The important role of strain on phonon hydrodynamics in diamond-like bi-layer graphene

In this work, combining first-principles calculation and the phonon Boltzmann transport equation, we explored the diffusive thermal conductivity of diamond-like bi-layer graphene. The converged iterative solution provides high room temperature thermal conductivity of 2034 W mK^-1, significantly higher than other 2D materials. More interesting, the thermal conductivity calculated by relaxation time approximation is about 33% underestimated, revealing a remarkable phonon hydrodynamic transport characteristic. Significant strain dependence is reported, for example, under 5% tensile strain, room temperature thermal conductivity (1081 W mK^-1) of only about 50% of the strain-free sample, and under 20% strain, it reduces dramatically to only about 11% of the intrinsic one (226 W mK^-1). Unexpectedly, in addition to the remarkable reduction in the absolute value of thermal conductivity, tensile strain can impact the hydrodynamic significance. For example, under 5% strain, the underestimation of relaxation time approximation in thermal conductivity is reduced to 20%. Furthermore, using a non-equilibrium Green's function calculation, high ballistic thermal conductance (2.95 GW m^-2 K^-1) is demonstrated, and the mean free path is predicted to be 700 nm at room temperature. The importance of the knowledge of phonon transport in diamond-like bi-layer graphene goes beyond fundamental physics owing to its relevance to thermal management applications due to the super-high thermal conduction.