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

Floating Interlayer and Surface Electrons in 2D Materials: Graphite, Electrides, and Electrenes

Structures for realizing hole-doped $\mathrm{Mg}{\mathrm{B}}_{2}$ without appealing to chemical substitutions are proposed. These structures that consist of alternating $\mathrm{Mg}{\mathrm{B}}_{2}$ and graphene layers have small excess energy compared to bulk graphite and $\mathrm{Mg}{\mathrm{B}}_{2}$. Density functional theory based first-principles electronic structure calculations show significant charge transfer from the $\mathrm{Mg}{\mathrm{B}}_{2}$ layer to graphene, resulting in effectively hole-doped $\mathrm{Mg}{\mathrm{B}}_{2}$ and electron-doped graphene. Substantial enhancement in the density of states at the Fermi level and significant in-plane lattice expansion of the proposed structures are predicted. These structures combines three important factors, namely, hole doping, high density of states at the Fermi level, and in-plane lattice expansion, that are favorable for a strong electron-phonon coupling.

Theory of the electronic structure of alternating Mg B 2 and graphene layered structures

Stable polymers of C74 and C78 fullerenes

We propose an alternative structure of ${\mathrm{TiO}}_{2}$ anatase that has a higher energy oxygen $p$-like valence band maximum than pristine ${\mathrm{TiO}}_{2}$ anatase and thus has a much better alignment with the water splitting levels. This alternative structure is unique when considering a large subspace of possible structural distortions of ${\mathrm{TiO}}_{2}$ anatase. We propose two routes towards this state and argue that one of them might have been realized in the recently discovered so-called black ${\mathrm{TiO}}_{2}$.

Alternative structure of TiO 2 with higher energy valence band edge

We have calculated the total energies of n-atom potassium clusters ${\mathrm{K}}_{\mathrm{n}}$ (1\ensuremath{\le}n\ensuremath{\le}23) using a jellium-sphere background model for the positive-ion cores and the local-spin-density-functional approximation for the valence electrons. We find that the K clusters which have exoergic fission channels have low abundances in the experimental mass spectra indicating the presence of thermal fissions of ${\mathrm{K}}_{\mathrm{n}}$. Most of the exoergic fissions are found to produce dimers, ${\mathrm{K}}_{2}$, as one of the daughter clusters. We have studied the ``dimer decay'' of ${\mathrm{K}}_{10}$ in an attempt to explain why ${\mathrm{K}}_{10}$ is one of the least abundant clusters in the ${\mathrm{K}}_{\mathrm{n}}$ mass spectra. Two overlapping jellium spheres with constant density are used for the positive background. The energy-barrier height for complete decay from the energy-minimum point is found to be 0.18 eV, which is a reasonable magnitude for thermal decay compared to the experimental temperature. The monomer decay of ${\mathrm{K}}_{9}$ and the dimer decay of ${\mathrm{K}}_{8}$ are found to have higher barriers.

Susumu Saito

Papers

Floating Interlayer and Surface Electrons in 2D Materials: Graphite, Electrides, and Electrenes

Theory of the electronic structure of alternating Mg B 2 and graphene layered structures

Stable polymers of C74 and C78 fullerenes

Alternative structure of TiO 2 with higher energy valence band edge

Jellium-model calculation for dimer decays of potassium clusters.