In recent years intercalated and pillared graphitic systems have come under increasing scrutiny because of their potential for modern energy technologies. While traditional \emph{ab initio} methods such as the LDA give accurate geometries for graphite they are poorer at predicting physicial properties such as cohesive energies and elastic constants perpendicular to the layers because of the strong dependence on long-range dispersion forces. `Stretching' the layers via pillars or intercalation further highlights these weaknesses. We use the ideas developed by [J. F. Dobson et al, Phys. Rev. Lett. {\bf 96}, 073201 (2006)] as a starting point to show that the asymptotic $C_3 D^{-3}$ dependence of the cohesive energy on layer spacing $D$ in bigraphene is universal to all graphitic systems with evenly spaced layers. At spacings appropriate to intercalates, this differs from and begins to dominate the $C_4 D^{-4}$ power law for dispersion that has been widely used previously. The corrected power law (and a calculated $C_3$ coefficient) is then unsuccesfully employed in the semiempirical approach of [M. Hasegawa and K. Nishidate, Phys. Rev. B {\bf 70}, 205431 (2004)] (HN). A modified, physicially motivated semiempirical method including some $C_4 D^{-4}$ effects allows the HN method to be used successfully and gives an absolute increase of about $2-3%$ to the predicted cohesive energy, while still maintaining the correct $C_3 D^{-3}$ asymptotics.
We present the full in-plane phonon dispersion of graphite obtained from inelastic x-ray scattering, including the optical and acoustic branches, as well as the mid-frequency range between the $K$ and $M$ points in the Brillouin zone, where experimental data have been unavailable so far. The existence of a Kohn anomaly at the $K$ point is further supported. We fit a fifth-nearest neighbour force-constants model to the experimental data, making improved force-constants calculations of the phonon dispersion in both graphite and carbon nanotubes available.
We combine high-level theoretical and \emph{ab initio} understanding of graphite to develop a simple, parametrised force-field model of interlayer binding in graphite, including the difficult non-pairwise-additive coupled-fluctuation dispersion interactions. The model is given as a simple additive correction to standard density functional theory (DFT) calculations, of form $ΔU(D)=f(D)[U^{vdW}(D)-U^{DFT}(D)]$ where $D$ is the interlayer distance. The functions are parametrised by matching contact properties, and long-range dispersion to known values, and the model is found to accurately match h…
A universal set of third--nearest neighbour tight--binding (TB) parameters is presented for calculation of the quasiparticle (QP) dispersion of $N$ stacked $sp^2$ graphene layers ($N=1... \infty$) with $AB$ stacking sequence. The QP bands are strongly renormalized by electron--electron interactions which results in a 20% increase of the nearest neighbour in--plane and out--of--plane TB parameters when compared to band structure from density functional theory. With the new set of TB parameters we determine the Fermi surface and evaluate exciton energies, charge carrier plasmon frequencies and t…
We review calculations and measurements of the phonon-dispersion relation of graphite. First-principles calculations using density-functional theory are generally in good agreement with the experimental data since the long-range character of the dynamical matrix is properly taken into account. Calculations with a plane-wave basis demonstrate that for the in-plane optical modes, the generalized-gradient approximation (GGA) yields frequencies lower by 2% than the local-density approximation (LDA) and is thus in better agreement with experiment. The long-range character of the dynamical matrix li…
We demonstrate that graphite phonon dispersions have two Kohn anomalies at the Gamma-E_2g and K-A'1 modes. The anomalies are revealed by two sharp kinks. By an exact analytic derivation, we show that the slope of these kinks is proportional to the square of the electron-phonon coupling (EPC). Thus, we can directly measure the EPC from the experimental dispersions. The Gamma-E_2g and K-A'1 EPCs are particularly large, whilst they are negligible for all the other modes at Gamma and K.
The structural, dynamical, and thermodynamical properties of diamond, graphite and layered derivatives (graphene, rhombohedral graphite) are computed using a combination of density-functional theory (DFT) total-energy calculations and density-functional perturbation theory (DFPT) lattice dynamics at the GGA-PBE level. 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 Gamma to A phonon dispersions are brough…
Angle resolved photoelectron spectroscopy (ARPES) on azimuthally disordered graphite demonstrates that sharp quasiparticle dispersions along the radial direction can coexist with a complete lack of dispersion along the azimuthal direction. This paradoxical coexistence can be explained in terms of van Hove singularities in the angular density of states. In addition, nondispersive features at the energies of band maxima and saddle points are observed and possible explanations are discussed. This work opens a possibility of studying the electronic structure of layered materials using ARPES even w…
The dispersion relation of the high energy optical π-plasmons of simple hexagonal intrinsic graphite was calculated within the self-consistent-field approximation. The plasmon frequency ω_p is determined as functions of the transferred momentum $q_{\parallel}$ along the hexagonal plane in the Brillouin zone and its perpendicular component $q_z$. These plasmons are isotropic within the plane in the long wavelength limit. As the in-plane transferred momentum is increased, the plasmon frequency strongly depends on its magnitude and direction (ϕ). With increasing angle, the dispersion relation wit…
We compute electron-phonon coupling (EPC) of selected phonon modes in graphene and graphite using various ab-initio methods. The inclusion of non-local exchange-correlation effects within the GW approach strongly renormalizes the square EPC of the A$'_1$ {\bf K} mode by almost 80$%$ with respect to density functional theory in the LDA and GGA approximations. Within GW, the phonon slope of the A$'_1$ {\bf K} mode is almost two times larger than in GGA and LDA, in agreement with phonon dispersions from inelastic x-ray scattering and Raman spectroscopy. The hybrid B3LYP functional overestimates t…
We have demonstrated a method to disperse and exfoliate graphite to give graphene suspended in water-surfactant solutions. Optical characterisation of these suspensions allowed the partial optimisation of the dispersion process. Transmission electron microscopy showed the dispersed phase to consist of small graphitic flakes. More than 40% of these flakes had <5 layers with ~3% of flakes consisting of monolayers. These flakes are stabilised against reaggregation by Coulomb repulsion due to the adsorbed surfactant. However, the larger flakes tend to sediment out over ~6 weeks, leaving only small…
We show that rhombohedral graphite may support surface superconductivity with an unusual relation between the BCS coupling constant and the order parameter. This feature results from the properties of the states localized on the graphite surfaces. In a description including only the nearest neighbour coupling of the graphene layers, the surface states are topologically protected and have a flat band dispersion. We show that including higher order couplings destroys this flat band character and leads to a particle-hole symmetry breaking quadratic dispersion with a large effective mass. Employin…
In this paper, we present a high resolution angle resolved photoemission spectroscopy (ARPES) study of the electronic properties of graphite. We found that the nature of the low energy excitations in graphite is particularly sensitive to interlayer coupling as well as lattice disorder. As a consequence of the interlayer coupling, we observed for the first time the splitting of the $π$ bands by $\approx$ 0.7 eV near the Brillouin zone corner K. At low binding energy, we observed signatures of massless Dirac fermions with linear dispersion (as in the case of graphene), coexisting with quasiparti…
Graphene is at the centre of nanotechnology research. In order to fully exploit its outstanding properties, a mass production method is necessary. Two main routes are possible: large-scale growth or large-scale exfoliation. Here, we demonstrate graphene dispersions with concentrations up to ~0.01 mg/ml by dispersion and exfoliation of graphite in organic solvents such as N-methyl-pyrrolidone. This occurs because the energy required to exfoliate graphene is balanced by the solvent-graphene interaction for solvents whose surface energy matches that of graphene. We confirm the presence of individ…
Via a novel experiment, Liu \emph{et al.} [Phys. Rev. B, {\bf 85}, 205418 (2012)] estimated the graphite binding energy, specifically the cleavage energy, an important physical property of bulk graphite. We re-examine the data analysis and note that within the standard Lennard-Jones model employed, there are difficulties in achieving internal consistency in the reproduction of the graphite elastic properties. By employing similar models which guarantee consistency with the elastic constant, we find a wide range of model dependent binding energy values from the same experimental data. We attrib…
Graphite, with many industrial applications, is one of the widely sought-after allotropes of carbon. The sp2 hybridized and thermodynamically stable form of carbon forms a layered structure with strong in-plane carbon bonds and weak inter-layer van der Waals bonding. Graphite is also a high-temperature ceramic, and shaping them into complex geometries is challenging, given its limited sintering behavior even at high temperatures. Although the geometric design of the graphite structure in many of the applications could dictate its precision performance, conventional synthesis methods for formul…
In this work, we report our results on the geometric and electronic properties of hybrid graphite-like structure made up of silicene and boron nitride (BN) layers. We predict from our calculations that this hybrid bulk system, with alternate layers of honeycomb silicene and BN, possesses physical properties similar to those of bulk graphite. We observe that there exists a weak van der Waals interaction between the layers of this hybrid system in contrast to the strong inter-layer covalent bonds present in multi-layers of silicene. Furthermore, our results for the electronic band structure and …
A novel WS2-graphite dual-ion battery (DIB) is developed by combining together a conventional graphite cathode and high-capacity few-layer WS2 flakes anode. The WS2 flakes are produced by exploiting wet-jet milling (WJM) exfoliation, which allows mass production of few-layer WS2 flakes in dispersion, with an exfoliation yield of 100%. The WS2-anodes enable DIBs, based on hexafluorophosphate (PF6-) and lithium (Li+) ions, to achieve charge specific capacities of 457, 438, 421, 403, 295 and 169 mAh g-1 at current rates of 0.1, 0.2, 0.3, 0.4, 0.8 and 1.0 A g-1, respectively, outperforming convent…
Using the standard tight binding model of 2d graphite with short range electron repulsion, we find a gapless spin-1, neutral collective mode branch {\em below the particle-hole continuum} with energy vanishing linearly with momenta at the $Γ$ and $K$ points in the BZ. This spin-1 mode has a wide energy dispersion, 0 to $\sim 2 eV$ and is not Landau damped. The `Dirac cone spectrum' of electrons at the chemical potential of graphite generates our collective mode; so we call this `spin-1 zero sound' of the `Dirac sea'. Epithermal neutron scattering experiments, where graphite single crystals are…
In the present work, the use of a commercial ionic liquid as a convenient solvent medium for graphite exfoliation in mild and easy conditions without any chemical modification is presented. To confirm the presence of few layer graphene, its dispersion was charachterized by Raman spectroscopy, atomic force miscroscopy and field emission electron microscopy. From the UV-Vis characterization, a graphene concentration as high as 2.543 mg/ml was obtained, which is the highest value reported so far in any solvent.
We have revisited the still unresolved puzzle of the dispersion of the Raman disordered-induced D band as a function of laser excitation photon energy E$_L$ in graphite-like materials. We propose that the D-mode is a combination of an optic phonon at the K-point in the Brillioun zone and an acoustic phonon whose momentum is determined uniquely by the double resonance condition. The fit of the experimental data with the double-resonance model yields the reduced effective mass of 0.025m$_{e}$ for the electron-hole pairs corresponding to the A$_{2}$ transition, in agreement with other experiments…
Electronic properties of bilayer and multilayer graphene have generally been interpreted in terms of AB or Bernal stacking. However, it is known that many types of stacking defects can occur in natural and synthetic graphite; rotation of the top layer is often seen in scanning tunneling microscopy (STM) studies of graphite. In this paper we consider a graphene bilayer with a relative small angle rotation between the layers and calculate the electronic structure near zero energy in a continuum approximation. Contrary to what happens in a AB stacked bilayer and in accord with observations in epi…
The intrinsic channel properties of monolayer and multilayer graphene were systematically investigated as a function of layer number by the exclusion of contact resistance using four-probe measurements. We show that the continuous change in normalized sheet resistivity from graphite to a bilayer graphene is governed by one unique property, i.e., the band overlap, which markedly increases from 1 meV for a bilayer graphene to 11 meV for eight layers and eventually reaches 40 meV for graphite. The monolayer graphene, however, showed a deviation in temperature dependence due to a peculiar linear d…
We highlight the non-universality of the asymptotic behavior of dispersion forces, such that a sum of inverse sixth power contributions is often inadequate. We analytically evaluate the cross-correlation energy Ec between two pi-conjugated layers separated by a large distance D within the electromagnetically non-retarded Random Phase Approximation, via a tight-binding model. For two perfect semimetallic graphene sheets at T=0K we find Ec = C D^{-3}, in contrast to the "insulating" D^{-4} dependence predicted by currently accepted approximations. We also treat the case where one graphene layer …
Low-energy electronic properties of ABC-stacked graphite are studied by the tight-binding model. There are linear and parabolic bands with and without degeneracy. They show strongly anisotropic dispersions. ABC-stacked grahite is a semimetal due to slight overlapping near the Fermi level beween conduction and valence bands. The interlayer interactions could change the energy dispersion, state degeneracy, and positions of band-crossing and band-edge state. Density of states exhibit a shoulder structure, owing to band-edge states near or at high symmetric points. Low-frequency Coulomb excitation…
Layered and nanotubular systems that are metallic or graphitic are known to exhibit unusual dispersive van der Waals (vdW) power laws under some circumstances. In this letter we investigate the vdW power laws of bulk and finite layered systems and their interactions with other layered systems and atoms in the electromagnetically non-retarded case. The investigation reveals substantial difference between `cleavage' and `exfoliation' of graphite and metals where cleavage obeys a $C_2 D^{-2}$ vdW power law while exfoliation obeys a $C_3 \log(D/D_0) D^{-3}$ law for graphitics and a $C_{5/2} D^{-5/…
Dispersing graphite in water to obtain true (single layer) graphene (SLG) in bulk quantity in a liquid has been an unreachable goal for materials scientists in the last decade. Likewise, a diagnostic tool for identifying solubilized SLG in situ has been long awaited. Homogeneous stable dispersions of SLG in water are obtained by mixing graphenide (negatively charged graphene) solutions in tetrahydrofuran (THF) with degassed water and evaporating the organic solvent. In situ Raman spectroscopy of these aqueous dispersions shows all the expected characteristics of single layer graphene, includin…
In this paper we study the excitation spectrum of single- and multi-layer graphene beyond the Dirac cone approximation. The dynamical polarizability of graphene is computed using a full $π$-band tight-binding model, considering the possibility of inter-layer hopping in the calculation. The effect of electron-electron interaction is considered within the random phase approximation. We further discuss the effect of disorder in the spectrum, which leads to a smearing of the absorption peaks. Our results show a redshift of the $π$-plasmon dispersion of single-layer graphene with respect to graphit…
We present a theoretical model to describe the double-resonant scattering process in arbitrary carbon nanotubes. We use this approach to investigate the defect-induced $D$ mode in CNTs and unravel the dependence of the $D$-mode frequency on the CNT diameter and on the energy of the resonant optical transition. Our approach is based on the symmetry of the hexagonal lattice and geometric considerations, hence the method is independent of the exact model that is chosen to describe the electronic band structure or the phonon dispersion. We finally clarify the diameter dependence of this Raman mode…
