Crossover of ballistic, hydrodynamic, and diffusive phonon transport in suspended graphene

Hydrodynamic phonon transport was recently predicted as an important regime for phonon transport in graphitic materials. Many of the past studies on hydrodynamic phonon transport have focused on the cases where the hydrodynamic regime is significantly stronger than other regimes such that hydrodynamic features can be clearly observed. However, this often requires stringent conditions of temperature and sample size. In many cases, the transport cannot be characterized by a single regime, but the features of all three regimes-ballistic, hydrodynamic, and diffusive regimes-exist to some extent. Here we assess the extent of three regimes by comparing momentum destruction rates by three different mechanisms, each of which represents a different regime: diffuse boundary scattering without internal phonon scattering (ballistic regime), diffuse boundary scattering combined with normal scattering (hydrodynamic regime), and umklapp scattering (diffusive regime). We solve the Peierls-Boltzmann equation with an ab initio full scattering matrix using a deviational Monte Carlo method. We sample distribution functions of ballistic and scattered particles separately, and thereby compare the momentum destruction rates by the three different mechanisms. Using this framework, we discuss a well-known phenomenon of ballistic-to-hydrodynamic crossover, called the phonon Knudsen minimum.