Abstract: Numerical calculations have been performed to elucidate unconventional electronic transport properties in disordered nanographene ribbons with zigzag edges (zigzag ribbons). The energy band structure of zigzag ribbons has two valleys that are well separated in momentum space, related to the two Dirac points of the graphene spectrum. The partial flat bands due to edge states make the imbalance between left- and right-going modes in each valley, i.e. appearance of a single chiral mode. This feature gives rise to a perfectly conducting channel in the disordered system, i.e. the average of conductance left angle bracketgright-pointing angle bracket converges exponentially to 1 conductance quantum per spin with increasing system length, provided impurity scattering does not connect the two valleys, as is the case for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through inter-valley scattering, display ordinary localization behavior. Symmetry considerations lead to the classification of disordered zigzag ribbons into the unitary class for long-range impurities, and the orthogonal class for short-range impurities. The electronic states of graphene nanoribbons with general edge structures are also discussed, and it is demonstrated that chiral channels due to the edge states are realized even in more general edge structures except for armchair edges.

Abstract: We study the conductance of phase-coherent disordered quantum wires focusing on the case in which the number of conducting channels is imbalanced between two propagating directions. If the number of channels in one direction is by one greater than that in the opposite direction, one perfectly conducting channel without backscattering is stabilized regardless of wire length. Consequently, the dimensionless conductance does not vanish but converges to unity in the long-wire limit, indicating the absence of Anderson localization. To observe the influence of a perfectly conducting channel, we numerically obtain the distribution of conductance in both cases with and without a perfectly conducting channel. We show that the characteristic form of the distribution is notably modified in the presence of a perfectly conducting channel.

Abstract: The low-energy spectrum of graphene nanoribbons with armchair edges (armchair nanoribbons) is described as the superposition of two nonequivalent Dirac points of graphene. In spite of the lack of well-separated two valley structures, the single-channel transport subjected to long-ranged impurities 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 multichannel energy regime, however, the conventional exponential decay of the averaged conductance occurs. Since the intervalley scattering is not completely absent, armchair nanoribbons can be classified into orthogonal universality class irrespective of the range of impurities. The nearly perfect single-channel conduction dominates the low-energy electronic transport in rather narrow nanorribbons.

Abstract: We study conductance fluctuations in disordered quantum wires with unitary symmetry focusing on the case in which the number of conducting channels in one propagating direction is not equal to that in the opposite direction. We consider disordered wires with N+m left-moving channels and N right-moving channels. In this case, m left-moving channels become perfectly conducting, and the dimensionless conductance g for the left-moving channels behaves as g →m in the long-wire limit. We obtain the variance of g in the diffusive regime by using the Dorokhov–Mello–Pereyra–Kumar equation for transmission eigenvalues. It is shown that the universality of conductance fluctuations breaks down for m ≠0 unless N is very large.

Abstract: The electronic transport properties in graphene quantum point contacts are numerically studied. The constriction of the quantum point contact induces the zero-conductance Fano resonances in the low-energy single channel transport region near the Dirac point, i.e., perfect reflection. Randomly distributed impurities which alter the resonance energies cause large conductance fluctuation comparable to the ensemble averaged dimensionless conductance. Our results identify a further intriguing effect of impurity scattering in the electronic transport properites of graphene.

Abstract: We study the conductance of disordered quantum wires with unitary symmetry focusing on the case where m excess one-way conducting channels are present. The excess channels make the channel number in one direction by m greater than that in the opposite direction, resulting in the stabilization of m perfectly conducting channels. The case of m=1 can be realized in zigzag nanographene ribbons. Due to the presence of perfectly conducting channels, the dimensionless conductance g behaves as g→m with increasing system length, indicating the absence of the Anderson localization. To describe the anomalous behavior, we generalize the unitary class to allow m excess one-way channels and derive the corresponding Fokker–Planck equation for transmission eigenvalues. It is shown that the conductance decay length is reduced with increasing m. We present an extended classification table for the standard three classes.

Abstract: To study electron transport in disordered wires with the channel-number imbalance between two propagating directions, we consider the three-edge Chalker–Coddington model consisting of one right-moving and two left-moving edge channels of length L coupled by random tunneling. Since the imbalance makes one left-moving channel being perfectly conducting, the dimensionless conductances g and g' for the left-moving and right-moving channels, respectively, differ from each other and satisfy g = g' + 1. Using a supersymmetry approach, we obtain the asymptotic form of the ensemble average <g>-1 = <g' > which decays exponentially with increasing L. It is shown that the corresponding decay length is four times shorter than that for the two-edge case. This result is in quantitative agreement with the existing random-matrix theory.

Abstract: 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.

Abstract: We numerically study the spatially resolved NMR around a single vortex in a noncentrosymmetric superconductor such as CePt3Si. The nuclear spin-lattice relaxation rate View the MathML source under the influence of the vortex core states is calculated for an s+p-wave Cooper pairing state. The result is compared with that for an s-wave pairing state.

Abstract: For a noncentrosymmetric superconductor such as CePt3Si, we consider a Cooper pairing model with a two-component order parameter composed of spin-singlet and spin-triplet pairing components. We calculate the superfluid density tensor in the clean limit on the basis of the quasiclassical theory of superconductivity. We demonstrate that such a pairing model accounts for an experimentally observed feature of the temperature dependence of the London penetration depth in CePt3Si, i.e., line-node-gap behavior at low temperatures.

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Abstract: We numerically study the vortex core structure in a noncentrosymmetric superconductor such as CePt3Si without mirror symmetry about the xy plane. A single vortex along the z axis and a mixed singlet–triplet Cooper pairing model are considered. The spatial profiles of the pair potential, local density of states, supercurrent density, and radially-textured magnetic moment density around the vortex are obtained in the clean limit on the basis of the quasiclassical theory of superconductivity.

Abstract: We have numerically studied the electronic transport properties of quantum wires with symplectic symmetry based on the tight-binding model. The asymptotic behavior of the conductance crucially depends on the even–odd effect of the conducting channel, since one perfectly conducting channel exists only in the odd-channel system. The decay length of the conductance and the distribution of the largest transmission eigenvalues clearly show the even–odd difference. Our results are in excellent agreement with the random-matrix theory.

Abstract: Superconductivity in non-centrosymmetric materials can display various intriguing properties. Using the example of the CePt3Si a phenomenological description of this non-centrosymmetric superconductor is given, in an attempt to identify the symmetry of the Cooper pairing state. A short overview on other recently discovered non-centrosymmetric superconductors mainly, in strongly correlated electron systems, is given.

Abstract: Noncentrosymmetric superconductors possess, in general, order parameters of mixed parity, i.e., the Cooper pairing state consists of spin-singlet and spin-triplet pairing components. We show that this property has important implications for the NMR and other measurable quantities in the heavy Fermion superconductor CePt3Si. The aspect of parity mixing explains the apparently contradicting observations of a Hebel-Slichter peak in the nuclear spin-lattice relaxation rate T₁^-1 and the presence of power law in the low-temperature behavior of certain physical quantities, indicating line nodes in the quasiparticle gap.

Abstract: Nanographite materials show novel electronic properties: spin glass like behaviors [1], the on/off switching of magnetism with molecule adsorptions [2], and so on. Here, we study electronic states in nanographite ribbons with zigzag edges. Effects of the nearest neighbor Coulomb interactions are investigated using the extended Hubbard model. The nearest Coulomb interactions stabilize a novel 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. Next, electric capacitance is calculated to examine nano functionalities. We find that the behavior of the capacitance is widely different depending on whether the system is in the magnetic or charge polarized phases. In the magnetic phase, the capacitance is dominated by the presence of the edge states while the ribbon width is small. As the ribbon becomes wider, the capacitance remains with large magnitudes as the system develops into metallic zigzag nanotubes. It is proportional to the inverse of the width, when the system corresponds to the semiconducting nanotubes and the system is in the charge polarized phase also. The latter behavior could be understood by the presence of an energy gap for charge excitations.

Abstract: The influence of Rashba spin-orbit coupling on zero conductance resonances appearing in one-dimensional conducting rings asymmetrically coupled to two leads is investigated. For this purpose, the transmission function of the corresponding one-electron scattering problem is derived analytically and analyzed in the complex energy plane with focus on the zero-pole structure characteristic of transmission (anti)resonances. The lifting of real conductance zeros due to spin-orbit coupling in the asymmetric Aharonov-Casher ring is related to the breaking of spin reversal symmetry in analogy to the time-reversal symmetry breaking in the asymmetric Aharonov-Bohm ring.

Abstract: Recent theoretical developments on topological materials, Möbius nanographite and Möbius conjugated polymers, are reported. (I) In nanographite systems with the Möbius boundary condition, there appears a novel magnetic domain. However, this domain state competes against the helical magnetic states. Total energies of the latter states are always lower than that of the former state. Additionally, the domain wall appears in the charge density wave states. (II) Optical properties of Möbius conjugated polymers are studied. We discuss that oligomers with a few structural units are more effective than polymers, in order to measure effects of discrete wave numbers which are shift by the Möbius boundary from those of the periodic boundary. Certain components of the optical absorption for the electric field perpendicular to the polymer axis mix with the absorption spectra for the electric filed parallel with the polymer axis. The polarization dependences of electric field of light can detect whether conjugated polymers have the Möbius boundary or not.

Abstract: Recent angle-resolved photoelectron spectroscopy experiments show a narrow quasiparticle peak at the gap edge along the antinodal [1,0] direction for the overdoped cuprate superconductors. We show that within weak coupling BCS theory for a d -wave superconductor, the s -wave single-impurity scattering cross section vanishes for energies ω=Δ (gap edge). This coherence effect occurs through multiple scattering off the impurity. For small impurity concentrations the spectral function has a pronounced increase of the (scattering) lifetime for antinodal quasiparticles but shows a very broad peak in the nodal direction, in qualitative agreement with the above-mentioned experiment and in strong contrast to the behavior observed in underdoped cuprates.

Abstract: In a nanographene ring with zigzag edges, the spin-polarized state and the charge-polarized state are stabilized by the on-site and the nearest-neighbor Coulomb repulsions, U and V, respectively, within the extended Hubbard model under the mean-field approximation. In a Möbius strip of the nanographene with a zigzag edge, U stabilizes two magnetic states, the domain wall state and the helical state. Both states have ferrimagnetic spins localized along the zigzag edge while the former connects the opposite ferrimagnetic orders resulting in a magnetic frustration forced by the topology and the latter rotates the ferrimagnetic spins uniformly to circumvent the frustration. The helical state is lower in energy than the domain wall state. On the other hand, V stabilizes another domain wall state connecting the opposite charge orders.

Abstract: We present the electronic states and persistent current of nanographite ring based on the nearest-neighbor tight-binding model under periodic or Möbius boundary conditions. It is found that the parity of transverse mode and edge structures are decisive to determine the electronic spectrum of nanographite ring under the Möbius boundary condition. The electronic states Möbius strip with zigzag edges are derived in the same way as the free-electron case. However, the Möbius strip with armchair edges has loop quantization rule of wave vector due to the characteristics of their parity. The difference of electronic states between edge structures can crucially affect the behavior of the persistent current caused by Aharonov–Bohm magnetic flux passing through the nanographite ring. We also present some scaling properties concerning the persistent current and the zero-field susceptibility.

Abstract: Antiferromagnetism in stacked nanographite is investigated with using the Hubbard-type model. We find that the open shell electronic structure can be an origin of the decreasing magnetic moment with the decrease of the inter-layer distance, as experiments on adsorption of molecules suggest. Next, possible charge-separated states are considered using the extended Hubbard model with nearest-neighbor repulsive interactions. The charge-polarized state could appear, when a static electric field is present in the graphene plane for example. Finally, superperiodic patterns with a long distance in a nanographene sheet observed by STM are discussed in terms of the interference of electronic wave functions with a static linear potential theoretically. In the analysis by the k·p model, the oscillation period decreases spatially in agreement with experiments.

Abstract: We theoretically study the electronic states in graphene ribbons which are strongly affected by the edge states, the peculiar non-bonding molecular orbitals localized along the zigzag edges of the ribbons. New kinds of edge localized electronic states with spin and charge polarizations are found in the mean field solutions of the extended Hubbard model with onsite and nearest-neighbor Coulomb repulsions. These novel states appear due to the interplay between the edge states and the Fermi instabilities. We also examine the competition between the charge polarized state and the spin polarized state to draw a phase diagram depending on Coulomb parameters. The results obtained by the mean field calculations with the extended Hubbard model modified to include Coulomb integrals provide useful insights to understand and functionalize the nanoscale materials.

Abstract: The DC Josephson current through a nano-graphite ribbon placed between two conventional superconductors is theoretically studied by using thermal Green function techniques based on the tight binding model. The electronic states of nanographite ribbons strongly depend on the shapes of their edges, and give a single channel for the electron transport. The nanographite ribbons with zigzag boundaries have partly flat bands due to the edge states, in which the low-energy energy spectrum is a power function of ribbon width. The power-law partly flat bands induce the dependence of ribbon width on both the length dependence of the DC Josephson current and the coherence length. Also, because Andreev bound states highly accumulate close to the zero-energy level, the exponential decay of the DC Josephson current at the zero-energy level to the junction length strongly persists at very low temperatures.

Abstract: The DC Josephson current through a nano-graphite ribbon sandwiched between two conventional superconductors is theoretically studied by using the thermal Green function techniques based on the tight binding model. The electronic states of nano-graphite ribbons strongly depend on their shapes of edges, hence the behavior of the DC Josephson current crucially depends on the network topology of nano-graphite ribbons.

Abstract: We consider the electronic and magnetic properties of the nanographite ribbon with zigzag edges under periodic or Möbius boundary conditions. The zigzag nano-graphite ribbons possess edge localized states at the Fermi level, which cause a ferrimagnetic spin polarization localized at the edge sites even in a very weak Coulomb interaction. The imposition of the Möbius boundary conditions makes the system a non-AB-bipartite lattice, and depresses the spin polarization, resulting in the formation of a magnetic domain wall. The width of the magnetic domain depends on the Coulomb interaction and decreases with increasing U/t.

Abstract: The properties of quantum electron transport through metallic carbon nanotubes with several conducting channels are investigated by the random-matrix approach. Starting from the unique scattering symmetry observed in metallic carbon nanotubes with long-range impurity potential, we can derive the random-matrix representation in which the classical and quantum processes are clearly separated. With increasing system length, the system approaches a fixed point, where only one channel is perfectly conducting and other channels are completely closed. It is shown that such behavior should be attributed to the antilocalization effect. We can describe the decoherence effect on the total transmission probability <T > within the random-matrix theory. For a nanotube of length L, we obtain <T >∼Lφ/L for l \lesssimLφ ≪L, where l and Lφ are the mean free path and the phase coherence length, respectively.

Abstract: 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.

Abstract: Lattice vacancy effects on electrical conductance of nanographite ribbon are investigated by means of the Landauer approach using a tight binding model. In the low-energy regime ribbons with zigzag boundary provide a single conducting channel whose origin is connected with the presence of edge states. It is found that the chemical potential dependence of conductance strongly depends on the difference (Δ) of the number of removed A and B sublattice sites. The large lattice vacancy with Δ≠0 shows 2Δ zero-conductance dips in the single-channel region, however, the large lattice vacancy with Δ=0 has no dip structure in this region. The connection between this conductance rule and the Longuet-Higgins conjecture is also discussed.

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Abstract: Collective electron transport in mesoscopic charge-density-wave (CDW) systems is studied theoretically. Sliding motion of the CDW is accompanied by thermally activated phase-slip processes near electrical contacts. Each phase-slip event gives rise to an addition or removal of a wavefront, resulting in deformation of the overall phase profile. Since the energy barrier for thermal nucleation of phase-slip centers strongly depends on the phase profile, its deformation affects the phase-slip rate, particularly in small samples. We calculate the nonlinear behavior between the CDW current and the phase-slip voltage Vps, taking account of the small-size effect on the phase-slip rate. Using the parameters for NbSe3, we find that the small-size effect reduces Vps when the sample length is smaller than a few micrometers. This behavior is consistent with the recent experiment by Mantel et al.: Phys. Rev. Lett. 84 (2000) 538 for mesoscopic NbSe3 wires.

Abstract: The electronic transport properties through junctions connecting nanographite ribbons of different or same width are investigated by means of the Landauer-Büttiker approach using a tight binding model. Graphite ribbon with zigzag boundary has a single conducting channel of edge states in the low-energy regime. The electrical conductance as a function of the chemical potential shows a rich structure with sharp dips of zero conductance. This perfect reflectivity originates from twofold degenerate resonant levels, i.e., flux states visible in the formation of strong current-current correlation with a Kekulé-like vortex pattern. At each energy of conductance-zeros, this degeneracy yields the formation of standing waves in the scattering region of the junctions. The origin of zero-conductance resonances is also discussed by the standard scattering matrix approach, and the similarities between the nanographite ribbon junctions and the asymmetric Aharanov-Bohm ring connected to current leads are pointed out. Since the zero-conductance resonances are connected with the time-reversal symmetry of the system, the application of a magnetic field removes these zero-conductance dips, yielding a pronounced negative magnetoresistance.

Abstract: 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 Kekulé-like current patterns. These zero-conductance dips are connected with a pronounced negative magnetoresistance.

Abstract: We compare different possible origins for the low-temperature splitting of the zero-energy peak in the local density of states at (110) surfaces of dx2-y2-wave superconductors. Using a tight-binding model with interactions in the Bogolyubov-de Gennes treatment, we discuss the instability of the superconductor against a current-carrying locally time-reversal symmetry-breaking phase (s+id-wave) and, alternatively, a spin density wave-like state. The former (latter) is more likely to occur in a regime corresponding to the overdoped (underdoped) situation of high-temperture superconductors.

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Abstract: Both orbital diamagnetic and Pauli paramagnetic contributions to the magnetic response in ribbon-shaped nanographite systems with zigzag and armchair edges are discussed. These systems possess edge states, strongly localized near zigzag edges. The edge states lead to a sharp peak in the density of states at the Fermi level and generate a Pauli spin susceptibility with a nearly Curie-like temperature dependence. In nanographite systems this paramagnetic contribution of the edge states can compete with the diamagnetic orbital magnetic signal of the bulk. At high temperature the system is diamagnetic and at low temperature the paramagnetic behavior dominates.

Abstract: Different scenarios for the low-temperature splitting of the zero-energy peak in the local density of states at (1 1 0) surfaces of dx2−y2-wave superconductors are compared with each other. For a pure dx2−y2-wave superconductor surface bound states generate a large density of states at the Fermi level. This causes local instabilities which occur either towards a time reversal symmetry breaking superconducting state (s+id-type) or a magnetic state with staggered magnetic moments. We show that both types of a local symmetry breaking would lead to similar splittings of the zero-energy peak.

Abstract: The electronic transport properties through junctions connecting nanographite ribbons of different width are investigated by means of the Landauer approach using a tight binding model. In the low-energy regime ribbons with zigzag boundary provide a single conducting channel whose origin is a zero-energy edge state. The conductance as a function of the chemical potential shows rich structure and a large number of dips of zero-conductance. This perfect reflectivity originates from the formation of a standing wave resonance in the junction.

Abstract: 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 (φ=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 high-temperature diamagnetic to low-temperature paramagnetic behavior in the magnetic susceptibility of nanographite ribbons with zigzag edges.

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Abstract: 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.

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Abstract: Examining the band structure of graphite ribbons with a typical edge shapes of armchair or zigzag, we find that minute graphite in a nanometer scale shows a striking contrast in the π electronic states depending on the edge shape. A wide armchair ribbon can reproduces the electronic state of graphite, but a zigzag ribbon shows a pair of partly flat bands which gives a remarkable peak of density of states at the Fermi level. We derive the analytic solution of this peculiar Edge State, disclosing the puzzle of its emergence.

Abstract: 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.

Abstract: A noble mechanism of spin polarization is proposed for finite graphite sheet with edge. For graphite ribbon with zigzag edge, there appear peculiar ‘edge states’. These localized states comprise nearly flat band at the Fermi level, which easily causes magnetic instability. Magnetic structure is suggested from Hartree-Fock analysis of the Hubbard model, where huge magnetic moments are induced at around both of edges by weak HubbardU and are coupled antiferromagnetically with each other.

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