Katsunori Wakabayashi

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.

Thickness-Dependent Interfacial Coulomb Scattering in Atomically Thin Field-Effect Transistors

Two-dimensional semiconductors are structurally ideal channel materials for the ultimate atomic electronics after silicon era. A long-standing puzzle is the low carrier mobility (μ) in them as compared with corresponding bulk structures, which constitutes the main hurdle for realizing high-performance devices. To address this issue, we perform a combined experimental and theoretical study on atomically thin MoS2 field effect transistors with varying the number of MoS2 layers (NLs). Experimentally, an intimate μ-NL relation is observed with a 10-fold degradation in μ for extremely thinned monolayer channels. To accurately describe the carrier scattering process and shed light on the origin of the thinning-induced mobility degradation, a generalized Coulomb scattering model is developed with strictly considering device configurative conditions, that is, asymmetric dielectric environments and lopsided carrier distribution. We reveal that the carrier scattering from interfacial Coulomb impurities (e.g., chemical residues, gaseous adsorbates, and surface dangling bonds) is greatly intensified in extremely thinned channels, resulting from shortened interaction distance between impurities and carriers. Such a pronounced factor may surpass lattice phonons and serve as dominant scatterers. This understanding offers new insight into the thickness induced scattering intensity, highlights the critical role of surface quality in electrical transport, and would lead to rational performance improvement strategies for future atomic electronics.

Electronic states of graphene nanoribbons and analytical solutions

Abstract Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of π-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron–electron interaction are briefly discussed.

Zero-conductance resonances due to flux states in nanographite ribbon junctions

Electronic transport properties through junctions in nanographite ribbons are investigated using the Landauer approach. In the low-energy regime ribbons with zigzag boundary have a single conducting channel of edge states. The conductance as a function of the chemical potential shows a rich structure with sharp dips of zero conductance. Each zero-conductance resonance is connected with a resonant state which can be interpreted as the superposition of two degenerate flux states with Kekule-like current patterns. These zero-conductance dips are connected with a pronounced negative magnetoresistance.

PERFECTLY CONDUCTING CHANNEL AND UNIVERSALITY CROSSOVER IN DISORDERED GRAPHENE NANORIBBONS

The band structure of graphene ribbons with zigzag edges have two valleys well separated in momentum space, related to the two Dirac points of the graphene spectrum. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at the band center. This feature gives rise to a perfectly conducting channel in the disordered system, if the impurity scattering does not connect the two valleys, i.e., for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through intervalley scattering display ordinary localization behavior. The two regimes belong to different universality classes: unitary for long-range impurities and orthogonal for short-range impurities.

Strong Enhancement of Raman Scattering from a Bulk-Inactive Vibrational Mode in Few-Layer MoTe2

Two-dimensional layered crystals could show phonon properties that are markedly distinct from those of their bulk counterparts, because of the loss of periodicities along the c-axis directions. Here we investigate the phonon properties of bulk and atomically thin α-MoTe2 using Raman spectroscopy. The Raman spectrum of α-MoTe2 shows a prominent peak of the in-plane E(1)2g mode, with its frequency upshifting with decreasing thickness down to the atomic scale, similar to other dichalcogenides. Furthermore, we find large enhancement of the Raman scattering from the out-of-plane B(1)2g mode in the atomically thin layers. The B(1)2g mode is Raman inactive in the bulk, but is observed to become active in the few-layer films. The intensity ratio of the B(1)2g to E(1)2g peaks evolves significantly with decreasing thickness, in contrast with other dichalcogenides. Our observations point to strong effects of dimensionality on the phonon properties of MoTe2.

Electronic transport properties of graphene nanoribbons

We will present a brief overview of the electronic and transport properties of graphene nanoribbons focusing on the effect of edge shapes and impurity scattering. The low-energy electronic states of graphene have two non-equivalent massless Dirac spectra. The relative distance between these two Dirac points in the momentum space and edge states due to the existence of zigzag-type graphene edges is a deciding factor in the electronic and transport properties of graphene nanoribbons. In graphene nanoribbons with zigzag edges (zigzag nanoribbons), two valleys related to each Dirac spectrum are well separated in momentum space. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at the band center. This feature gives rise to a perfectly conducting channel in the disordered system, if impurity scattering does not connect the two valleys, i.e. for long-range impurity (LRI) potentials. Ribbons with short-range impurity potentials, however, display ordinary localization behavior through inter-valley scattering. On the other hand, the low-energy spectrum of graphene nanoribbons with armchair edges (armchair nanoribbons) is described as the superposition of two non-equivalent Dirac points of graphene. In spite of the lack of two well separated valley structures, the single-channel transport subjected to LRIs is nearly perfectly conducting, where the backward scattering matrix elements in the lowest order vanish as a manifestation of internal phase structures of the wave function. For the multi-channel energy regime, however, conventional exponential decay of the averaged conductance occurs. Symmetry considerations lead to the classification of disordered zigzag ribbons into the unitary class for LRIs, and the orthogonal class for short-range impurities. Since inter-valley scattering is not completely absent, armchair nanoribbons can be classified into the orthogonal universality class irrespective of the range of impurities.

Spin- and charge-polarized states in nanographene ribbons with zigzag edges

Effects of the nearest-neighbor Coulomb interaction on nanographene ribbons with zigzag edges are investigated using the extended Hubbard model within the unrestricted Hartree-Fock approximation. The nearest Coulomb interaction stabilizes an electronic state with the opposite electric charges separated and localized along both edges, resulting in a finite electric dipole moment pointing from one edge to the other. This charge-polarized state competes with the peculiar spin-polarized state caused by the on-site Coulomb interaction and is stabilized by an external electric field.