We investigated thermal conductivity of free-standing reduced graphene oxide films subjected to a high-temperature treatment of up to 1000°C. It was found that the hightemperature annealing dramatically increased the in-plane thermal conductivity, K, of the films from ~3 W/mK to ~61 W/mK at room temperature. The cross-plane thermal conductivity, K  , revealed an interesting opposite trend of decreasing to a very small value of ~0.09 W/mK in the reduced graphene oxide films annealed at 1000 o C. The obtained films demonstrated an exceptionally strong anisotropy of the thermal conductivity, K/K  ~ 675, which is substantially larger even than in the high-quality graphite. The electrical resistivity of the annealed films reduced to 1 / -19 /. The observed modifications of the in-plane and cross-plane thermal conductivity components resulting in an unusual K/K  anisotropy were explained theoretically. The theoretical analysis suggests that K can reach as high as ~500 W/mK with the increase in the sp 2 domain size and further reduction of the oxygen content. The strongly anisotropic heat conduction properties of these films can be useful for applications in thermal management.  Corresponding author (AAB): balandin@ee.ucr.edu ; web: http://ndl.ee.ucr.edu/ University of California -Riverside and Graphenea Inc. (2015) 2 | P a g e

We theoretically investigated phonon dispersion in AA-stacked, AB-stacked and twisted bilayer graphene with various rotation angles. The calculations were performed using the Born-von-Karman model for the intra-layer atomic interactions and the Lennard-Jones potential for the inter-layer interactions. It was found that the stacking order affects the outof-plane acoustic phonon modes the most. The difference in the phonon densities of states in the twisted bilayer graphene and in AA-or AB-stacked bilayer graphene appears in the phonon frequencies range 90 -110 cm -1 . Twisting bilayer graphene leads to emergence of new phonon branchestermed entangled phononswhich originate from mixing of phonon modes from different high-symmetry directions in the Brillouin zone. The frequencies of the entangled phonon depend strongly on the rotation angle and can be used for non-contact identification of the twist angles in graphene samples. The obtained results and tabulated frequencies of phonons in twisted bilayer graphene are important for interpretation of experimental Raman data and determining thermal conductivity of these materials systems.

We have investigated experimentally the thermal conductivity of suspended twisted bilayer graphene. The measurements were performed using an optothermal Raman technique. It was found that the thermal conductivity of twisted bilayer graphene is lower than that of monolayer graphene and the reference, Bernal stacked bilayer graphene in the entire temperature range examined (∼300-700 K). This finding indicates that the heat carriers - phonons - in twisted bilayer graphene do not behave in the same manner as that observed in individual graphene layers. The decrease in the thermal conductivity found in twisted bilayer graphene was explained by the modification of the Brillouin zone due to plane rotation and the emergence of numerous folded phonon branches that enhance the phonon Umklapp and normal scattering. The results obtained are important for understanding thermal transport in two-dimensional systems.