Phonon thermal transport in strained and unstrained graphene from first principles

A rigorous first principles Boltzmann-Peierls equation (BPE) for phonon transport approach is employed to examine the lattice thermal conductivity, ${\ensuremath{\kappa}}_{L}$, of strained and unstrained graphene. First principles calculations show that the out-of-plane, flexural acoustic phonons provide the dominant contribution to ${\ensuremath{\kappa}}_{L}$ of graphene for all strains, temperatures, and system sizes considered, supporting a previous prediction that used an optimized Tersoff empirical interatomic potential. For the range of finite system sizes considered, we show that the ${\ensuremath{\kappa}}_{L}$ of graphene is relatively insensitive to strain. This provides validation for use of the BPE approach to calculate ${\ensuremath{\kappa}}_{L}$ for unstrained graphene, which has recently been called into question. The temperature and system size dependence of the calculated ${\ensuremath{\kappa}}_{L}$ of graphene is in good agreement with experimental data. The enhancement of ${\ensuremath{\kappa}}_{L}$ with isotopic purification is found to be relatively small due to strong anharmonic phonon-phonon scattering. This work provides insight into the nature of phonon thermal transport in graphene, and it demonstrates the power of first principles thermal transport techniques.