periods.