Magnetism as a mass term of the edge states in graphene

The magnetism by the edge states in graphene is investigated theoretically. An instability of the pseudo-spin order of the edge states induces ferrimagnetic order in the presence of the Coulomb interaction. Although the next nearest-neighbor hopping can stabilize the pseudo-spin order, a strong Coulomb interaction makes the pseudo-spin unpolarized and real spin polarized. The magnetism of the edge states makes two peaks of the density of states in the conduction and valence energy bands near the Fermi point. Using a continuous model of the Weyl equation, we show that the edge-induced gauge field and the spin dependent mass terms are keys to make the magnetism of the edge states. A relationship between the magnetism of the edge states and the parity anomaly is discussed.Comment: 7 pages, 5 figure

Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor

The electronic density of states of graphene is equivalent to that of relativistic electrons. In the absence of disorder or external doping the Fermi energy lies at the Dirac point where the density of states vanishes. Although transport measurements at high carrier densities indicate rather high mobilities, many questions pertaining to disorder remain unanswered. In particular, it has been argued theoretically, that when the average carrier density is zero, the inescapable presence of disorder will lead to electron and hole puddles with equal probability. In this work, we use a scanning single electron transistor to image the carrier density landscape of graphene in the vicinity of the neutrality point. Our results clearly show the electron-hole puddles expected theoretically. In addition, our measurement technique enables to determine locally the density of states in graphene. In contrast to previously studied massive two dimensional electron systems, the kinetic contribution to the density of states accounts quantitatively for the measured signal. Our results suggests that exchange and correlation effects are either weak or have canceling contributions.Comment: 13 pages, 5 figure

Clar's Theory, STM Images, and Geometry of Graphene Nanoribbons

We show that Clar's theory of the aromatic sextet is a simple and powerful tool to predict the stability, the \pi-electron distribution, the geometry, the electronic/magnetic structure of graphene nanoribbons with different hydrogen edge terminations. We use density functional theory to obtain the equilibrium atomic positions, simulated scanning tunneling microscopy (STM) images, edge energies, band gaps, and edge-induced strains of graphene ribbons that we analyze in terms of Clar formulas. Based on their Clar representation, we propose a classification scheme for graphene ribbons that groups configurations with similar bond length alternations, STM patterns, and Raman spectra. Our simulations show how STM images and Raman spectra can be used to identify the type of edge termination

Theory of superconductivity of carbon nanotubes and graphene

We present a new mechanism of carbon nanotube superconductivity that originates from edge states which are specific to graphene. Using on-site and boundary deformation potentials which do not cause bulk superconductivity, we obtain an appreciable transition temperature for the edge state. As a consequence, a metallic zigzag carbon nanotube having open boundaries can be regarded as a natural superconductor/normal metal/superconductor junction system, in which superconducting states are developed locally at both ends of the nanotube and a normal metal exists in the middle. In this case, a signal of the edge state superconductivity appears as the Josephson current which is sensitive to the length of a nanotube and the position of the Fermi energy. Such a dependence distinguishs edge state superconductivity from bulk superconductivity.Comment: 5 pages, 2 figure

Half-Metallic Graphene Nanoribbons

Electrical current can be completely spin polarized in a class of materials known as half-metals, as a result of the coexistence of metallic nature for electrons with one spin orientation and insulating for electrons with the other. Such asymmetric electronic states for the different spins have been predicted for some ferromagnetic metals - for example, the Heusler compounds- and were first observed in a manganese perovskite. In view of the potential for use of this property in realizing spin-based electronics, substantial efforts have been made to search for half-metallic materials. However, organic materials have hardly been investigated in this context even though carbon-based nanostructures hold significant promise for future electronic device. Here we predict half-metallicity in nanometre-scale graphene ribbons by using first-principles calculations. We show that this phenomenon is realizable if in-plane homogeneous electric fields are applied across the zigzag-shaped edges of the graphene nanoribbons, and that their magnetic property can be controlled by the external electric fields. The results are not only of scientific interests in the interplay between electric fields and electronic spin degree of freedom in solids but may also open a new path to explore spintronics at nanometre scale, based on graphene

Direct Imaging of Graphene Edges: Atomic Structure and Electronic Scattering

We report an atomically-resolved scanning tunneling microscopy (STM) investigation of the edges of graphene grains synthesized on Cu foils by chemical vapor deposition (CVD). Most of the edges are macroscopically parallel to the zigzag directions of graphene lattice. These edges have microscopic roughness that is found to also follow zigzag directions at atomic scale, displaying many ~120 degree turns. A prominent standing wave pattern with periodicity ~3a/4 (a being the graphene lattice constant) is observed near a rare-occurring armchair-oriented edge. Observed features of this wave pattern are consistent with the electronic intervalley backscattering predicted to occur at armchair edges but not at zigzag edges

Electron Wave Function in Armchair Graphene Nanoribbons

By using analytical solution of a tight-binding model for armchair nanoribbons, it is confirmed that the solution represents the standing wave formed by intervalley scattering and that pseudospin is invariant under the scattering. The phase space of armchair nanoribbon which includes a single Dirac singularity is specified. By examining the effects of boundary perturbations on the wave function, we suggest that the existance of a strong boundary potential is inconsistent with the observation in a recent scanning tunneling microscopy. Some of the possible electron-density superstructure patterns near a step armchair edge located on top of graphite are presented. It is demonstrated that a selection rule for the G band in Raman spectroscopy can be most easily reproduced with the analytical solution.Comment: 7 pages, 4 figure

Experimentally Engineering the Edge Termination of Graphene Nanoribbons

The edges of graphene nanoribbons (GNRs) have attracted much interest due to their potentially strong influence on GNR electronic and magnetic properties. Here we report the ability to engineer the microscopic edge termination of high quality GNRs via hydrogen plasma etching. Using a combination of high-resolution scanning tunneling microscopy and first-principles calculations, we have determined the exact atomic structure of plasma-etched GNR edges and established the chemical nature of terminating functional groups for zigzag, armchair and chiral edge orientations. We find that the edges of hydrogen-plasma-etched GNRs are generally flat, free of structural reconstructions and are terminated by hydrogen atoms with no rehybridization of the outermost carbon edge atoms. Both zigzag and chiral edges show the presence of edge states.Comment: 16+9 pages, 3+4 figure

A modified BlÄzka–type respirometer for the study of swimming metabolism in fishes having deep, laterally compressed bodies or unusual locomotor modes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73888/1/j.1095-8649.2000.tb00890.x.pd