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

Layered electrides, as typified by ${\mathrm{Ca}}_{2}\mathrm{N}$, are unconventional quasi-two-dimensional metals with low work functions, in which the conduction electrons are localized between the cation layers as well as outside the surface. We have investigated the electronic structure of the interface between a layered electride and another material, using graphene on ${\mathrm{Ca}}_{2}\mathrm{N}$ as an example. Our first-principles calculation shows that a graphene layer on ${\mathrm{Ca}}_{2}\mathrm{N}$ remains flat and is doped to an extremely high density of $n=5\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ with its Fermi level (${E}_{F}$) aligned with the logarithmically divergent van Hove singularity (VHS) at a saddle point of graphene's ${\ensuremath{\pi}}^{*}$ band. This finding shows that graphene/${\mathrm{Ca}}_{2}\mathrm{N}$ is an ideal testing ground for the exploration of the many-body ground states, most notably superconducting states ($p+ip$ wave, $d$ wave, and $f$ wave), predicted to appear when ${E}_{F}$ is close to a VHS. The work function decreases abruptly upon monolayer attachment but reverts to that of ${\mathrm{Ca}}_{2}\mathrm{N}$ upon bilayer attachment. This peculiar behavior is explained in terms of the distinctive electronic structures of the constituent materials and their bonding.

https://link.aps.org/accepted/10.1103/PhysRevB.96.245303

Probing a divergent van Hove singularity of graphene with a Ca 2 N support: A layered electride as a solid-state dopant

To clarify the microscopic formation process of ${\mathrm{C}}_{60}$ and other fullerenes, we study the geometries and energetics of small carbon clusters and the reaction between carbon clusters using the long-range transferable tight-binding model parametrized by Omata et al. (Omata TB), the local-density-approximation (LDA) in the framework of the density-functional theory, and the constant-temperature molecular dynamics combined with Omata-TB (Omata TBMD). From the LDA geometry-optimization study, we find that the binding energy per atom of the ${\mathrm{C}}_{10}$ ring is $0.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$/atom larger than that of the ${\mathrm{C}}_{10}$ chain. This energetic preference of a ring to a chain in ${\mathrm{C}}_{10}$ is most prominent among all ${\mathrm{C}}_{n}$ clusters studied $(5\ensuremath{\leqslant}n\ensuremath{\leqslant}17)$. Moreover, the study of $sp$-hybridized small carbon clusters with Omata TBMD reveals that ${\mathrm{C}}_{10}$ is the smallest stable ring at the temperature of $2000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which can explain the high abundance of ${\mathrm{C}}_{10}$ in the experimental $\mathrm{C}_{n}{}^{\ensuremath{-}}$ mass spectra. From the remarkable stability of the ${\mathrm{C}}_{10}$ ring as well as from its high abundance, it is considered that the $sp$-hybridized ${\mathrm{C}}_{10}$ ring should play a role of major constituent units of larger clusters and fullerenes. Therefore we perform various sets of simulations of reactions between carbon clusters possessing the C atoms in multiples of 10, ${\mathrm{C}}_{10m}+{\mathrm{C}}_{10n}$ ($m+n=2,3,4,5,6$, $m\ensuremath{\geqslant}n\ensuremath{\geqslant}1$), at several temperatures with Omata TBMD. As a result, it is found that, in most cases studied, ${\mathrm{C}}_{20}$ and ${\mathrm{C}}_{30}$ clusters possess the $s{p}^{2}$-hybridized planar geometries, while ${\mathrm{C}}_{40}$, ${\mathrm{C}}_{50}$, and ${\mathrm{C}}_{60}$ take the $s{p}^{2}$-hybridized ``fullerenelike'' closed-cage geometries. These ${\mathrm{C}}_{40}$, ${\mathrm{C}}_{50}$, and ${\mathrm{C}}_{60}$ cages can be formed at as low as $1500\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which is in good accord with the experimental temperature of fullerene formation. In a few cases, even the ${\mathrm{C}}_{30}$ cluster is found to take the cage structure. These results are in good accord with the experimental results of the gas ion chromatography. The straightforward growth process from the $sp$-hybridized ring to the $s{p}^{2}$-hybridized plane and that from the $s{p}^{2}$-hybridized plane to the $s{p}^{2}$-hybridized fullerenelike cage revealed in the present study are considered to be the main road of the formation of fullerenes. Finally, the study of structural stabilities of cage geometries obtained through the reaction between a fullerenelike cage $({\mathrm{C}}_{40})$ or a symmetrical fullerene (${D}_{5h}$ ${\mathrm{C}}_{50}$ or ${I}_{h}$ ${\mathrm{C}}_{60}$) and a carbon cluster (${\mathrm{C}}_{10}$ or ${\mathrm{C}}_{12}$) at various temperatures with Omata TBMD indicates that ${\mathrm{C}}_{2n}$ fullerenelike cages larger than ${\mathrm{C}}_{60}$ tend to decay into ${\mathrm{C}}_{2n\ensuremath{-}2}$ through the ${\mathrm{C}}_{2}$ loss process at the higher rate than ${\mathrm{C}}_{60}$ or smaller fullerenelike cages. Therefore this ${\mathrm{C}}_{2}$ loss process is considered to be one of the most important processes leading to the extreme abundance of ${\mathrm{C}}_{60}$.

Geometries, stabilities, and reactions of carbon clusters : Towards a microscopic theory of fullerene formation

We study the electronic structure of the superconducting body-centered-orthorhombic fulleride ${\mathrm{Ba}}_{4}{\mathrm{C}}_{60}$ using the local-density approximation in the density-functional theory. It is found that Ba states are strongly hybridized with ${\mathrm{C}}_{60}$ states through pentagons, explaining the observed lattice-constant differences, $agbgc.$ Due to this hybridization and to a rather low symmetry of the lattice causing the splitting of states, the ${t}_{1g}$-derived conduction band partially occupied by two electrons is found to be relatively wide. Fermi surfaces also show noncubic nature and contain dual quasiplanar sheets parallel to the $a\ensuremath{-}b$ plane in the momentum space, giving rise to a quasinesting vector parallel to the c axis.

Electronic structure of the Ba 4 C 60 superconductor

On the basis of the density functional theory, we study pressure and orientation effects on geometric and electronic structures of crystalline bundles consisting of single-wall carbon nanotubes, (6,0), (8,0), (6,6), and (12,0). We find that mutual orientation angles of adjacent nanotubes in stable geometries correspond to a common intertube atomic arrangement which is similar to an interlayer atomic arrangement of the graphite “AB stacking”. In the (6,6) bundle, it is found that a pseudogap appears at the Fermi level and its width depends strongly on the intertube orientation. Interestingly, this pesudogap becomes the widest at the most stable intertube orientation which in this case is slightly off the ideal AB-stacking geometry, indicating that the electronic energy gain enhances the pseudogap effect in metallic nanotube bundles. Under lateral pressure, large structural deformation (buckling) is found in the (6,6) bundle and the cross section of the tube in the bundle is deformed from circular to polygo...

Pressure and Orientation Effects on the Electronic Structure of Carbon Nanotube Bundles

We present the first-principles electronic-structure calculation which provides outstanding features in the Fermi surface of KxC60. We have found that there exist two main Fermi surfaces: One is a hole pocket around the center of the Brillouin zone, and the other a large hole surface extending to the zone boundary. We have also found Fermi-surface nesting resulting in a peak at q=(1, 0, 0)2π/a in the susceptibility χ(q), which may induce an instability in this exotic material.

Susumu Saito

Papers

Probing a divergent van Hove singularity of graphene with a Ca 2 N support: A layered electride as a solid-state dopant

Geometries, stabilities, and reactions of carbon clusters : Towards a microscopic theory of fullerene formation

Electronic structure of the Ba 4 C 60 superconductor

Pressure and Orientation Effects on the Electronic Structure of Carbon Nanotube Bundles

Fermi surfaces of alkali-metal-doped C60 solid