Phonon mediated loss in a graphene nanoribbon

Periodic stretching of a string, under adiabatic condition (no thermal coupling with the environment), will increase its temperature. This represents the case of intrinsic damping where the energy associated with stretching motion is converted into thermal energy. We study this phenomenon in a graphene nanoribbon (GNR), a nano-string. We utilize classical molecular dynamics and study the scaling of dissipation rate (Q factor) with frequency. The dissipation is shown to result from strong non-linear coupling between the stretching vibration and the out-of-plane thermal phonons. A Langevin dynamics framework is developed to describe the out-of-plane phonon dynamics under in-plane stretching. The dissipation mechanism is analyzed using this framework. From the analysis, a bi-relaxation time model is obtained to explain the observed scaling of Q factor with frequency. We also compute the size and temperature dependence of Q factor. The decrease in Q factor with decrease in size (width) is shown to result from the elastic softening of GNR.