Impact of the mean free path distribution on hydrodynamic thermal transport in graphene

Thermal transport in two-dimensional (2D) materials has garnered interest due to the emergence of a hydrodynamic regime, where high rates of momentum-conserving phonon scattering events, stemming from a selection rule involving phonons in the flexural (out-of-plane) phonon branch, lead to a thermal viscosity. Many macroscopic models of hydrodynamic transport approximate nonlocal interactions using an average phonon mean free path; however, most 2D materials exhibit a broad distribution of mean free paths, ranging from short mean free paths associated with flexural phonons to long mean free paths characteristic of in-plane modes. Here, we will implement a Monte Carlo solution of the Peierls–Boltzmann transport equation to examine how the mean free path distribution influences the formation of hydrodynamic phenomena. Simulations using a single average mean free path will be compared with those incorporating the full phonon mean free path spectrum derived from first principles. Our central hypothesis is that using a single average mean free path will overestimate the viscosity of the system as the density of in-plane phonons increases. This work offers new insights into the role of phonon mean-free-path diversity in shaping hydrodynamic thermal transport and enhancing nonlocal thermal models.