F. Guinea

The electronic properties 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.

Biased bilayer graphene: Semiconductor with a gap tunable by the electric field effect

We demonstrate that the electronic gap of a graphene bilayer can be controlled externally by applying a gate bias. From the magnetotransport data (Shubnikov-de Haas measurements of the cyclotron mass), and using a tight-binding model, we extract the value of the gap as a function of the electronic density. We show that the gap can be changed from zero to midinfrared energies by using fields of less, approximately < 1 V/nm, below the electric breakdown of SiO2. The opening of a gap is clearly seen in the quantum Hall regime.

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

Strain-induced Pseudo-Magnetic Fields Greater Than 300 Tesla in Graphene Nanobubbles

Straining Graphenes Electronic States The conduction electrons in graphene, single sheets of graphite, can have very high mobilities. Under the influence of an applied magnetic field, a series of energy steps, or Landau levels, can be observed that correspond to the conduction electrons traveling in cyclotron orbits. Recent theoretical work has indicated that if graphene layers are strained, the strain field creates a pseudomagnetic field that should also lead to observable Landau levels. Levy et al. (p. 544) used scanning tunneling microscopy to probe the energy levels of graphene grown on a platinum surface, which forms highly strained “nanobubbles.” The strain is equivalent to applying very high magnetic fields (in excess of 300 tesla). Thus, the electronic properties of graphene can indeed be modified using applied strain. Strain creates energy levels in graphene that are similar to those seen in very high applied magnetic fields. Recent theoretical proposals suggest that strain can be used to engineer graphene electronic states through the creation of a pseudo–magnetic field. This effect is unique to graphene because of its massless Dirac fermion-like band structure and particular lattice symmetry (C3v). Here, we present experimental spectroscopic measurements by scanning tunneling microscopy of highly strained nanobubbles that form when graphene is grown on a platinum (111) surface. The nanobubbles exhibit Landau levels that form in the presence of strain-induced pseudo–magnetic fields greater than 300 tesla. This demonstration of enormous pseudo–magnetic fields opens the door to both the study of charge carriers in previously inaccessible high magnetic field regimes and deliberate mechanical control over electronic structure in graphene or so-called “strain engineering.”

Periodically Rippled Graphene: Growth and Spatially Resolved Electronic Structure

We grow epitaxial graphene monolayers on Ru(0001) that cover uniformly the substrate over lateral distances larger than several microns. The weakly coupled graphene monolayer is periodically rippled and it shows charge inhomogeneities in the charge distribution. Real space measurements by scanning tunneling spectroscopy reveal the existence of electron pockets at the higher parts of the ripples, as predicted by a simple theoretical model. We also visualize the geometric and electronic structure of edges of graphene nanoislands.

Damping pathways of mid-infrared plasmons in graphene nanostructures

Mid-infrared plasmons in scaled graphene nanostructures Hugen Yan*, Tony Low, Wenjuan Zhu, Yanqing Wu, Marcus Freitag, Xuesong Li, Francisco Guinea, Phaedon Avouris* and Fengnian Xia* IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598 Instituto de Ciencia de Materiales de Madrid. CSIC. Sor Juana Inés de la Cruz 3. 28049 Madrid, Spain Plasmonics takes advantage of the collective response of electrons to electromagnetic waves, enabling dramatic scaling of optical devices beyond the diffraction limit. Here, we demonstrate the mid-infrared (4 to 15 μm) plasmons in deeply scaled graphene nanostructures down to 50 nm, more than 100 times smaller than the onresonance light wavelength in free space. We reveal, for the first time, the crucial damping channels of graphene plasmons via its intrinsic optical phonons and scattering from the edges. A plasmon lifetime of 20 femto-seconds and smaller is observed, when damping through the emission of an optical phonon is allowed. Furthermore, the surface polar phonons in SiO2 substrate underneath the graphene nanostructures lead to a significantly modified plasmon dispersion and damping, in contrast to a non-polar diamond-like-carbon (DLC) substrate. Much reduced damping is realized when the plasmon resonance frequencies are close to the polar phonon frequencies. Our study paves the way for applications of graphene in plasmonic waveguides, modulators and detectors in an unprecedentedly broad wavelength range from sub-terahertz to mid-infrared.

Dynamical polarization of graphene at finite doping

The polarization of graphene is calculated exactly within the random phase approximation for arbitrary frequency, wavevector and doping. At finite doping, the static susceptibility saturates to a constant value for low momenta. At q = 2kF it has a discontinuity only in the second derivative. In the presence of a charged impurity this results in Friedel oscillations which decay with the same power law as the Thomas?Fermi contribution, the latter being always dominant. The spin density oscillations in the presence of a magnetic impurity are also calculated. The dynamical polarization for low q and arbitrary ? is employed to calculate the dispersion relation and the decay rate of plasmons and acoustic phonons as a function of doping. The low screening of graphene, combined with the absence of a gap, leads to a significant stiffening of the longitudinal acoustic lattice vibrations.

Spin-orbit coupling in curved graphene, fullerenes, nanotubes, and nanotube caps

A continuum model for the effective spin-orbit interaction in graphene is derived from a tight-binding model which includes the

Cloning of Dirac fermions in graphene superlattices

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Electron-Electron Interactions in Graphene: Current Status and Perspectives

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