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 studied the electronic structure of the superconducting fullerides ${\mathrm{K}}_{3}{\mathrm{Ba}}_{3}{\mathrm{C}}_{60}$ and ${\mathrm{Rb}}_{3}{\mathrm{Ba}}_{3}{\mathrm{C}}_{60}$ using the local-density approximation in the density functional theory. Their conduction-band profiles are found to be quantitatively very similar to each other although the lattice constant of ${\mathrm{K}}_{3}{\mathrm{Ba}}_{3}{\mathrm{C}}_{60}$ is definitely smaller than that of ${\mathrm{Rb}}_{3}{\mathrm{Ba}}_{3}{\mathrm{C}}_{60}.$ The density of states at Fermi level of ${\mathrm{K}}_{3}{\mathrm{Ba}}_{3}{\mathrm{C}}_{60}$ is slightly larger than that of ${\mathrm{Rb}}_{3}{\mathrm{Ba}}_{3}{\mathrm{C}}_{60}.$ In addition, ${\mathrm{C}}_{60}$ states are found to be hybridized not only with Ba states but also with K (Rb) states. These results are in sharp contrast to ${A}_{3}{\mathrm{C}}_{60}$ superconductors $(A=\mathrm{K}$ and Rb). The hybridization is expected to play an important role in their superconducting properties since carriers are found to be not only on ${\mathrm{C}}_{60}$ but also around K (Rb) sites as well as Ba sites.

Electronic structure of K 3 Ba 3 C 60 and Rb 3 Ba 3 C 60 superconductors

Coherent optical processes of 1s ortho-excitons in Cu2O by two-photon excitations

Using the density functional theory, we report energetics and electronic structure of double-walled BN nanotubes, (n,0)@(15,0) and (m,0)@(20,0). We find that the most favorable double-walled nanotubes are (7,0)@(15,0) and (12,0)@(20,0) in which the inter-wall distance is about 3 A . We observe that the energy gap of double-walled BN nanotubes narrows due to the hybridization between σ and π states. We also find that the nearly free-electron state of the nanotubes induces peculiar charge transfer from the π states to the inter-wall region.

Electronic and geometric structures of multi-walled BN nanotubes

Electronic structure and scanning tunneling microscopy images of heterostructures consisting of graphene and carbon-doped hexagonal boron nitride layers

We report the electronic and geometric structures of certain fullerenes and metallofullerenes. First, results on all the possible candidates for C84 are shown. Their geometries have been optimized by means of the empirical model potential and their electronic structure has been obtained by means of the generalized tight-binding model. Comparison of the density of states (DOS) with the experimental photoemission spectrum shows the preference of one candidate proposed according to the ring-stacking growth model as a major C84 isomer. The present results on C84 are found to be able to give a conclusive answer for the C84 structure after the separation of isomers in the near future. Next, we show the electronic structure of the endohedral metallofullerene C60 Ca obtained using the local-density approximation in the density-functional theory. Finally, the growth model and the geometry of the metallofullerene LaC82 are presented.

Susumu Saito

Papers

Electronic structure of K 3 Ba 3 C 60 and Rb 3 Ba 3 C 60 superconductors

Coherent optical processes of 1s ortho-excitons in Cu2O by two-photon excitations

Electronic and geometric structures of multi-walled BN nanotubes

Electronic structure and scanning tunneling microscopy images of heterostructures consisting of graphene and carbon-doped hexagonal boron nitride layers

Electronic and geometric structures of fullerenes and metallofullerenes