Commensurate Lattice Vector Dependent Thermal Conductivity of Twisted Bilayer Graphene

The in-plane thermal conductivity, as well as phonon dispersion of twisted bilayer graphene (TBG), are investigated as a function of temperature and rotation angle using both nonequilibrium molecular dynamics (NEMD) and density functional theory (DFT) combined with the phonon Boltzmann transport equation. The central result from the NEMD calculations is that the thermal conductivity decreases approximately linearly with the increasing lattice constant of the commensurate TBG unit cell. Comparisons of the phonon dispersions from both the DFT and NEMD calculations show that misorientation has the negligible effect on the low-energy phonon frequencies and velocities. However, the larger periodicity of TBG reduces the Brillouin zone size to the extent that the zone edge acoustic phonons are thermally populated allowing Umklapp scattering to reduce their lifetimes. This explanation is supported by DFT calculations of phonon-phonon lifetimes.