Mitsutaka Fujita

Peculiar Localized State at Zigzag Graphite Edge

We study the electronic states of graphite ribbons with edges of two typical shapes, armchair and zigzag, by performing tight binding band calculations, and find that the graphite ribbons show striking contrast in the electronic states depending on the edge shape. In particular, a zigzag ribbon shows a remarkably sharp peak of density of states at the Fermi level, which does not originate from infinite graphite. We find that the singular electronic states arise from the partly flat bands at the Fermi level, whose wave functions are mainly localized on the zigzag edge. We reveal the puzzle for the emergence of the peculiar edge state by deriving the analytic form in the case of semi-infinite graphite with a zigzag edge. Applying the Hubbard model within the mean-field approximation, we discuss the possible magnetic structure in nanometer-scale micrographite.

Electronic and magnetic properties of nanographite ribbons

Electronic and magnetic properties of ribbon-shaped nanographite systems with zigzag and armchair edges in a magnetic field are investigated by using a tight-binding model. One of the most remarkable features of these systems is the appearance of edge states, strongly localized near zigzag edges. The edge state in a magnetic field, generating a rational fraction of the magnetic flux ( f5 p/q) in each hexagonal plaquette of the graphite plane, behaves like a zero-field edge state with q internal degrees of freedom. The orbital diamagnetic susceptibility strongly depends on the edge shapes. The reason is found in the analysis of the ring currents, which are very sensitive to the lattice topology near the edge. Moreover, the orbital diamagnetic susceptibility is scaled as a function of the temperature, Fermi energy, and ribbon width. Because the edge states lead to a sharp peak in the density of states at the Fermi level, the graphite ribbons with zigzag edges show Curie-like temperature dependence of the Pauli paramagnetic susceptibility. Hence, there is a crossover from hightemperature diamagnetic to low-temperature paramagnetic behavior in the magnetic susceptibility of nanographite ribbons with zigzag edges. @S0163-1829~99!02111-6#

Spin wave mode of edge-localized magnetic states in nanographite zigzag ribbons

We consider the low-energy magnetic excitations of nanographite ribbons with zigzag edges. The zigzag ribbons possess almost flat bands at the Fermi level which cause a ferrimagnetic spin polarization localized at the edge sites. The spin wave mode of this magnetic state is investigated by a random phase approximation of the corresponding Hubbard model. This result is used to derive an effective Heisenberg model with ladder structure. Although this system has a spin gap (Haldane type), our analysis shows that the gap is small and the tendency towards ferrimagnetic correlation at the edges is strong.

Soliton Lattice Modulation of Incommensurate Spin Density Wave in Two Dimensional Hubbard Model : A Mean Field Study

Spatially modulated magnetic phases are investigated within the mean field theory for an itinerant electron model, i.e. the Hubbard model on a two-dimensional square lattice. By numerically diagonalizing the Hamiltonian for finite-size systems under a periodic boundary condition, we examine relative stability and physical properties of several possible magnetic states. When the electron fillings are nearly half-full, the diagonally or vertically modulated spin density wave (SDW) state is stabilized over the uniform antiferromagnetic state and a crossover from the vertical to the diagonal states appears. The diagonal or vertical stripe state is characterized by the presence of the midgap band due to the soliton lattice formation inside the main SDW gap, being an insulator. The wave length λ SDW is linearly proportional to the excess carrier concentration. Excess carriers are accommodated in the form of the soliton lattice, forming a charge density wave whose wave length is λ SDW /2.

Lattice Distortion in Nanographite Ribbons

We study the lattice distortion in graphite ribbons of a nanometer width by taking account of the electron-phonon interaction in the tight binding model. In the ribbons with armchair edges, the typical Kekule structure appears near the edges depending on the distribution of the bond orders. On the other hand, the zigzag ribbons do not undergo bond alternations along the ribbon axis, implying less Peierls instability. Special emphasis is put on the survival of the edge state which forms almost flat bands and a sharp peak in the density of states in consideration of the electron-phonon interaction.

Electronic structure and growth mechanism of carbon tubules

Abstract A one-dimensional electronic band structure model for carbon tubules is summarized. The general structure of carbon tubules and fullerenes projected in a two-dimensional hexagonal lattice sheet with +12 defects representing the pentagonal faces. The possible caps which are fitted smoothly to a tubule can be generated by this projection method. Growth of the tubule can occur by absorbing C2 clusters at such topological defects (i.e. pentagonal faces) on generalized fullerenes. The tubule electronic structure is obtained from a simple tight-binding model for a single-layer carbon tubule. The model shows that approximately one-third of the tubules are metallic and two-thirds are semiconducting, depending on the tubule diameter and chirality. Metallic one-dimensional electronic energy bands are stable under a Peierls distortion. As the tubule diameter, d increases, the semiconductor energy gap decreases approximately as 1/d . The calculation of the electronic structure of two concentric tubules shows that pairs of concentric metal—semiconductor (orsemiconductor—metal) and metal—metal tubules are stable under the weak turbostratic interlayer interaction. Possible applications of concentric carbon tubules to semiconductor—metal devices are discussed.

Dimerization structures of metallic and semiconducting fullerene tubules.

Possible dimerization patterns and electronic structures in fullerene tubules as the one-dimensional pi-conjugated systems are studied with the extended Su-Schrieffer-Heeger model. We assume various lattice geometries, including helical and nonhelical tubules. The model is solved for the half-filling case of

Shape and Fantasy of Fullerenes

\pi

Phonon dispersion of nano-graphite ribbons

-electrons. (1) When the undimerized systems do not have a gap, the Kekule structures prone to occur. The energy gap is of the order of the room temperatures at most and metallic properties would be expected. (2) If the undimerized systems have a large gap (about 1eV), the most stable structures are the chain-like distortions where the direction of the arranged trans-polyacetylene chains is along almost the tubular axis. The electronic structures are ofsemiconductors due to the large gap.

Magnetic properties of nano-graphites at low temperature

One of the many wonders that fullerenes have brought to us during the past few years is the variety of their shapes. When the elusive C 60 finally showed up in 1990, the perfect symmetry and astounding beauty of its molecular structure touched the hearts of scientists before they could consider the molecules vast technical possibilities. Already much has been said about the unique shape of C 60 and its potentialities. C 70 and higher fullerenes have simultaneously been found in the same soot that produced C 60 and were quickly revealed to be shaped like rugby balls or oblong eggs. Hence we were aware that there had to be an extensive series of roundish polyhedral clusters of carbon atoms. Then, in the following year, multilayered tubular fullerenes (Figures 1a and 1b) were discovered by Iijima and were named buckytubes (see the article by Iijima in this issue). Iijima also observed similarly huge and multilayered carbon balls, before C 60 was discovered. Soon after, buckyonions were recognized as an important class of fullerene (Figure 1c, see article by Ugarte in this issue). So, in the early days of fullerene research, we already knew three forms of fullerene: sphere, tube, and particle. At that time, however, nobody anticipated that this was only the beginning of a big show of stunning variations in the shapes of fullerenes. This article introduces current developments in the study of these fullerene styles.