Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green’s-function equations, starting with a one-electron propagator and considering the electron-hole Green’s function for the response. Key ingredients are the electron’s self-energy S and the electron-hole interaction. A good approximation for S is obtained with Hedin’s GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of S. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green’s functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green’s functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

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Electronic excitations: density-functional versus many-body Green's-function approaches

Recently discovered carbon nanotubes have exhibited many unique material properties including very high thermal conductivity. Strong sp 2 bonding configurations in carbon network and nearly perfect self-supporting atomic structure in nanotubes give unusually high phonon-dominated thermal conductivity along the tube axis, possibly even surpassing that of other carbon-based materials such as diamond and graphite (in plane). In this chapter, we explore theoretical and experimental investigations for the thermal-transport properties of these materials.

Unusually High Thermal Conductivity of Carbon Nanotubes

Hexagonal boron nitride (h-BN) is a layered material with a graphite-like structure in which planar networks of BN hexagons are regularly stacked. As the structural analogue of a carbon nanotube (CNT), a BN nanotube (BNNT) was first predicted in 1994; since then, it has become one of the most intriguing non-carbon nanotubes. Compared with metallic or semiconducting CNTs, a BNNT is an electrical insulator with a band gap of ca. 5 eV, basically independent of tube geometry. In addition, BNNTs possess a high chemical stability, excellent mechanical properties, and high thermal conductivity. The same advantages are likely applicable to a graphene analogue-a monatomic layer of a hexagonal BN. Such unique properties make BN nanotubes and nanosheets a promising nanomaterial in a variety of potential fields such as optoelectronic nanodevices, functional composites, hydrogen accumulators, electrically insulating substrates perfectly matching the CNT, and graphene lattices. This review gives an introduction to the rich BN nanotube/nanosheet field, including the latest achievements in the synthesis, structural analyses, and property evaluations, and presents the purpose and significance of this direction in the light of the general nanotube/nanosheet developments.

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Boron Nitride Nanotubes and Nanosheets

Modeling hardness of polycrystalline materials and bulk metallic glasses

Carbon nanotubes are unique tubular structures of nanometer diameter and large length/diameter ratio. The nanotubes may consist of one up to tens and hundreds of concentric shells of carbons with adjacent shells separation of ∼0.34 nm. The carbon network of the shells is closely related to the honeycomb arrangement of the carbon atoms in the graphite sheets. The amazing mechanical and electronic properties of the nanotubes stem in their quasi-one-dimensional (1D) structure and the graphite-like arrangement of the carbon atoms in the shells. Thus, the nanotubes have high Young’s modulus and tensile strength, which makes them preferable for composite materials with improved mechanical properties. The nanotubes can be metallic or semiconducting depending on their structural parameters. This opens the ways for application of the nanotubes as central elements in electronic devices including field-effect transistors (FET), single-electron transistors and rectifying diodes. Possibilities for using of the nanotubes as high-capacity hydrogen storage media were also considered. This report is intended to summarize some of the major achievements in the field of the carbon nanotube research both experimental and theoretical in connection with the possible industrial applications of the nanotubes.

Carbon nanotubes: properties and application

We have investigated by first principles the electronic, vibrational, and structural properties of bct C4, a new form of crystalline sp{3} carbon recently found in molecular dynamics simulations of carbon nanotubes under pressure. This phase is transparent, dynamically stable at zero pressure, and more stable than graphite beyond 18.6 GPa. Coexistence of bct C4 with M carbon can explain better the x-ray diffraction pattern of a transparent and hard phase of carbon produced by the cold compression of graphite. Its structure appears to be intermediate between that of graphite and hexagonal diamond. These facts suggest that bct C4 is an accessible form of sp{3} carbon along the graphite-to-hexagonal diamond transformation path.

Body-centered tetragonal C4: a viable sp3 carbon allotrope.

We report total-energy electronic structure calculations that provide energetics of encapsulation of ${\mathrm{C}}_{60}$ in the carbon nanotube and electronic structures of the resulting carbon peapods. We find that the encapsulating process is exothermic for the $(10,10)$ nanotube, whereas the processes are endothermic for the $(8,8)$ and $(9,9)$ nanotubes, indicative that the minimum radius of the nanotube for the encapsulation is 6.4 \AA{}. We also find that the ${\mathrm{C}}_{60}@(10,10)$ is a metal with multicarriers each of which distributes either along the nanotube or on the ${\mathrm{C}}_{60}$ chain. This unusual feature is due to the nearly free electron state that is inherent to hierarchical solids with sufficient space inside.

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Energetics and electronic structures of encapsulated C60 in a carbon nanotube.

We investigate nitrogen-doping effects in a graphene sheet using a first-principles electronic-structure study in the framework of density-functional theory. As possible configurations of nitrogen impurities in graphene, substitutional nitrogen and pyridine-type defects around a monovacancy and around a divacancy are considered, and their energetics and electronic structures are discussed. The formation-energy calculations suggest that substitutional doping of the nitrogen atom into a graphene sheet is energetically the most favorable among the possible nitrogen-doping configurations. Furthermore, by comparison of the total energy of the pyridine-type defects with that of the substitutional nitrogen defect in graphene, it is revealed that formation of the pyridine-type defects becomes energetically favorable compared with formation of the substitutional nitrogen defect in the presence of a vacancy. From the results of electronic-band-structure calculations, it is found that the nitrogen-impurity states appear around the Fermi level as either acceptorlike or donorlike states, depending on the atomic geometries of the nitrogen impurities in graphene. We also calculate the scanning tunneling microscopy (STM) images associated with impurity-induced electronic states for future experimental identification of nitrogen impurities. The simulated STM images of the three N-doping configurations considered here are found to be strongly dependent on the local density of states around the nitrogen impurity, and therefore the doping configurations should be distinguishable from one another. The similarities and differences of the electronic structures and STM corrugations between N-doped and undoped graphenes are also discussed.

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Formation, stabilities, and electronic properties of nitrogen defects in graphene

Experimentally Determined Redox Potentials of Individual (n,m) Single-Walled Carbon Nanotubes

We calculate the structural and electronic properties of an ordered ``bundle'' of (10,10) carbon nanotubes. Our results indicate that intertube coupling causes an additional band dispersion of $\ensuremath{\lesssim}0.2 \mathrm{eV}$ and opens up a pseudogap of the same magnitude at ${E}_{F}.$ Soft librations at $\ensuremath{\nu}\ensuremath{\approx}12 {\mathrm{cm}}^{\ensuremath{-}1}$ are predicted to occur below the orientational melting temperature which marks the onset of tube rotations about their axis. Whereas the density of states near ${E}_{F}$ increases by 7% due to intertube coupling and by one order of magnitude due to K doping in ${\mathrm{KC}}_{8},$ these states do not couple to tube librations.

Susumu Saito

Papers

Body-centered tetragonal C4: a viable sp3 carbon allotrope.

Energetics and electronic structures of encapsulated C60 in a carbon nanotube.

Formation, stabilities, and electronic properties of nitrogen defects in graphene

Experimentally Determined Redox Potentials of Individual (n,m) Single-Walled Carbon Nanotubes

Effect of intertube coupling on the electronic structure of carbon nanotube ropes