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

Based on the local density approximation (LDA) in the framework of the density-functional theory, we study the details of electronic structure, energetics and geometric structure of the chiral carbon nanotubes. For the electronic structure, we study all the chiral nanotubes with the diameters between 0.8 and 2.0 nm (154 nanotubes). This LDA result should give the important database to be compared with the experimental studies in the future. We plot the peak-to-peak energy separations of the density of states (DOS) as a function of the nanotube diameter ( D ). For the semiconducting nanotubes, we find the peak-to-peak separations can be classified into two types according to the chirality. This chirality dependence of the LDA result is opposite to that of the simple π tight-binding result. We also perform the geometry optimization of chiral carbon nanotubes with different chiral-angle series. From the total energy as a function of D , it is found that chiral nanotubes are less stable than zigzag nanotubes. We also find that the distribution of bond lengths depends on the chirality.

Electronic structure, energetics and geometric structure of carbon nanotubes: A density-functional study

We investigate hydrogen adsorption effects on stabilities and electronic properties of nitrogen defects in graphene using first-principles electronic-structure calculations within the density-functional theory. We find that the adsorption of hydrogen atoms on the pyridine-type nitrogen defects in graphene becomes energetically favorable, whereas in the case of the substitutional nitrogen defect the hydrogen adsorption becomes unfavorable. We also find that a transition from p-type to n-type doping properties occurs by hydrogen adsorption on the pyridine-type defects, suggesting that even the carrier type is controllable in nitrogen-doped graphene.

Hydrogen adsorption and anomalous electronic properties of nitrogen-doped graphene

We design a new class of carbon-network materials with a periodically modified graphite sheet. The modified part corresponds to (6,6) carbon-nanotube geometry. Their tube parts form triangular lattice on graphite sheet. On these systems each tube has six heptagons at the bottom, giving rise to a seamless s p 2 -C network with a negative curvature. We consider these nanotube arrays on graphite sheet with three kinds of tube-end geometries and various sizes for both graphite and tube parts. We report their electronic structures obtained by using a realistic tight-binding model, and for selected systems the density-functional theory. Interestingly, results show that most of them are semiconductors although both (6,6) tube and graphite are metallic. The difference in their tube-end geometries and the sizes of graphite and tube parts affect their electronic structures. Some have nearly flat band states around the Fermi level, showing a possibility of ferromagnetic behavior if hole or electron is doped. Some ar...

Geometric and Electronic Structure of New Carbon-Network Materials: Nanotube Array on Graphite Sheet

We study superlattices with alternate stacking of graphene and boron nitride monolayers. We propose several candidate stacking sequences of the superlattices, and optimize their geometries based on the energetics in the framework of the density functional theory. From the total energies of the superlattices with the candidate stacking sequences, we identify the most stable stacking sequence. The atomic configuration of the superlattice with the most stable stacking sequence is found to have the shortest B-C distance among all the optimized superlattice geometries, indicating a strong interaction between the carbon and boron atoms. We also study the electronic structure of the superlattices in detail. It is revealed that the most stable structure exhibits metallic electronic properties.

Electronic structure and stability of layered superlattice composed of graphene and boron nitride monolayer

We study the two-dimensionally polymerized rhombohedral phase of ${\mathrm{C}}_{60}$ by using the local-density approximation in the density-functional theory. The electronic structure of this hybrid solid carbon of ${\mathrm{sp}}^{2}$ and ${\mathrm{sp}}^{3}$ C atoms is found to be essentially three dimensional with a narrow fundamental gap due to a strong interlayer interaction, which also stabilizes the system considerably. Possible modifications of this elemental semiconductor are also discussed.

Susumu Saito

Papers

Electronic structure, energetics and geometric structure of carbon nanotubes: A density-functional study

Hydrogen adsorption and anomalous electronic properties of nitrogen-doped graphene

Geometric and Electronic Structure of New Carbon-Network Materials: Nanotube Array on Graphite Sheet

Electronic structure and stability of layered superlattice composed of graphene and boron nitride monolayer

Rhombohedral C 60 spolymer:mA semiconducting solid carbon structure