The spectral components of the phonon transport in the locally thermally excited graphene samples were studied by molecular dynamics (MD) method. In order to be able to select and analyze separate phonon modes in the time of propagation, the transient Green-Kubo approach to the definitions of density of states (DOS) and thermal conductivity was tested in quasi-equilibrium regimes for limited region of the graphene sample studied. Propagation of single modes at the background of diffusional phonon distribution and energy decay of such modes are studied by calculation of the DOS and dispersion relations, their dependence on the heating condition and temperature is studied. Similar conditions can be generated at localized heating of small areas of graphene structures in electronic devices. In transient regime, many issues of thermal transport evaluation still remain not sufficiently tested, especially phonon dynamics. Thermal conductivity of graphene samples related to transport of separate phonon modes is still not completely investigated, however, recent result give indication on the difference in the contribution of phonon modes. In the study, we consider mostly high temperature transport modes that are generated at the heated spot in order to be able to define their velocities and lifetimes in the limit of transient MD sampling.

The single-layer graphene nanoribbon of 150 nm to 40 nm was relaxed and prepared in equilibrium in zigzag and armchair orientations. REBO potential for graphene was utilized. Our calculation has shown that at the heating to high temperatures of 1000K and higher, the G mode of graphene remains stationary and has a minimal contribution into thermal transport by coherent modes. The coherent phonon mode or modes that contribute the most into thermal transport were confined in the vicinity of 30 THz and can possibly be attributed to the D modes of graphene.

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