Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

The rise of graphene

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

Recent years have witnessed many breakthroughs in research on graphene (the first two-dimensional atomic crystal) as well as a significant advance in the mass production of this material. This one-atom-thick fabric of carbon uniquely combines extreme mechanical strength, exceptionally high electronic and thermal conductivities, impermeability to gases, as well as many other supreme properties, all of which make it highly attractive for numerous applications. Here we review recent progress in graphene research and in the development of production methods, and critically analyse the feasibility of various graphene applications.

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A roadmap for 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

When annealed at elevated temperatures under vacuum, silicon carbide surfaces show a tendency towards graphitization. Using the sensitivity of empty conduction-band states dispersion towards the structural quality of the overlayer, we have used angular-resolved inverse photoemission spectroscopy (KRIPES) to monitor the progressive formation of crystalline graphite on $6H\ensuremath{-}\mathrm{SiC}(0001)$ surfaces. The KRIPES spectra obtained after annealing at 1400 \ifmmode^\circ\else\textdegree\fi{}C are characteristic of azimuthally oriented, graphite multilayers of very good single-crystalline quality. For lower annealing temperatures, the ordered interface already presents most of the fingerprints of graphite as soon as 1080 \ifmmode^\circ\else\textdegree\fi{}C. The observation of unshifted ${\ensuremath{\pi}}^{*}$ states, which reveals a very weak interaction with the substrate, is consistent with the growth of a van der Waals heteroepitaxial graphite lattice on top of silicon carbide, with a coincidence lattice of $(6\sqrt{3}\ifmmode\times\else\texttimes\fi{}6\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ symmetry. The growth of the first graphene sheet proceeds on top of adatoms characteristic of the $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ reconstruction. These adatoms reduce the chemical reactivity of the substrate. A strong feature located at 6.5 eV above the Fermi level is attributed to states derived from Si vacancies in the C-rich subsurface layers of the SiC substrate. This strongly perturbed substrate can be viewed as a diamondlike phase which acts as a precursor to graphite formation by collapse of several layers. In this framework, previously published soft x-ray photoemission spectra find a natural explanation.

Heteroepitaxial graphite on 6h-sic(0001): interface formation through conduction-band electronic structure

High-temperature graphitization of the 6H-SiC (0001̄) face

Three-dimensional unoccupied band structure of graphite: Very-low-energy electron diffraction and band calculations

Applying k-resolved inverse photoemission (KRIPES) to the √3×√3 R30°-reconstructed 6H-SiC(0001) face, we have observed a sharp surface state U located at 1.10 ± 0.05 eV above the Fermi level at the centre of the surface Brillouin zone. Its bandwidth of 0.34 ± 0.05 eV is in good agreement with the 0.35 eV predicted by first-principle calculations based on a Si-adatom model. However, LDA calculations predict a half-filled Σ1 state and a metallic character for this reconstruction. Together with recent ARUPS data, our results reveal that the one-electron band Σ1 is split into two bands, giving a semiconducting surface with a reduced indirect bandgap around 2.0 eV at the ' point. Many-body correlation effects may give rise, in the limit of strong localization, to this bandgap opening.

J.-M. Debever

Papers

Heteroepitaxial graphite on 6h-sic(0001): interface formation through conduction-band electronic structure

High-temperature graphitization of the 6H-SiC (0001̄) face

Three-dimensional unoccupied band structure of graphite: Very-low-energy electron diffraction and band calculations

Unoccupied surface state on the (√3 × √3) R30° of 6H-SiC(0001)

Electron correlation effects at Sn/Si(1 1 1)–3×3,3×3 and Sn/Ge(1 1 1)–3×3,3×3 reconstructions