The authors reported on investigation of the thermal conductivity of graphene suspended across trenches in Si/ SiO 2 wafer. The measurements were performed using a noncontact technique based on micro-Raman spectroscopy. The amount of power dissipated in graphene and corresponding temperature rise were determined from the spectral position and integrated intensity of graphene's G mode. The extremely high thermal conductivity in the range of ϳ3080-5150 W / m K and phonon mean free path of ϳ775 nm near room temperature were extracted for a set of graphene flakes. The obtained results suggest graphene's applications as thermal management material in future nanoelectronic circuits.

Graphene, in addition to its unique electronic and optical properties, reveals unusually high thermal conductivity. The fact that the thermal conductivity of large enough graphene sheets should be higher than that of basal planes of bulk graphite was predicted theoretically by Klemens. However, the exact mechanisms behind the drastic alteration of a material's intrinsic ability to conduct heat as its dimensionality changes from two to three dimensions remain elusive. The recent availability of high-quality few-layer graphene (FLG) materials allowed us to study dimensional crossover experimentally. Here we show that the room-temperature thermal conductivity changes from approximately 2,800 to approximately 1,300 W m(-1) K(-1) as the number of atomic planes in FLG increases from 2 to 4. We explained the observed evolution from two dimensions to bulk by the cross-plane coupling of the low-energy phonons and changes in the phonon Umklapp scattering. The obtained results shed light on heat conduction in low-dimensional materials and may open up FLG applications in thermal management of nanoelectronics.

Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering, Phys. Rev. B (2009) -Editors' Suggestion . 1 arXiv:0812.0518 [cond-mat.mtrl-sci] Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering, Phys. Rev. B (2009) -Editors' Suggestion .2 AbstractWe investigated theoretically the phonon thermal conductivity of single layer graphene. The phonon dispersion for all polarizations and crystallographic directions in graphene lattice was obtained using the valence-force field method. The three-phonon Umklapp processes were treated exactly using an accurate phonon dispersion and Brillouin zone, and accouting for all phonon relaxation channels allowed by the momentum and energy conservation laws. The uniqueness of graphene was reflected in the two-dimensional phonon density of states and restrictions on the phonon Umklapp scattering phase-space. The phonon scattering on defects and graphene edges has been also included in the model. The calculations were performed for the Gruneisen parameter, which was determined from the ab initio theory as a function of the phonon wave vector and polarization branch, and for a range of values from experiments. It was found that the near room-temperature thermal conductivity of single layer graphene, calculated with a realistic Gruneisen parameter, is in the range ~ 2000 -5000 W/mK depending on the defect concentration and roughness of the edges. Owing to the long phonon mean free path the graphene edges produce strong effect on thermal conductivity even at room temperature. The obtained results are in good agreement with the recent measurements of the thermal conductivity of suspended graphene.

Properties of phonons -quanta of the crystal lattice vibrations -in graphene have attracted strong attention of the physics and engineering communities. Acoustic phonons are the main heat carriers in graphene near room temperature while optical phonons are used for counting the number of atomic planes in Raman experiments with few-layer graphene. It was shown both theoretically and experimentally that transport properties of phonons, i.e. energy dispersion and scattering rates, are substantially different in the quasi two-dimensional system such as graphene compared to basal planes in graphite or three-dimensional bulk crystals. The unique nature of two-dimensional phonon transport translates to unusual heat conduction in graphene and related materials. In this review we outline different theoretical approaches developed for phonon transport in graphene, discuss contributions of the in-plane and cross-plane phonon modes and provide comparison with available experimental thermal conductivity data. Particular attention is given to analysis of recent theoretical results for the phonon thermal conductivity of graphene and few-layer graphene, and the effects of the strain, defects and isotopes on the phonon transport in these systems.

The authors proposed a simple model for the lattice thermal conductivity of graphene in the framework of Klemens approximation.

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

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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.