The thermal conductivity (TC) of isolated graphene with different concentrations of isotopes (C13) is studied with equilibrium molecular dynamics method at 300K. In the limit of pure C12 or C13 graphene, TC of graphene in zigzag and armchair directions are ~630 W/mK and ~1000W/mK, respectively. We find that the TC of graphene can be maximally reduced by ~80%, in both armchair and zigzag directions, when a random distribution of C12 and C13 is assumed at different doping concentrations. Therefore, our simulation results suggest an effective way to tune the TC of graphene without changing its atomic and electronic structure, thus yielding a promising application for nanoelectronics and thermoelectricity of graphene based nano-device.
Based on Zhang and Li's molecular dynamics calculations, the heat conductivity ($κ$) of metallic single-wall Carbon nanotubes (SNTs) was incorrectly concluded as mainly influenced by the radius. Apart from that, their isotope effect interpretation on $κ(T)$ for the metallic SNTs using solely the phonon scattering mechanism is also highlighted to be incorrect.
We find that introducing segmented isotopic disorder patterns may considerably reduce the thermal conductivity of pristine carbon nanotubes below the uncorrelated disorder value. This is a result of the interplay between different length scales in the phonon scattering process. We use ab-initio atomistic Green's function calculations to quantify the effect of various types of segmentation similar to that experimentally produced by coalescence of isotope-engineered fullerenes.
We developed a method of precise isotope labeling to visualize the continuous growth of graphene by chemical vapor deposition (CVD). This method allows us to see in real time the growth of graphene monocrystals at a resolution of a few seconds. This technique is used to extract the anisotropic growth rates, the formation of dendrites, and the dependence on adsorption area of methane on copper. We obtain a physical picture of the growth dynamics of graphene and its dependence on various parameters. Finally, our method is relevant to other CVD grown materials.
Large-area graphene is a new material with properties that make it desirable for advanced scaled electronic devices1. Recently, chemical vapor deposition (CVD) of graphene and few-layer graphene using hydrocarbons on metal substrates such as Ni and Cu has shown to be a promising technique2-5. It has been proposed in recent publications that graphene growth on Ni occurs by C segregation2 or precipitation3, while that on Cu is by surface adsorption5. In this letter, we used a carbon isotope labeling technique to elucidate the growth kinetics and unambiguously demonstrate that graphene growth on …
Boron arsenide (BAs) with a zinc blende structure has recently been discovered to exhibit unusual and ultrahigh thermal conductivity (k), providing a new outlook for research on BAs and other high thermal conductivity materials. Technology for BAs crystal growth has been continuously improving, however, the influence of boron isotopes, pure or mixed, on the thermal conductivity in BAs is still not completely clear. Here we report detailed studies on the growth of single crystals of BAs with different isotopic ratios and demonstrate that the k of isotopically pure BAs is at least 10% higher tha…
Thousands of tons of isotopic mixtures are processed annually for heavy-water production and tritium decontamination. The existing technologies remain extremely energy intensive and require large capital investments. New approaches are needed to reduce the industry's footprint. Recently, micron-size crystals of graphene were shown to act as efficient sieves for hydrogen isotopes pumped through graphene electrochemically. Here we report a fully-scalable approach, using graphene obtained by chemical vapor deposition, which allows a proton-deuteron separation factor of ca. 8, despite cracks and i…
We study the dependence of thermal conductivity of single walled nanotubes (SWNT) on chirality and isotope impurity by nonequilibrium molecular dynamics method with accurate potentials. It is found that, contrary to electronic conductivity, the thermal conductivity is insensitive to the chirality. The isotope impurity, however, can reduce the thermal conductivity up to 60% and change the temperature dependence behavior. We also study the dependence of thermal conductivity on tube length for tubes of different radius at different temperatures.
We study the optical conductivity in the low-energy regime of gapped mono- and bilayer graphene. A scaling relation is found, in which the four parameters frequency, gap, Fermi energy and temperature appear only as combination of three independent parameters. The ratio of the optical conductivity of bilayer and mononlayer graphene is exactly 2.
Ultra-wide-band-gap group-III nitrides are of interest for applications in deep-ultraviolet optoelectronics and power electronics. Such devices must be able to efficiently dissipate heat generated from their operation, making the thermal conductivity of the constituent materials an important parameter for high-power applications. We have investigated the phonon-limited thermal conductivity of AlN, GaN, and Al$_x$Ga$_{1-x}$N using first-principles calculations, with a focus on the effects of compositional and isotopic disorder. Our Boltzmann-transport-equation calculations show that the maximum…
We studied the thermal conductivity of graphene phononic crystal (GPnC), also named as graphene nanomesh, by molecular dynamics simulations. The dependences of thermal conductivity of GPnCs on both length and temperature are investigated. It is found that the thermal conductivity of GPnCs is significantly lower than that of graphene and can be efficiently tuned by changing the porosity and period length. For example, the ratio of thermal conductivity of GPnC to thermal conductivity of graphene can be changed from 0.1 to 0.01 when the porosity is changed from about 21% to 65%. The phonon partic…
We report on the first measurement of the thermal conductivity of a suspended single layer graphene. The measurements were performed using a non-contact optical technique. The near room-temperature values of the thermal conductivity in the range ~ 4840 to 5300 W/mK were extracted for a single-layer graphene. The extremely high value of the thermal conductivity suggests that graphene can outperform carbon nanotubes in heat conduction.
The thermal conductivity of isotopically enriched 28Si (enrichment better than 99.9%) was redetermined independently in three laboratories by high precision experiments on a total of 4 samples of different shape and degree of isotope enrichment in the range from 5 to 300 K with particular emphasis on the range near room temperature. The results obtained in the different laboratories are in good agreement with each other. They indicate that at room temperature the thermal conductivity of isotopically enriched 28Si exceeds the thermal conductivity of Si with a natural, unmodified isotope mixture…
Conductivity of the defectless, perfect crystal graphene is found at the neutrality point at zero temperature and in the limit of large dielectric constant of the substrate. The steady state of the graphene with weak current is assumed to be an ideal, rare plasma of particle and hole excitations governed by the Boltzmann kinetic equation.
Declining the lattice thermal conductivity in graphene is essential for its thermoelectric applications. In high electron density systems, scatterings of phonons by electrons are no less than the phonon scatterings by other phonons. With the aid of first-principle calculations we examine the lattice thermal conductivity in graphene by inducing electron-phonon scattering externally. With experimentally tunable charge carrier density we find $\sim 50\%$ reduction of the lattice thermal conductivity at 200 K. The present study opens up new avenues for potential thermoelectric applications of grap…
It is shown that the experimentally observed increase of the Young's modulus in single-layer graphene with low density of point defects leads to a noticeably enhancement of the thermal conductivity in a wide temperature range due to increasing the longitudinal and transverse phonon velocities.
The extremely high thermal conductivity of graphene has received great attention both in experiments and calculations. Obviously, new feature in thermal properties is of primary importance for application of graphene-based materials in thermal management in nanoscale. Here, we studied the thermal conductivity of graphene helicoid, a newly reported graphene-related nanostructure, using molecular dynamics simulation. Interestingly, in contrast to the converged cross-plane thermal conductivity in multi-layer graphene, axial thermal conductivity of graphene helicoid keeps increasing with thickness…
We investigate the effect of hydrogen coverage on the optical conductivity of single-side hydrogenated graphene from first principles calculations. To account for different degrees of uniform hydrogen coverage we calculate the complex optical conductivity for graphene supercells of various sizes, each containing a single additional hydrogen atom. We use the linearized augmented plane wave (LAPW) method, as implemented in the WIEN2k density functional theory code, to show that the hydrogen coverage strongly influences the complex optical conductivity and thus the optical properties, such as abs…
The optical conductivities of graphene layers are strongly dependent on their stacking orders. Our first-principle calculations show that while the optical conductivities of single layer graphene (SLG) and bilayer graphene (BLG) with Bernal stacking are almost frequency independent in the visible region, the optical conductivity of twisted bilayer graphene (TBG) is frequency dependent, giving rise to additional absorption features due to the band folding effect. Experimentally, we obtain from contrast spectra the optical conductivity profiles of BLG with different stacking geometries. Some TBG…
The topological effect on thermal conductivity is investigated through the comparison among graphene nanoribbons, carbon nanotubes and the Mobius-like graphene strips (MGS), by molecular dynamics simulation. It is found that the thermal conductivity of MGS is less than one half of that of graphene nanoribbons. The underlying mechanism whereby MGS acquire such low thermal conductivity may be attributable to the enhanced phonon-phonon scattering and localization property, which are induced by the nontrivial topology of Mobius strip. Moreover by counting in the dimensions of MGS, a lower length/w…
We perform molecular dynamics simulations to study the registry effect on the thermal conductivity of few-layer graphene. The interlayer interaction is described by either the Lennard-Jones potential or the registry-dependent potential. Our calculations show that the thermal conductivity in few-layer graphene from both potentials are close to each other, i.e the registry effect is essentially not important. It is because the thermal transport in few-layer graphene is mainly limited by the interlayer breathing mode, which is insensitive to the registry.
In this paper, the effect of B and N doping on the phonon induced thermal conductivity of graphene has been investigated. This study is important when one has to evaluate the usefulness of electronic properties of B and N doped graphene. We have performed the calculations by employing density functional perturbation theory(DFPT) to calculate the inter-atomic forces=force constants of pristine/doped graphene. Thermal conductivity calculations have been carried out by making use of linearized Boltzmann transport equations (LBTE) under single-mode relaxation time approximation (RTA). The thermal …
Prior ultralow thermal conductivity materials are not suitable for thermoelectric applications due to the limited electronic transport in the materials. Here, we present a new class of ultralow thermal conductivity materials with substantial electronic heat transport. Our samples are graphene/metal heterostructures of transferred graphene and ultrathin metal films (Pd, Au and Ni) deposited by either thermal evaporation or rf magnetron sputtering. For the evaporated samples, we achieve an ultralow thermal conductivity of 0.06 W m-1 K-1, with phonons as the dominant heat carriers. The ultralow t…
The thermal conductivity of silicon nanowires (SiNWs) is investigated by molecular dynamics (MD) simulation. It is found that the thermal conductivity of SiNWs can be reduced exponentially by isotopic defects at room temperature. The thermal conductivity reaches the minimum, which is about 27% of that of pure 28Si NW, when doped with fifty percent isotope atoms. The thermal conductivity of isotopic-superlattice structured SiNWs depends clearly on the period of superlattice. At a critical period of 1.09 nm, the thermal conductivity is only 25% of the value of pure Si NW. An anomalous enhancemen…
We reveal the hydrogen isotope effect of three chemical reactions, i.e, the reflection, the absorption and the penetration ratios, by classical molecular dynamics simulation with a modified Brenner's reactive empirical bond order (REBO) potential potential. We find that the reflection by pi-electron does not depend on the mass of the incident isotope, but the peak of the reflection by nuclear moves to higher side of incident energy. In addition to the reflection, we also find that the absorption ratio in the positive z side of the graphene becomes larger, as the mass of the incident isotope be…
We report a non-contact method for conductivity and sheet resistance measurements of graphene samples using a high Q microwave dielectric resonator perturbation technique, with the aim of fast and accurate measurement of microwave conductivity and sheet resistance of monolayer and few layers graphene samples. The dynamic range of the microwave conductivity measurements makes this technique sensitive to a wide variety of imperfections and impurities and can provide a rapid non-contacting characterisation method. Typically the graphene samples are supported on a low-loss dielectric substrate, su…
Heat conduction of single-walled carbon nanotubes (SWNTs) isotope-superlattice is investigated by means of classical molecular dynamics simulations. Superlattice structures were formed by alternately connecting SWNTs with different masses. On varying the superlattice period, the critical value with minimum effective thermal conductivity was identified, where dominant physics switches from zone-folding effect to thermal boundary resistance of lattice interface. The crossover mechanism is explained with the energy density spectra where zone-folding effects can be clearly observed. The results su…
Using calculations from first principles we have investigated the lattice thermal conductivity of ideal mono- and bi-layer graphene sheets. Our results demonstrate that the intrinsic thermal conductivity of both mono- and bi-layer graphene is around 2200 W/mK at 300 K, a value close to the one observed theoretically and experimentally in graphite basal plane, and at higher temperatures it decreases with the expected 1/T dependence. The little variation between mono- and bi-layer thermal conductivity suggests that increasing the number of layers does not affect significantly the in-plane therma…
A recently derived formula for complex conductivity of the monolayer graphene is analyzed. We show that the real and imaginary parts in this formula obey the Kramers and Kronig dispersion relations which are a good test for validity of the formula for complex conductivity of monolayer graphene. We consider also an additional test for this formula, sensitive to the integral characteristic of the conductance such as the famous f sum rule. We write it in the two dimensional form and show that it fulfils identically if we admit the cyclotron mass as an effective one and take the principal value of…
We report strong THz-induced transparency in CVD-grown graphene where 92%-96% of the peak-field is transmitted compared to 74% at lower field strength. Time-resolved THz-pump/THz-probe studies reveal that the absorption recovers in 2-3 ps. The induced transparency is believed to arise from nonlinear pumping of carriers in graphene which suppresses the mobility and consequently the conductivity in a spectral region where the light-matter interaction is particularly strong.
Thermal transport in single layer molybdenum disulfide (MoS2) is critical to advancing its applications. In this paper, we use molecular dynamics (MD) simulations with first-principles force constants to study the isotope effect on the thermal transport of single layer MoS2. Through phonon modal analysis, we found that isotopes can strongly scatter phonons with intermediate frequencies, and the scattering behavior can be radically different from that predicted by conventional scattering model based on perturbation theory (Tamura's formula). Such a discrepancy becomes smaller for low isotope co…
Transport measurements have revealed several exotic electronic properties of graphene. The possibility to influence the electronic structure and hence control the conductivity by adsorption or doping with adatoms is crucial in view of electronics applications. Here, we show that in contrast to expectation, the conductivity of graphene increases with increasing concentration of vacancy defects, by more than one order of magnitude. We obtain a pronounced enhancement of the conductivity after insertion of defects by both quantum mechanical transport calculations as well as experimental studies of…
Hydrogen isotope separation has been effectively achieved using gaseous H2/D2 filtered through graphene/Nafion composite membranes. Nevertheless, deuteron nearly does not exist in the form of gaseous D2 in nature but in liquid water. Thus, it is a more feasible way to separate and enrich deuterium from water. Herein we have successfully transferred monolayer graphene to a rigid and porous polymer substrate PITEM (polyimide tracked film), which could avoid the swelling problem of the Nafion substrate, as well as keep the integrity of graphene. Meanwhile, defects in large area of CVD graphene co…
Recent studies reveal that four-phonon scattering is generally important in determining thermal conductivities of solids. However, these studies have been focused on materials where thermal conductivity $κ$ is dominated by acoustic phonons, and the impact of four phonon scattering, although significant, is still generally smaller than three-phonon scattering. In this work, taking AlSb as example, we demonstrated that four-phonon scattering is even more critical to three-phonon scattering as it diminishes optical phonon thermal transport, and therefore significantly reduces the thermal conducti…
The understanding of the kinetic properties of hydrogen (isotopes) adatoms on graphene is important in many fields. The kinetic properties of hydrogen-isotope (H, D and T) monomers were simulated using a composite method consisting of density functional theory, density functional perturbation theory and harmonic transition state theory. The kinetic changes of the magnetic property and the aromatic $π$ bond of the hydrogenated graphene during the desorption and diffusion of the hydrogen monomer was discussed. The vibrational zero-point energy corrections in the activation energies were found to…
We investigate the electronic transport properties of copper-graphene composites using a density-functional framework. Conduction in composites by varying the interface distance of a copper/graphene/copper (Cu/G/Cu) interface models was studied. The electronic density of states reveals increasing contributions from both copper and carbon atoms near the Fermi level with decreasing Cu-G interfacial distance. Electronic conductivity of the models computed using the Kubo-Greenwood formula showed the conductivity increases with decreasing Cu-G distance. We also find that the conductivity saturates …
Penta-graphene (PG) has been identified as a novel 2D material with an intrinsic bandgap, which makes it especially promising for electronics applications. In this work, we use first-principles lattice dynamics and iterative solution of the phonon Boltzmann transport equation (BTE) to determine the thermal conductivity of PG and its more stable derivative - hydrogenated penta-graphene (HPG). As a comparison, we also studied the effect of hydrogenation on graphene thermal conductivity. In contrast to hydrogenation of graphene, which leads to a dramatic decrease in thermal conductivity (from 359…
Thermal conductivity of graphene nanoribbons (GNR) with length 106~Å and width 4.92~Å after isotopic doping is investigated by molecular dynamics with quantum correction. Two interesting phenomena are found: (1) isotopic doping reduces thermal conductivity effectively in low doping region, and the reduction slows down in high doping region; (2) thermal conductivity increases with increasing temperature in both pure and doped GNR; but the increasing behavior is much more slowly in the doped GNR than that in pure ones. Further studies reveal that the physics of these two phenomena is related to …
We use non-equilibrium molecular dynamics simulations to study the adverse role of defects including isotopic impurities on the thermal conductivity of carbon nanotubes, graphene and graphene nanoribbons. We find that even in structurally perfect nanotubes and graphene, isotopic impurities reduce thermal conductivity by up to one half by decreasing the phonon mean free path. An even larger thermal conductivity reduction, with the same physical origin, occurs in presence of structural defects including vacancies and edges in narrow graphene nanoribbons. Our calculations reconcile results of for…
We report the Raman spectroscopy of 12C/13C graphene isotope superlattices synthesized by chemical vapour deposition. At large periods the Raman spectra corresponds to the sum of the bulk 12C and 13C contributions. However, at small periods we observe the formation of mixed 12C/13C modes for Raman processes that involve two phonons, which results in the tripling of the 2D and 2D' Raman peaks. This tripling can be well understood in the framework of real space Raman spectroscopy, where the two emitted phonons stem from different regions of the superlattice. The intensity of the mixed peak incre…
The minimum conductivity value as well as the linear dependence of conductivity on the charge density near the Dirac point in single and doublelayer graphene is derived from the energy-time uncertainty principle applied to ballistic charge carriers.
Graphene-based laminates, with ultralong and tortuous nanocapillaries formed by simply stacking graphene flakes together, have great promises in filtration and separation. However, the information on liquid water trans-membrane permeation is lacking, which is the most fundamental problem and of crucial importance in solution-based mass transport. Here, based on isotope labelling, we investigate the liquid water transportation through graphene-based nanocapillaries under no external hydrostatic pressures. Liquid water can afford an unimpeded permeation through graphene-based nanochannels with a…
In this letter, we investigate numerically (by non-equilibrium molecular dynamics) and analytically the thermal conductivity of nanoscale graphene disks (NGDs), and discussed the possibility to realize FGM with only one material, NGDs. We found that the NGD has a graded thermal conductivity and can be used as FGM in a large temperature range. Moreover, we show the dependent of NGDs' thermal conductivity on radius and temperature. Our study may inspire experimentalists to develop NGD based FGMs and help heat removal of hot spots on chips by graphene.
The thermal conductivity of doped graphene flake of finite size is investigated with emphasis on the influence of mass of substituting atoms on this property. It is shown that the graphene doping by small concentrations of relatively heavy atoms results in a disproportionately impressive drop of lattice thermal conductivity.
In this work, we demonstrate that edge-oxidation of graphene can enable larger enhancement in thermal conductivity (k) of graphene-nanoplatelet (GnP)/polyetherimide (PEI) composites relative to oxidation of the basal plane of graphene. Edge oxidation (EGO) offers the advantage of leaving the basal plane of graphene intact, preserving its high in-plane thermal conductivity (kin > 2000 Wm-1K-1), while, simultaneously, the oxygen groups introduced on graphene edge enhance interfacial thermal conductance through hydrogen bonding with oxygen groups of polyetherimide (PEI), enhancing overall polymer…
An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimally-thin, local and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green's functions represented as Sommerfeld integrals. The solution of plane-wave reflection and transmission is presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductivity, a proper tra…
We study the conductivity of a graphene strip taking into account electrostatically-induced charge accumulation on its edges. Using a local dependency of the conductivity on the carrier concentration we find that the electrostatic size effect in doped graphene strip of the width of 0.5 - 3 $% μ$m can result in a significant (about 40%) enhancement of the effective conductivity in comparison to the infinitely wide samples. This effect should be taken into account both in the device simulation as well as for verification of scattering mechanisms in graphene.
We theoretically study current dynamics of graphene nanoribbons subject to bias dc and ac driven fields. We showed that graphene nanoribbons exhibit negative high-harmonic differential conductivity. Negative differential conductivity appears when bias electric filed is in the neighborhood of applied ac filed amplitude. We also observe both even and odd high-harmonic negative differential conductivity at wave mixing of two commensurate frequencies. The even harmonics are more pronounced than the odd harmonics. A possible use of the present method for generating terahertz frequencies at even har…
We investigate the conductivity of doped graphene in the semiclassical Boltzmann limit, as well as the conductivity minimum within the self-consistent transport theory. Using the hard-disk model for a two-dimensional distribution of impurities gives rise to both strong increase in the slope of conductivity at low charge carrier densities in graphene and a strongly sub-linear behavior of the conductivity at high charge carrier densities when the correlation distance between the impurities is large. On the other hand, we find that a super-linear dependence of the conductivity on charge carrier d…
Applying a quasiclassical equation to carriers in graphene we found a way how to distinguish between samples with the domination of short and long range scatterers from the conductivity measurements. The model proposed explains recent transport experiments with chemically doped as well as suspended graphene.
The conductivity of doped graphene is considered taking into account scattering by short-range nonsymmetric defects, when the longitudinal and transverse components of conductivity tensor appear to be different. The calculations of the anisotropic conductivity tensor are based on the quasiclassical kinetic equation for the case of monopolar transport at low temperatures. The effective longitudinal conductivity and the transverse voltage, which are controlled by orientation of sample and by gate voltage (i.e. doping level), are presented.
We have investigated thermal conductivity of graphene laminate films deposited on polyethylene terephthalate substrates. Two types of graphene laminate were studied - as deposited and compressed - in order to determine the physical parameters affecting the heat conduction the most. The measurements were performed using the optothermal Raman technique and a set of suspended samples with the graphene laminate thickness from 9 to 44 micrometers. The thermal conductivity of graphene laminate was found to be in the range from 40 W/mK to 90 W/mK at room temperature. It was found unexpectedly that th…
All-carbon heterostructures have been produced recently via focused ion beam patterning of single layer graphene. Amorphized graphene is similar to a graphene sheet in which some hexagons are replaced by a combination of pentagonal, heptagonal and octagonal rings. The present investigation provides a general view regarding phonon and load transfer along amorphous graphene. The developed models for the evaluation of mechanical and thermal conductivity properties yield accurate results for pristine graphene and acquired findings for amorphized graphene films are size independent. Our atomistic r…
The next-nearest neighbor interaction (NNN) is included in a tight-binding calculation of the electronic spectrum and conductivity of doped graphene. As a result, we observe a wide variation of the conductivity behavior, since the Fermi energy and the resonance peak are not shifted by the same amount. Such effect can have a profound effect in the idea of explaining the minimal conductivity of graphene as a consequence of impurities or defects. Finally, we also estimate the mean free path and relaxation time due to resonant impurity scattering.
It is a fact that the minimal conductivity $σ_0$ of most graphene samples is larger than the well-established universal value for ideal graphene $4e^2/πh$; in particular, larger by a factor $\gtrsimπ$. Despite intense theoretical activity, this fundamental issue has eluded an explanation so far. Here we present fully atomistic quantum mechanical estimates of the graphene minimal conductivity where electron-electron interactions are considered in the framework of density functional theory. We show the first conclusive evidence of the dominant role on the minimal conductivity of charged impuriti…
We describe Raman spectroscopy based method of measuring thermal conductivity of thin films, and review significant results achieved with this technique pertinent to graphene and other two-dimensional materials. The optothermal Raman method was instrumental for the discovery of unique heat conduction properties of graphene. In this method, Raman spectroscopy is used to determine the local temperature of the sample while the excitation laser is utilized as a heat source. The success of Raman spectroscopy in investigating thermal conductivity of suspended graphene and graphene-based thin films m…
We show that the origin of the universal optical conductivity in a normal $N$-layer graphene multilayer is an emergent chiral symmetry which guarantees that $σ(ω)=Nσ_{uni}$ in both low and high frequency limits. [$σ_{uni}=(π/2) e^2/h$]. We use this physics to relate intermediate frequency conductivity trends to qualitative characteristics of the multilayer stacking sequence.
The authors proposed a simple model for the lattice thermal conductivity of graphene in the framework of Klemens approximation. The Gruneisen parameters were introduced separately for the longitudinal and transverse phonon branches through averaging over phonon modes obtained from the first-principles. The calculations show that Umklapp-limited thermal conductivity of graphene grows with the increasing linear dimensions of graphene flakes and can exceed that of the basal planes of bulk graphite when the flake size is on the order of few micrometers. The obtained results are in agreement with e…
