High-Order Anharmonicities Shape Phonon Hydrodynamic Effects in Graphene.

Prominent phonon hydrodynamic phenomena were predicted in graphene at low temperatures due to the abundance of momentum-conserving three-phonon interactions. Recent studies, however, have shown that higher-order interactions constitute an additional resistive channel that significantly reduces the thermal conductivity of this material. Here, we show that the occurrence of hydrodynamic effects in graphene is severely conditioned by four-phonon interactions. Contrary to conventional understanding, we first demonstrate that the collective limit assumption, in which the phonon distribution is fully correlated, is not adequate to understand the hydrodynamic transport mechanisms in graphene. Then we report the key hydrodynamic parameters, namely the nonlocal length and the heat flux relaxation time, and we show that they are significantly reduced if considering full anharmonicity. Finally, we discuss observable implications in a variety of experimental configurations and we critically review previous predictions on the necessary conditions for the manifestation of collective phonon behavior and phonon hydrodynamics.