Tuning the polarized quantum phonon transmission in graphene nanoribbons.

We propose systems that allow a tuning of the phonon transmission function T(ω) in graphene nanoribbons by using C13 isotope barriers, antidot structures, and distinct boundary conditions. Phonon modes are obtained by an interatomic fifth-nearest neighbor force-constant model (5NNFCM) and T(ω) is calculated using the non-equilibrium Green's function formalism. We show that by imposing partial fixed boundary conditions it is possible to restrict contributions of the in-plane phonon modes to T(ω) at low energy. On the contrary, the transmission functions of out-of-plane phonon modes can be diminished by proper antidot or isotope arrangements. In particular, we show that a periodic array of them leads to sharp dips in the transmission function at certain frequencies which can be pre-defined as desired by controlling their relative distance and size. With this, we demonstrated that by adequate engineering it is possible to govern the magnitude of the ballistic transmission functions in graphene nanoribbons. We discuss the implications of these results in the design of controlled thermal transport at the nanoscale as well as in the enhancement of thermo-electric features of graphene-based materials.