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 investigate atomic and electronic structures and energetics of the pyridine-type defects in the nitrogen-doped carbon nanotubes (CNTs) using first-principles density-functional calculations. To discuss the stability of pyridine-type configurations, we calculate the total energies of the possible nitrogen formations in the nitrogen-doped (10,0) CNT. From the results of total-energy calculations, it is found that the pyridine-type defects in the nitrogen-doped (10,0) CNT is energetically preferred to the substitutional nitrogen defects under the existence of the vacancy in the nanotube. We also discuss the impurity states induced by the pyridine-type configurations in the nitrogen-doped nanotube.

Energetics and electronic structures of pyridine-type defects in nitrogen-doped carbon nanotubes

We report electronic and geometric structures of four main candidates for C 84 obtained by using quantitatively reliable models. From a comparison to the recent photoemission spectra (PES), we show that a rather round fullerene with D 2 symmetry proposed by Achiba et al. is the most abundant C 84 cluster in the graphite-arc soot. Other C 84 clusters with T d and D 6h symmetries are also expected to be present. The previously proposed rather that D 2 -symmetry C 84 is found to be unfavorable. The electronic structure of D 2 C 76 is also obtained and the egreement with PES is found to be excellent

Electronic and geometric structures of C76 and C84.

We perform first-principles total-energy calculations to investigate stabilities and electronic properties of hexagonal boron nitride ($h$-BN) bilayers under biaxial tensile strains. The possible stacking patterns of $h$-BN bilayers are investigated in detail. We show that the interlayer distances between two layers in $h$-BN bilayers can be changed under applied strains, and furthermore, they can decrease and increase depending on the stacking patterns of $h$-BN bilayers. We find that the band gaps are tunable by applying strains. We also find that tensile strains can give rise to a transformation from an indirect- to a direct-gap semiconductor in the case of the most stable stacking bilayer. These results indicate the high importance of $h$-BN bilayers as future electronic and optoelectronic device materials.

Band engineering and relative stabilities of hexagonal boron nitride bilayers under biaxial strain

We report first-principles total-energy electronic-structure calculations that provide energetics of encapsulation of ${\mathrm{C}}_{60}$ in nanotubes consisting of boron and nitrogen atoms and electronic structures of resulting ``BNC peapods.'' We find that the encapsulating process is exothermic for (10,10) and (9,9) nanotubes. The energy gain upon the encapsulation is larger than that for carbon peapods, so that the BN nanotube is a promising candidate to accommodate the fullerenes inside. The material is predicted to be a new form of ternary semiconductor with interesting structural hierarchy.

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Semiconducting form of the first-row elements: C60 chain encapsulated in BN nanotubes

First-principles electronic-structure calculations have been performed to examine electronic properties of hexagonal boron nitride (h-BN) monolayers. The dispersion of the energy bands and the width of the band gaps are calculated under biaxial strains. It is found that the band gap decreases as the tensile strain increases, whereas the band gap increases and then it decreases as the compressive strain increases. The relationship between the energy-band structures and the applied strains is reported to clarify the unique behaviors of the band gaps induced by biaxial strains.

Susumu Saito

Papers

Energetics and electronic structures of pyridine-type defects in nitrogen-doped carbon nanotubes

Electronic and geometric structures of C76 and C84.

Band engineering and relative stabilities of hexagonal boron nitride bilayers under biaxial strain

Semiconducting form of the first-row elements: C60 chain encapsulated in BN nanotubes

Electronic structures of hexagonal boron-nitride monolayer: strain-induced effects