Investigation of Phonon Hydrodynamics in Graphene via Monte Carlo Simulations

In materials where momentum conserving phonon scattering events (normal) dominate momentum destroying scattering events (umklapp), such as in graphene due to its light atoms and strong carbon-carbon bonding, hydrodynamic phenomena arise. Such phenomena include negative thermal resistance regions, flux vortices, and viscous damping effects on thermal transport which may prove useful for the development of thermal devices powered by the heat dissipated from their electronic counter parts. Boundary scattering has recently been shown to play a more dominant role in the creation of hydrodynamic signatures than the ratio of normal to umklapp scattering events, but the relationship between boundary scattering and hydrodynamics is not yet well understood. In this hydrodynamic regime, Fourier's law fails, and heat transport must be modeled through solving the Boltzmann transport equation (BTE). Here we generate scattering rates for graphene from first principles and implement them in Monte Carlo simulations to directly solve the time-dependent BTE. We integrate phonon scattering with atomically rough edges in order to explore the relationship between sample size, roughness, and hydrodynamic phenomena. We establish the limits of the thermal conductivity under a range of sample sizes, bondary configurations, and temperatures while including both normal or umklapp scattering events. Our work will aid in taking advantage of phonon hydrodynamics in future thermal management solutions for 2D materials and devices.