Effects of nonlinearity on phonon hydrodynamics in graphite

The recent experimental observation of thermal rectification in a graphite tesla valve indicates the existence of nonlinear effects in the phonon hydrodynamic regime, which remains yet an open puzzle currently. In this work, we explore the effects of nonlinearity on phonon hydrodynamics in graphite based on a semianalytical solution of the nonlinear phonon Boltzmann transport equation with first-principles input. Our theoretical study predicts the saturation of macroscopic drift velocity of phonons to the minimal phase velocity with increasing temperature gradient, and the asymmetric heat flux distributions in reciprocal space that yield the nonlinearity. We also demonstrate an enhanced nonlinear effect with broadening graphite width, and an appreciable reduction of the thermal conductivity from the linear result. This work thus provides a foundation for future theoretical and experimental work on nonlinear phonon hydrodynamics and heat manipulation in graphitic structures.