Phonon dispersion relation and phonon thermal conductivity in trilayer graphene at low temperatures

In this work, phonon dispersion relation of trilayer graphene with ABA stacking has been calculated by using force-constant model. In our calculation we have considered fifth nearest neighbors in plane of graphene and the interaction between the nearest layers. By using the calculated phonon dispersion relation, phonon thermal conductivity of trilayer graphene is investigated by Landaur theory at low temperatures. In force constant model, atoms are considered as a point masses that move according to the classical mechanics laws. By formation of dynamical matrix and solving the secular equation det D(kappa) = 0 the eigen frequencies can be achieved. It can be seen that the degeneracy of the lowest acoustic branch is splited into the three branches near the Briloan zone for trilayer graphene, which is due to weak van der waals interaction between two layers. In addition, the phonon thermal conductivity increases by raising the number of layers.