Thermal conductivity of graphene mediated by strain and size

Based on first-principles calculations and full iterative solution of the linearized Boltzmann-Peierls transport equation for phonons within three-phonon scattering framework, we characterize the lattice thermal conductivities $\kappa$ of strained and unstrained graphene. We find $\kappa$ converges to 5450 W/m-K for infinite unstrained graphene, while $\kappa$ diverges for strained graphene with increasing system size at room temperature. The different $\kappa$ behaviors for these systems are further validated mathematically through phonon lifetime analysis. Flexural acoustic phonons are the dominant heat carriers in both unstrained and strained graphene within the temperature considered. Ultralong mean free paths of flexural phonons contribute to finite size effects on $\kappa$ for samples as large as 8 cm at room temperature. The calculated size-dependent and temperature-dependent $\kappa$ for finite samples agree well with experimental data, demonstrating the ability of the present approach to predict $\kappa$ of larger graphene sample. Tensile strain hardens the flexural modes and increases their lifetimes, causing interesting dependence of $\kappa$ on sample size and strain due to the competition between boundary scattering and intrinsic phonon-phonon scattering. These findings shed light on the nature of thermal transport in two-dimensional materials and may guide predicting and engineering $\kappa$ of graphene by varying strain and size.