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 C$^{13}$ 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 $ω_ν$ 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 T$(ω)$ 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.

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