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 study pressure-induced structural phase transition of carbon nanotube solids using the constant-pressure tight-binding molecular-dynamics method. We find that the bundle with armchair nanotube transforms into a new phase consisting of so-called zigzag graphene nanoribbons and sp 3 carbon atoms by applying the pressure of 10 GPa. Under higher pressure of 30 GPa, anisotropic sp 3 phases possessing high hardness comparable to cubic diamond are obtained from armchair nanotube solid, whereas amorphous diamond phases are obtained from the bundle with chiral nanotubes. Using the density-functional theory, we also study electronic structure of a new sp 3 phase obtained in the molecular-dynamics simulation.

Pressure-induced structural phase transition of small-diameter carbon nanotubes

Isotope composition dependence of the band-gap energy in diamond

We study geometries and electronic properties of unstrained and strained zigzag $\mathrm{Mo}X{}_{2}$ ($X$ = O, S, and Se) nanotubes and $\mathrm{Mo}XY$ ($X,Y$ = O, S, and Se) nanotubes in the framework of density functional theory. Using the local density approximation, we obtain fully relaxed geometries of (10,0) and (14,0) nanotubes for all $\mathrm{Mo}X{}_{2}$, and (7,0) and (28,0) nanotubes for selected $\mathrm{Mo}X{}_{2}$. From the detailed analysis of the optimized geometries it is revealed that, although in the planar case these transition metal dichalcogenides (TMDs) normally take so-called H structures, zigzag nanotubes turn into geometries between H-like and T-like nanotubes having different height for inner and outer chalcogen site. Electronic property investigations reveal that TMD nanotubes without oxygen atoms are found to have narrower gaps than TMD nanotubes with oxygen atoms. These narrow direct gaps of TMD nanotubes should be attractive properties for infrared optoelectronic devices. On the other hand, energy-gap values of the TMD nanotubes with oxygen atoms are found to depend rather strongly on the strain. Therefore, they should be potential future device materials for mechanical sensors. We also find a global strong correlation between the fundamental-gap values and some combined structural parameters in strained $\mathrm{Mo}X{}_{2}$ ($X$ = S, Se) nanotubes and planar $\mathrm{Mo}X{}_{2}$ ($X$ = S, Se), which will be useful to predict gap values of other strained and unstrained ($n,0$) nanotubes.

Geometrical and electronic properties of unstrained and strained transition metal dichalcogenide nanotubes

Electronic structures and three-dimensional effects of boron-doped carbon nanotubes

Carbon nanotubes (CNTs), which are one-dimensional (1D) molecular conductors, have attracted considerable attention. However, none of the research has reported on superconductivity (SC) in carrier-doped CNTs. Here, we report on SC with the world’s highest transition temperature (T
 c) of 12 K in highly uniform thin films of boron-doped single-walled CNTs (B-SWNTs). We clarify correlation of SC with Fermi level tuning with van Hove singularities (VHS) in electronic density of states (DOS) in the SWNT. Moreover, we show fabrication of paper-like thin films consisting of a pseudo two-dimensional network of weakly coupled B-SWNTs (called the Buckypaper) and show an enhancement of the onset T
 c up to 19 K by applying only a small pressure. The present observations will shed light on the high feasibility of using CNTs as a 1D superconductor and also on the research of 1D electron correlation.

Susumu Saito

Papers

Pressure-induced structural phase transition of small-diameter carbon nanotubes

Isotope composition dependence of the band-gap energy in diamond

Geometrical and electronic properties of unstrained and strained transition metal dichalcogenide nanotubes

Electronic structures and three-dimensional effects of boron-doped carbon nanotubes

Superconductivity in Boron-Doped Carbon Nanotubes