This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

Raman spectroscopy in graphene

Ultrathin epitaxial graphite was grown on single-crystal silicon carbide by vacuum graphitization. The material can be patterned using standard nanolithography methods. The transport properties, which are closely related to those of carbon nanotubes, are dominated by the single epitaxial graphene layer at the silicon carbide interface and reveal the Dirac nature of the charge carriers. Patterned structures show quantum confinement of electrons and phase coherence lengths beyond 1 micrometer at 4 kelvin, with mobilities exceeding 2.5 square meters per volt-second. All-graphene electronically coherent devices and device architectures are envisaged.

https://science.sciencemag.org/content/sci/312/5777/1191.full.pdf

Electronic Confinement and Coherence in Patterned Epitaxial Graphene

http://absimage.aps.org/image/MAR07/MWS_MAR07-2006-006269.pdf

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 nature 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 devices. 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 properties can be controlled by the external electric fields. The results are not only of scientific interest 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 the nanometre scale, based on graphene.

https://arxiv.org/pdf/cond-mat/0611600.pdf

Half-metallic graphene nanoribbons

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.

Peculiar Localized State at Zigzag Graphite Edge

A probable heterodiamond ${\mathrm{BC}}_{2}$N structure that can be obtained from compression of graphitic ${\mathrm{BC}}_{2}$N at low temperature is proposed using first-principles calculations. The structure consists of a rhombohedral atomic arrangement and has a large bulk modulus comparable to that of diamond as well as a wide band gap. We also found that the structure can be synthesized from a superlattice with alternate stacking of graphite and hexagonal BN monolayers. Transformations from such layered superlattices open a possibility for control of the properties in synthesized materials.

Proposed synthesis path for heterodiamond BC 2 N

We have investigated the activation barriers and the intermediate paths of the transformation to cubic diamond and that to hexagonal diamond from graphite under pressure, allowing both atomic geometry and unit-cell shape to vary, in order to clarify the difference of the microscopic mechanisms between them. For this investigation, we have developed a method of finding a saddle point of the potential surface automatically on the basis of constant-pressure first-principles molecular dynamics. At the transition states, the length of the interlayer bonding is universal irrespective of the transformations and pressures, while there is a difference in the lateral displacement of atoms on the paths. It is found that the activation barrier from graphite to cubic diamond is lower than that to hexagonal diamond by \ensuremath{\sim}70 meV/atom. These results suggest that, whenever collective slide of graphite planes is allowed, the transformation to cubic diamond is favored, and that hexagonal diamond can be obtained only when such slide is prohibited.

Constant-pressure first-principles studies on the transition states of the graphite-diamond transformation.

Magnetic structure is studied for several π-networks of graphite-like structures with edge and/or topological defects using the tight-binding model (the Huckel model). Zigzag-edged graphite have ed...

Magnetism of nanometer-scale graphite with edge or topological defects

Phase diagram of the extended Hubbard model with on-site repulsion and nearest-neighbor attraction is obtained for various band fillings, covering the strong-correlation regime, in one dimension by mapping the system to the Tomonaga-Luttinger model with use of exact diagonalization of finite systems. We find that the strong electron correlation makes the superconducting region, which is sandwiched between spin-density wave and phase-separation regions, significantly wider than expected from the weak-coupling g-ology.

Koichi Kusakabe

Papers

Peculiar Localized State at Zigzag Graphite Edge

Proposed synthesis path for heterodiamond BC 2 N

Constant-pressure first-principles studies on the transition states of the graphite-diamond transformation.

Magnetism of nanometer-scale graphite with edge or topological defects

Phase diagram of the extended attractive Hubbard model in one dimension.