Showing papers on "Graphene published in 2005"
TL;DR: In this paper, an experimental investigation of magneto-transport in a high-mobility single layer of Graphene is presented, where an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene is observed.
Abstract: When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron–hole degeneracy and vanishing carrier mass near the point of charge neutrality1,2. Indeed, a distinctive half-integer quantum Hall effect has been predicted3,4,5 theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction—a consequence of the exceptional topology of the graphene band structure6,7. Recent advances in micromechanical extraction and fabrication techniques for graphite structures8,9,10,11,12 now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
11,122 citations
TL;DR: The use of Raman spectroscopy to reveal the remarkable structure and the unusual electronic and phonon properties of single wall carbon nanotubes (SWNTs) is reviewed comprehensively in this article.
3,835 citations
TL;DR: It is demonstrated that monolayer graphite films have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory, which produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed.
Abstract: Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by $(2+1)$-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity ${\ensuremath{\sigma}}_{xy}=\ensuremath{-}(2{e}^{2}/h)(2n+1)$ with $n=0,1,\dots{}$, which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the $n=0$ Landau level and was discovered in recent experiments on ultrathin graphite films.
1,148 citations
TL;DR: The structural, dynamical, and thermodynamic properties of diamond, graphite and layered derivatives (graphene, rhombohedral graphite) are computed using a combination of density-functional theory total-energy calculations and density functional perturbation theory lattice dynamics in the generalized gradient approximation as mentioned in this paper.
Abstract: The structural, dynamical, and thermodynamic properties of diamond, graphite and layered derivatives (graphene, rhombohedral graphite) are computed using a combination of density-functional theory total-energy calculations and density-functional perturbation theory lattice dynamics in the generalized gradient approximation. Overall, very good agreement is found for the structural properties and phonon dispersions, with the exception of the c/a ratio in graphite and the associated elastic constants and phonon dispersions. Both the C-33 elastic constant and the F to A phonon dispersions are brought to close agreement with available data once the experimental c/a is chosen for the calculations. The vibrational free energy and the thermal expansion, the temperature dependence of the elastic moduli and the specific heat are calculated using the quasiharmonic approximation. Graphite shows a distinctive in-plane negative thermal-expansion coefficient that reaches its lowest value around room temperature, in very good agreement with experiments. Thermal contraction in graphene is found to be three times as large; in both cases, bending acoustic modes are shown to be responsible for the contraction, in a direct manifestation of the membrane effect predicted by Lifshitz over 50 years ago. Stacking directly affects the bending modes, explaining the large numerical difference between the thermal-contraction coefficients in graphite and graphene, notwithstanding their common physical origin.
971 citations
TL;DR: The Born-Oppenheimer approximation (BO) has proven effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems as discussed by the authors.
Abstract: The Born-Oppenheimer approximation (BO) has proven effective for the accurate determination of chemical reactions, molecular dynamics and phonon frequencies in a wide range of metallic systems. Graphene, recently discovered in the free state, is a zero band-gap semiconductor, which becomes a metal if the Fermi energy is tuned applying a gate-voltage Vg. Graphene electrons near the Fermi energy have twodimensional massless dispersions, described by Dirac cones. Here we show that a change in Vg induces a stiffening of the Raman G peak (i.e. the zone-center E2g optical phonon), which cannot be described within BO. Indeed, the E2g vibrations cause rigid oscillations of the Dirac-cones in the reciprocal space. If the electrons followed adiabatically the Dirac-cone oscillations, no change in the phonon frequency would be observed. Instead, since the electron-momentum relaxation near the Fermi level is much slower than the phonon motion, the electrons do not follow the Dirac-cone displacements. This invalidates BO and results in the observed phonon stiffening. This spectacular failure of BO is quite significant since BO has been the fundamental paradigm to determine crystal vibrations from the early days of quantum mechanics.
971 citations
TL;DR: A proper account of the contribution of quantum effects to the free energy and the equilibrium constant for hydrogen adsorption suggest that the U.S. Department of Energy specification can be approached in a graphite-based physisorption system by optimizing the structures of nano-graphite platelets, which are light-weight, cheap, chemically inert, and environmentally benign.
Abstract: Many methods have been proposed for efficient storage of molecular hydrogen for fuel cell applications. However, despite intense research efforts, the twin U.S. Department of Energy goals of 6.5% mass ratio and 62 kg/m3 volume density has not been achieved either experimentally or via theoretical simulations on reversible model systems. Carbon-based materials, such as carbon nanotubes, have always been regarded as the most attractive physisorption substrates for the storage of hydrogen. Theoretical studies on various model graphitic systems, however, failed to reach the elusive goal. Here, we show that insufficiently accurate carbon–H2 interaction potentials, together with the neglect and incomplete treatment of the quantum effects in previous theoretical investigations, led to misleading conclusions for the absorption capacity. A proper account of the contribution of quantum effects to the free energy and the equilibrium constant for hydrogen adsorption suggest that the U.S. Department of Energy specification can be approached in a graphite-based physisorption system. The theoretical prediction can be realized by optimizing the structures of nano-graphite platelets (graphene), which are light-weight, cheap, chemically inert, and environmentally benign.
575 citations
TL;DR: This work fabricates a paper-like material that consists of hexagonally packed bundles of clean, coaxial carbon nanotubes whose double walls vary little in diameter, which will enable investigation of the physical properties of double-walled carbon Nanotubes, which are predicted to be superior to those of both their single- and multiwalled relatives.
Abstract: Double-walled carbon nanotubes (DWNTs) consist of two concentric graphene cylinders, a structure intermediate between single-walled and multiwalled carbon nanotubes. A coaxial structure could be ideal for use in nanocomposites and electronic devices. Previously it has not been possible to obtain DWNTs in a pure crystalline form, but now Endo et al. report fabrication of a paper-like material made up of hexagonally packed bundles of clean, coaxial carbon nanotubes. With this ‘buckypaper’ it will be possible to determine the physical properties of DWNTs, predicted to be superior to those of their single-walled and multiwalled relatives for some applications. Double-walled carbon nanotubes are needed in a pure, highly crystalline form before features such as their electronic properties, thermal transport and mechanical behaviour can be investigated. Here we fabricate a paper-like material that consists of hexagonally packed bundles of clean, coaxial carbon nanotubes whose double walls vary little in diameter; it is prepared in high yields using chemical-vapour deposition with a conditioning catalyst and two-step purification. Our results will enable investigation of the physical properties of double-walled carbon nanotubes, which are predicted to be superior to those of both their single- and multiwalled relatives.
531 citations
TL;DR: It is proposed that under ambient conditions a significant fraction of the oxygen-free edge sites are neither H-terminated nor unadulterated sigma free radicals, as universally assumed, which can explain the recently documented and heretofore puzzling ferromagnetic properties of some impurity-free carbon materials.
Abstract: Heretofore disconnected experimental observations are combined with a theoretical study to develop a model of the chemical composition of the edges of graphene sheets in both flat and curved sp2-hybridized carbon materials. It is proposed that under ambient conditions a significant fraction of the oxygen-free edge sites are neither H-terminated nor unadulterated σ free radicals, as universally assumed. The zigzag sites are carbene-like, with the triplet ground state being most common. The armchair sites are carbyne-like, with the singlet ground state being most common. This proposal is not only consistent with the key electronic properties and surface (re)activity behavior of carbons, but it can also explain the recently documented and heretofore puzzling ferromagnetic properties of some impurity-free carbon materials.
495 citations
TL;DR: Graphite nanoplatelets with thicknesses down to 2-10 nm are synthesized by alkali metal intercalation followed by ethanol exfoliation and microwave drying as mentioned in this paper, which can be achieved either by heating graphite and potassium or caesium at 200 °C, or at room temperature using a sodium-potassium alloy.
Abstract: Graphite nanoplatelets with thicknesses down to 2–10 nm are synthesized by alkali metal intercalation followed by ethanol exfoliation and microwave drying. Graphite that has already been intercalated and exfoliated with an oxidizing acid is reintercalated with an alkali metal to form a first stage compound, as confirmed by powder X-ray diffraction. This can be achieved either by heating graphite and potassium or caesium at 200 °C, or at room temperature using a sodium–potassium alloy. Reaction of the intercalated graphite with ethanol causes exfoliation of the graphene layers. Microwave radiation aids in drying and results in further separation of the sheets. Thermogravimetric analysis indicates that the graphite nanoplatelets are approximately 150 °C less stable in air than pristine graphite. High aspect ratio graphite nanoplatelets offer promise as reinforcements for high strength carbon–carbon composites.
435 citations
Journal Article•
TL;DR: In this paper, Zhou et al. investigated the simulation of vacancy defects in graphene layers and showed that two single vacancies coalesce into a 5-8-5 double vacancy at the temperature of 3000 K, and four single vacancies reconstruct into two collective 555-777 defects at higher temperatures.
Abstract: Diffusion, coalescence, and reconstruction of vacancy defects in graphene layers are investigated by tight-binding molecular dynamics (TBMD) simulations and by first principles total energy calculations. It is observed in the TBMD simulations that two single vacancies coalesce into a 5-8-5 double vacancy at the temperature of 3000 K, and it is further reconstructed into a new defect structure, the 555-777 defect, by the Stone-Wales type transformation at higher temperatures. First principles calculations confirm that the 555-777 defect is energetically much more stable than two separated single vacancies, and the energy of the 555-777 defect is also slightly lower than that of the 5-8-5 double vacancy. In TBMD simulation, it is also found that the four single vacancies reconstruct into two collective 555-777 defects which is the unit for the hexagonal haeckelite structure proposed by Terrones et al. [Phys. Rev. Lett. 84, 1716 (2000)].
380 citations
TL;DR: It is suggested that the efficiency of macromolecular dispersion agents for NT solubilization correlates with the topological and electronic similarity of polymer-NT and NT-NT interactions in the nanotube bundles.
Abstract: Poor solubility of single-walled and multiwalled carbon nanotubes (NTs) in water and organic solvents presents a considerable challenge for their purification and applications. Macromolecules can be convenient solubilizing agents for NTs and a structural element of composite materials for them. Several block copolymers with different chemical functionalities of the side groups were tested for the preparation of aqueous NT dispersions. Poly(N-cetyl-4-vinylpyridinium bromide-co-N-ethyl-4-vinylpyridinium bromide-co-4-vinylpyridine) was found to form exceptionally stable NT dispersions. It is suggested that the efficiency of macromolecular dispersion agents for NT solubilization correlates with the topological and electronic similarity of polymer-NT and NT-NT interactions in the nanotube bundles. Raman spectroscopy and atomic force and transmission electron microcopies data indicate that the polycations are wrapped around NTs forming a uniform coating 1.0-1.5 nm thick. The ability to wind around the NT originates in the hydrophobic attraction of the polymer backbone to the graphene surface and topological matching. Tetraalkylammonium functional groups in the side chains of the macromolecule create a cloud of positive charge around NTs, which makes them hydrophilic. The prepared dispersions could facilitate the processing of the nanotubes into composites with high nanotube loading for electronic materials and sensing. Positive charge on their surface is particularly important for biological and biomedical applications because it strengthens interactions with negatively charged cell membranes. A high degree of spontaneous bundle separation afforded by the polymer coating can also be beneficial for NT sorting.
TL;DR: Room-temperature piranha treatments have the capability of cutting existing damage sites with minimal carbon loss, slow etch rates, and little sidewall damage and combined with a method of introducing controlled amounts of damage sites have the potential to yield an efficient means of creating short, cut nanotubes.
Abstract: The oxidation reaction of piranha solutions with purified HiPco carbon nanotubes was measured as a function of temperature. At high temperatures, piranha is capable of attacking existing damage sites, generating vacancies in the graphene sidewall, and consuming the oxidized vacancies to yield short, cut nanotubes. Increased reaction time results in increasingly shorter nanotubes. However, significant sidewall damage occurs as well as selective etching of the smaller diameter nanotubes. On the other hand, room-temperature piranha treatments show the capability of cutting existing damage sites with minimal carbon loss, slow etch rates, and little sidewall damage. Combined with a method of introducing controlled amounts of damage sites, these room-temperature piranha solutions have the potential to yield an efficient means of creating short, cut nanotubes.
TL;DR: Calculations of the quantum-mechanical ballistic thermal conductance of single-walled carbon nanotubes, graphene, and graphite are presented, which explain previous experimental results, and directly disprove earlier theoretical calculations.
Abstract: Calculations of the quantum-mechanical ballistic thermal conductance of single-walled carbon nanotubes, graphene, and graphite are presented, which explain previous experimental results, and directly disprove earlier theoretical calculations. The ballistic thermal conductances are smaller than had been previously thought, whereas the maximum sample lengths in which phonon transport remains ballistic are orders of magnitude larger than previously suggested. Good agreement with previous experiments is obtained, which shows that measured lower bounds to the thermal conductance of multiwalled carbon nanotubes are very close to the upper theoretical bounds for graphite. The bounds shown here draw a line between what is physical and unphysical in any measurements or calculations of carbon nanotube thermal conductance, and constitute a necessary test to their validity.
IBM1
TL;DR: The electron-phonon scattering and binding in semiconducting carbon nanotubes, within a tight-binding model, is calculated and the mobility as a function of temperature, electric field, and nanotube chirality are well reproduced by a simple interpolation formula.
Abstract: We calculate the electron-phonon scattering and binding in semiconducting carbon nanotubes, within a tight-binding model. The mobility is derived using a multiband Boltzmann treatment. At high fields, the dominant scattering is interband scattering by $LO$ phonons corresponding to the corners $K$ of the graphene Brillouin zone. The drift velocity saturates at approximately half the graphene Fermi velocity. The calculated mobility as a function of temperature, electric field, and nanotube chirality are well reproduced by a simple interpolation formula. Polaronic binding give a band-gap renormalization of $\ensuremath{\sim}70\text{ }\text{ }\mathrm{m}\mathrm{e}\mathrm{V}$, an order of magnitude larger than expected. Coherence lengths can be quite long but are strongly energy dependent.
TL;DR: The results show that a sp2 bonded cap is formed on an iron catalyst, following the diffusion of C atoms from hydrocarbon precursors on the nanoparticle surface, which enables the graphene sheet to "float" on the curved surface, as additional C atoms covalently bonded to the catalyst "hold the tube walls".
Abstract: We report on ab initio molecular dynamics simulations of the early stages of single-walled carbon nanotube (SWCNT) growth on metal nanoparticles. Our results show that a sp2 bonded cap is formed on an iron catalyst, following the diffusion of C atoms from hydrocarbon precursors on the nanoparticle surface. The weak adhesion between the cap and iron enables the graphene sheet to "float" on the curved surface, as additional C atoms covalently bonded to the catalyst "hold" the tube walls. Hence the SWCNT grows capped. At the nanoscale, we did not observe any tendency of C atoms to penetrate inside the catalyst, consistent with total energy calculations showing that alloying of Fe and C is very unlikely for 1 nm particles. Root growth was observed on Fe but not on Au, consistent with experiment.
TL;DR: In this article, the changes in the electronic structure induced by lattice defects in graphene planes were studied and it was shown that lattice distortions give rise to localized states at the Fermi level.
Abstract: We study the changes in the electronic structure induced by lattice defects in graphene planes. In many cases, lattice distortions give rise to localized states at the Fermi level. Electron-electron interactions lead to the existence of local moments. The RKKY interaction between these moments is always ferromagnetic, due to the semimetallic properties of graphene.
TL;DR: The results support and explain qualitatively the enhancement of the hydrogen storage capacity observed in some experiments of hydrogen adsorption on carbon nanotubes doped with alkali atoms.
Abstract: Density-functional calculations of the adsorption of molecular hydrogen on a planar graphene layer and on the external surface of a (4,4) carbon nanotube, undoped and doped with lithium, have been carried out. Hydrogen molecules are physisorbed on pure graphene and on the nanotube with binding energies about 80-90 meV/molecule. However, the binding energies increase to 160-180 meV/molecule for many adsorption configurations of the molecule near a Li atom in the doped systems. A charge-density analysis shows that the origin of the increase in binding energy is the electronic charge transfer from the Li atom to graphene and the nanotube. The results support and explain qualitatively the enhancement of the hydrogen storage capacity observed in some experiments of hydrogen adsorption on carbon nanotubes doped with alkali atoms.
TL;DR: A spin-polarized first-principles calculation of the atomic and electronic structure of the graphene/Ni(111) interface is presented in this article, where different structural models have been considered, which differ in the positions of the carbon atoms with respect to the nickel topmost layer.
Abstract: A spin-polarized first-principles calculation of the atomic and electronic structure of the graphene/Ni(111) interface is presented. Different structural models have been considered, which differ in the positions of the carbon atoms with respect to the nickel topmost layer. The most probable structure, which has the lowest energy, has been determined. The distance between the floating carbon layer and the nickel surface is found smaller than the distance between graphene sheets in bulk graphite, in accordance with experimental measurements. The electronic structure of the graphene layer is strongly modified by interaction with the substrate and the magnetic moment of the surface nickel atoms is lowered in the presence of the graphene layer. Several interface states have been identified in different parts of the interface two-dimensional Brillouin zone. Their influence on the electron energy loss spectra has been evaluated.
TL;DR: In this article, a vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium is investigated and the corresponding natural frequencies and the associated modes are determined based on the fact that the elastic moduli of a graphene sheet in two perpendicular orientations are different, so the plate is considered to be anisotropic.
TL;DR: In this article, the presence of ferromagnetic magnetism in the phase diagram of the two-dimensional honeycomb lattice close to half-filling (graphene) as a function of the strength of the Coulomb interaction and doping was studied.
Abstract: We study the presence of ferromagnetism in the phase diagram of the two-dimensional honeycomb lattice close to half-filling (graphene) as a function of the strength of the Coulomb interaction and doping. We show that exchange interactions between Dirac fermions can stabilize a ferromagnetic phase at low doping when the coupling is sufficiently large. In clean systems the zero-temperature phase diagram shows both first-order and second-order transition lines and two distinct ferromagnetic phases: one phase with only one type of carriers (either electrons or holes) and another with two types of carriers (electrons and holes). Using the coherent potential approximation we argue that disorder further stabilizes the ferromagnetic phase. This work should estimulate Monte Carlo calculations in graphene dealing with the long-range nature of the Coulomb potencial.
TL;DR: In this paper, the electronic local density of states (LDOS) near single-step edges at the surface of exfoliated graphite was studied experimentally and theoretically, and it was shown that these superstructures can coexist if the two types of edges admix each other in real graphite step edges.
TL;DR: In this article, the quantum magnetic oscillations of electrical (Shubnikov--de Haas effect) and thermal conductivities are studied for graphene which represents a distinctive example of planar systems with a linear, Dirac-like spectrum of quasiparticle excitations.
Abstract: The quantum magnetic oscillations of electrical (Shubnikov--de Haas effect) and thermal conductivities are studied for graphene which represents a distinctive example of planar systems with a linear, Dirac-like spectrum of quasiparticle excitations. We show that if utmost care is taken to separate electron and phonon contributions in the thermal conductivity, the oscillations of electron thermal conductivity $\ensuremath{\kappa}(B)$ and Lorenz number, $L(B)$ would be observable in the low-field (less than a few teslas) regime.
TL;DR: In this article, the atomic, electronic and magnetic structure of nitrogen impurities in graphite and carbon nanotubes was studied using ab initio methods to calculate the migration energy barrier for an N adatom on the graphite surface and the activation energy for the coalescence of two N adatoms into a molecule.
Abstract: We use ab initio methods to study the atomic, electronic, and magnetic structure of nitrogen impurities in graphite and carbon nanotubes. We show that the probable configurations for the N impurity atoms are bridgelike adatoms on graphene sheets/nanotubes, substitutional sites and intercalated ${\mathrm{N}}_{2}$ molecules. We further calculate the migration energy barrier for an N adatom on the graphite surface and the activation energy for the coalescence of two N adatoms into a molecule, which are $1.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and $0.8\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, respectively. We also find that the N adatom has a magnetic moment of $0.6{\ensuremath{\mu}}_{B}$ and that substitutional N enhances the magnetism of C adatoms on graphite and nanotubes, acting as a general promoter of magnetism in carbon systems.
TL;DR: This work investigates theoretically the nonequilibrium transport properties of carbon nanotube quantum dots and finds an SU(4) Kondo effect at low temperatures, which manifests as a four-peak splitting in the nonlinear conductance when an axial magnetic field is applied.
Abstract: We investigate theoretically the nonequilibrium transport properties of carbon nanotube quantum dots. Owing to the two-dimensional band structure of graphene, a double orbital degeneracy plays the role of a pseudospin, which is entangled with the spin. Quantum fluctuations between these 4 degrees of freedom result in an SU(4) Kondo effect at low temperatures. This exotic Kondo effect manifests as a four-peak splitting in the nonlinear conductance when an axial magnetic field is applied.
TL;DR: In this paper, the diameter and length of armchair single wall carbon nanotubes from 4,4 to 15,15 were calculated using semi-empirical PM3 and PM5 and density functional PBEPBE and B3LYP methods.
TL;DR: In this article, the synthesis of carbon nanotubes (CNTs) through the catalytic decomposition of acetylene was carried out over gold nanoparticles supported on SiO 2 -Al 2 O 3.
TL;DR: In this article, the authors have grown epitaxial thin sheets of graphene on BC 3 /NbB 2 (0001) and measured phonon dispersion curves of the graphene sheets by means of high-resolution electron energy-loss spectroscopy (HREELS).
Abstract: We have grown epitaxial thin sheets of graphene on BC 3 /NbB 2 (0001) and measured phonon dispersion curves of the graphene sheets by means of high-resolution electron energy-loss spectroscopy (HREELS). The phonon dispersion curves have been calculated on the basis of ab initio calculations. The observed curves were in good agreement with theoretical curves. The quality of crystallinity of the graphene layers was high compared with the bulk graphite crystals. In this paper, we demonstrate that the combination of HREELS measurement and ab initio calculations is extremely effective for investigation of honeycomb-structured materials.
01 Jan 2005
TL;DR: In this paper, the formation of vertically aligned carbon nanowalls using fluorocarbon (radio-frequency) rf plasma-enhanced chemical vapor deposition (PECVD) assisted by H radical injection was demonstrated.
Abstract: Carbon nanowalls, two-dimensional carbon nanostructures consisting of plane graphene layers standing on the substrate, have been grown recently. The large surface area of carbon nanowalls may provide us with various new applications. We proposed novel plasma processing, radical-controlled processing using radical injection technique, and demonstrated the successful formation of vertically aligned carbon nanowalls using fluorocarbon (radio-frequency) rf plasma-enhanced chemical vapor deposition (PECVD) assisted by H radical injection. Radical injection technique enables us to control multiple radicals individually and has great possibilities in fabricating novel nanometer-scaled functional materials. In view of the practical application of carbon nanowalls, further investigations should be performed in order to enable control over the structure and electronic properties and understand their growth mechanism.
TL;DR: The local atomic correlation as a commensurate graphene stacking was repeatedly found in eccentric DWNTs and circumscribed nanotubes, which should lead to elastic deformation and bundling of nanot tubes.
Abstract: Atomic correlation between adjacent graphene layers was elucidated for double-wall carbon nanotubes (DWNTs) through a chiral index assignment of two nested nanotubes by high-resolution transmission electron microscopy. Our analysis provides a rather constant diameter difference close to 0.75 nm but no chiral angle correlation between the constituent nanotubes in the concentric DWNTs. The local atomic correlation as a commensurate graphene stacking was repeatedly found in eccentric DWNTs and circumscribed nanotubes, which should lead to elastic deformation and bundling of nanotubes.