# Is Thermal Conductivity of Graphene Divergent and Higher Than Diamond?

## TL;DR

This study uses advanced first-principles calculations to determine that monolayer graphene's thermal conductivity converges at about 1300 W/(m·K) when four-phonon scattering is considered, and is lower than diamond's.

## Contribution

It provides the first comprehensive first-principles analysis including four-phonon scattering, resolving the debate on graphene's thermal conductivity and its size dependence.

## Key findings

- Thermal conductivity converges at 1300 W/(m·K) with four-phonon scattering.
- Considering only three-phonon scattering leads to divergence.
- Graphene's thermal conductivity is lower than diamond's.

## Abstract

The thermal conductivity of monolayer graphene is an outstanding challenge with no consensus reached on its exact value and length convergence so far. We consider four-phonon scattering, phonon renormalization, and an exact solution to phonon Boltzmann transport equation (BTE) from first principles. Using this computational formalism with unprecedented sampling grid, we show that when four-phonon scattering is included the thermal conductivity is convergent with system size at a room temperature value of 1300 W/(m$\cdot$K), which is lower than that of diamond. On the contrary, considering three-phonon scattering only yields divergence with size due to the momentum-conserving normal processes of flexural phonons.