Heat conductivity in graphene and related materials: A time-domain modal analysis

We use molecular dynamics (MD) simulations to study heat conductivity in single-layer graphene and graphite. We analyze the MD trajectories through a time-domain modal analysis and show that this is essential for obtaining a reliable representation of the heat flow in graphene and graphite as it permits the proper treatment of collective vibrational excitations, in contrast to a frequency-domain formulation. Our temperature-dependent results are in very good agreement with experiment and, for temperatures in the range 300-1200 K, we find that the ZA branch allows more heat flow than all other branches combined while the contributions of the TA, LA, and ZO branches are comparable at all temperatures. Conductivity mappings reveal strong collective excitations associated with low-frequency ZA modes. We demonstrate that these collective effects are a consequence of the quadratic nature of the ZA branch as they also show up in graphite but are reduced in strained graphene, where the dispersion becomes linear, and are absent in diamond, where acoustic branches are linear. In general, neglecting collective excitations yields errors similar to those from the single-mode relaxation-time approximation.