Hydrodynamic thermal transport in suspended graphene ribbons

In this paper, we have studied the response of thermal conductivity to the frequency of the temperature gradient at various temperatures and for different ribbon sizes. The frequency-dependent thermal conductivity in suspended graphene resembles the behavior of a low pass thermal filter, whose cut-off frequency, found to be much smaller than silicon, approaches the clock frequencies of current CPUs but can be tuned over a wide range by ribbon size and temperature. The cut-off frequencies are found to be proportional to the average scattering rates. At low temperatures when the phonon-phonon scattering is weak, boundary scattering is the dominant scattering mechanism, and hence, the cutoff frequency shows dependence on ribbon sizes. However, at RT when the phonon-phonon scattering dominates over edge-roughness scattering, the cut-off frequency shows a very weak dependence on ribbon sizes. The normal and resistive contribution towards thermal conductivity showing different cut-off can be employed for studying hydrodynamic phenomenon like second sound.