There are few phenomena in condensed matter physics that are defined only by the fundamental constants and do not depend on material parameters. Examples are the resistivity quantum, h/e2 (h is Planck's constant and e the electron charge), that appears in a variety of transport experiments and the magnetic flux quantum, h/e, playing an important role in the physics of superconductivity. By and large, sophisticated facilities and special measurement conditions are required to observe any of these phenomena. We show that the opacity of suspended graphene is defined solely by the fine structure constant, a = e2/hc feminine 1/137 (where c is the speed of light), the parameter that describes coupling between light and relativistic electrons and that is traditionally associated with quantum electrodynamics rather than materials science. Despite being only one atom thick, graphene is found to absorb a significant (pa = 2.3%) fraction of incident white light, a consequence of graphene's unique electronic structure.

The polarization of graphene is calculated exactly within the random phase approximation for arbitrary frequency, wave vector, and doping. At finite doping, the static susceptibility saturates to a constant value for low momenta. At q = 2k F 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 ω 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.

We compute the optical conductivity of graphene beyond the usual Dirac cone approximation, giving results that are valid in the visible region of the conductivity spectrum. The effect of next nearest neighbor hoping is also discussed. Using the full expression for the optical conductivity, the transmission and reflection coefficients are given. We find that even in the optical regime the corrections to the Dirac cone approximation are surprisingly small (a few percent). Our results help in the interpretation of the experimental results reported by Nair et al.

Using the semi-classical Boltzmann theory, we calculate the conductivity as function of the carrier density. As usually, we include the scattering from charged impurities, but conclude that the estimated impurity density is too low in order to explain the experimentally observed mobilities. We thus propose an additional scattering mechanism involving midgap states which leads to a similar k-dependence of the relaxation time as charged impurities. The new scattering mechanism can account for the experimental findings such as the sublinear behavior of the conductivity versus gate voltage and the increase of the minimal conductivity for clean samples. We also discuss temperature dependent scattering due to acoustic phonons.

We study the changes in the electronic structure induced by lattice defects in graphene planes. In many cases, lattice distortions give rise to localized states at the Fermi level. Electron-electron interactions lead to the existence of local moments. The RKKY interaction between these moments is always ferromagnetic, due to the semimetallic properties of graphene.PACS numbers: 75.10. Jm, 75.10.Lp, 75.30.Ds Introduction. A number of recent experiments suggest that pure graphite behaves as a highly correlated electron system [1]. In particular it shows a metalinsulator transition in magnetic fields and insulating behavior in the direction perpendicular to the planes in different samples [1,2,3,4,5,6,7,8]. Recent results show ferromagnetic behavior [9], enhanced by proton bombardment [10], what opens up a new way to the creation of organic magnets [11]. In this paper we study the formation of local moments near simple defects. It is shown that many tyoes of lattice distortions, like cracks and vacancies, can induce localized states at the Fermi level, leading to the existence of local moments. The RKKY interaction between these moments is always ferromagnetic due to the semimetallic properties of graphite. Hence, the RKKY interaction does not lead to frustration and spin glass features.The model. The conduction band of graphite is well described by a tight binding model which includes the π orbitals which are perpendicular to the graphite planes at each C atom [12]. If the interplane hopping is neglected, this model describes a semimetal, with zero density of states at the Fermi energy, and where the Fermi surface is reduced to two inequivalent K-points located at the corner of the hexagonal Brillouin Zone. The low-energy excitations with momenta in the vicinity of the Fermi points have a linear dispersion and can be described by a continuum model which reduces to the Dirac equation in two dimensions [12,13,14,15,16]. The Hamiltonian density of the system is

Graphene is an atomically thin plasmonic medium that supports highly confined plasmon polaritons, or nano-light, with very low loss. Electronic properties of graphene can be drastically altered when it is laid upon another graphene layer, resulting in a moiré superlattice. The relative twist angle between the two layers is a key tuning parameter of the interlayer coupling in thus obtained twisted bilayer graphene (TBG). We studied propagation of plasmon polaritons in TBG by infrared nano-imaging. We discovered that the atomic reconstruction occurring at small twist angles transforms the TBG into a natural plasmon photonic crystal for propagating nano-light. This discovery points to a pathway towards controlling nano-light by exploiting quantum properties of graphene and other atomically layered van der Waals materials eliminating need for arduous top-down nanofabrication.One Sentence Summary: Atomically relaxed twisted bilayer graphene hosts periodic arrays of topological conducting channels that act as a photonic crystal for surface plasmons.

Recent developments in the emerging field of plasmonics in graphene and other Dirac systems are reviewed and a comprehensive introduction to the standard models and techniques is given. In particular, we discuss intrinsic plasmon excitation of single and bilayer graphene via hydrodynamic equations and the random phase approximation, but also comment on double and multilayer structures. Additionally, we address Dirac systems in the retardation limit and also with large spin–orbit coupling including topological insulators. Finally, we summarize basic properties of the charge, current and photon linear response functions in an appendix.

The interplay between different types of disorder and electron-electron interactions in graphene planes is studied by means of Renormalization Group techniques. The low temperature properties of the system are determined by fixed points where the strength of the interactions remains finite, as in one dimensional Luttinger liquids. These fixed points can be either stable (attractive), when the disorder is associated to topological defects in the lattice or to a random mass term, or unstable (repulsive) when the disorder is induced by impurities outside the graphene planes. In addition, we analyze mid-gap states which can arise near interfaces or vacancies.Introduction. Graphite is a widely studied material, which has attracted recent interest due to the observation of anomalous properties, such as magnetism or insulating behavior in the direction perpendicular to the planes in different samples [1,2,3,4,5,6,7,8].The conduction band of graphite is well described by tight binding models which include only the π orbitals which are perpendicular to the graphite planes at each C atom [9]. If the interplane hopping is neglected, this model describes a semi metal, with zero density of states at the Fermi energy, and where the Fermi surface is reduced to two inequivalent points in the Brillouin Zone. The states near these Fermi points can be described by a continuum model which reduces to the Dirac equation in two dimensions. Due the the vanishing of the density of states at the Fermi level, the long range Coulomb interaction is imperfectly screened. This implies that a standard perturbative treatment leads to logarithmic divergences, and to non trivial deviations from Fermi liquid theory [10,11,12]. In the strong coupling regime, the model can exhibit a phase transition which leads to a rearrangement of the charges and spins within the unit cell, and which is similar to the chiral symmetry breaking transition found in field theories [13,14].It is known that disorder significantly changes the states described by the two dimensional Dirac equation [15,16,17], and, usually, the density of states at low energies is increased. Lattice defects, such as pentagons and heptagons, or dislocations, can be included by means of a non Abelian gauge field [18,19]. In general, disorder enhances the effect of the interactions. In addition, a graphene plane can show states localized at interfaces [20,21], which, in the absence of other types of disorder, lie at the Fermi energy. Changes in the local coordination can also lead to localized states [22].The present work attempts to study, within the same footing, the role of long range interactions and disorder. This problem has already been studied in relation with critical points between integer and fractional fillings in the Quantum Hall Effect [23,24], and we will be able to translate some of the results there to the problem at hand. We find, as in[24] a rich phase diagram, with different fixed points. The stability of these fixed points