The electronic properties of graphene, a two-dimensional crystal of carbon atoms, are exceptionally novel. For instance the low-energy quasiparticles in graphene behave as massless chiral Dirac fermions which has led to the experimental observation of many interesting effects similar to those predicted in the relativistic regime. Graphene also has immense potential to be a key ingredient of new devices such as single molecule gas sensors, ballistic transistors, and spintronic devices. Bilayer graphene, which consists of two stacked monolayers and where the quasiparticles are massive chiral fermions, has a quadratic low-energy band structure which generates very different scattering properties from those of the monolayer. It also presents the unique property that a tunable band gap can be opened and controlled easily by a top gate. These properties have made bilayer graphene a subject of intense interest.In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties.Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphanegapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.

We analyze the spectroscopic features of bilayer graphene determined by the formation of pairs of low-energy and split bands in this material. We show that the inter-Landau-level absorption spectrum in bilayer graphene at high magnetic field is much denser in the far-infrared range than that in monolayer material, and that the polarization dependence of its lowest energy peak can be used to test the form of the bilayer ground state in the quantum Hall-effect regime.Comment: 4 pages, 2 figure

No abstract

We model the optical visibility of monolayer and bilayer graphene deposited on a SiO2/Si substrate or thermally annealed on the surface of SiC. Visibility is much stonger in reection than in transmission, reaching the optimum conditions when the bare substrate transmits light resonantly. In the optical range of frequencies a bilayer is approximately twice as visible as a monolayer thereby making the two types of graphene distinguishable from each other.Monolayer graphene is a single two-dimensional honeycomb lattice of carbon atoms. Although the rst graphene-based structures were only recently fabricated [1] they have quickly become the subject of an extensive research eort [2,3,4]. Monolayer graphene is a zero-gap semiconductor with a Dirac-like dispersion of chiral quasiparticles near the K points of the hexagonal rst Brillouin zone [5]. Bilayer graphene is a pair of graphene sheets with the Bernal (AB) stacking arrangement. In the low-energy spectrum of this material [6] the conduction and valence bands both consist of two quadratic branches split by the inter-layer coupling γ 1 . Measurements of the quantum Hall eect [1,2,7] and ARPES experiments [8] have conrmed that these are the low-energy band structures of these materials.The widespread microcleavage technique used to fabricate graphene-based devices requires a visual inspection of the substrate [1] to nd akes of one or two layers thickness. In this Letter, we aim to determine the optimum conditions for making these akes optically visible when they are deposited on various substrates. The parameters at one's disposal (see Fig. 1) are the frequency ω, angleᾱ and aperture δα of the focused incident radiation, as well as the thicknesses of the various layers of the underlying dielectric materials.Below we calculate the reection of non-polarized incident light taking the geometry of the substrate intoBare substrate, σ = 0Bilayer flake, σ2 substrate geometry: Fig. 1, we analyze the reection R of light from a substrate with a ake on it and compare this to the reection R 0 of a bare (graphenefree) substrate. The optical visibility of a ake is then determined as the contrast between two such parts of the sample studied using a monochromatic light source:The scattering of light is analyzed using the electromagnetic wave equations in vacuum and dielectric media and the standard boundary conditions at interfaces between dierent materials,The superscripts and ⊥ stand for the components of the eld parallel and perpendicular to the interface respectively, n is the unit vector normal to the interface, the subscript 1 (2) denotes the eld below (above) the interface, and σ(ω) is the frequency-dependent conductivity of a graphene ake and D = (ω) E. One more boundary condition (on the perpendicular components of H) duplicates Snell's law.Having in mind an optical setup used to locate a small ake, we consider a beam of light focused by a lens, so that the light in the beam arrives at the substrate surface with some aperture δα (see Fig. 1). Therefore the measurable reecta...

No abstract

We propose a device for the generation of valley polarized electronic current in bilayer graphene. By analyzing the response of this material to intense terahertz frequency light in the presence of a transverse electric field, we demonstrate that dynamical states are induced in the gapped energy region, and if the system parameters are properly tuned, these states exist only in one valley. The valley polarized states can then be used to filter an arbitrary electron current, so generating a valley polarized current.Comment: 4 pages, 3 colour figures. Published version. Journal reference is Applied Physics Letters 95, 062107 (2009

We discuss the conditions under which the predicted (but not yet observed) zero-field interlayer excitonic condensation in double layer graphene has a critical temperature high enough to allow detection. Crucially, disorder arising from charged impurities and corrugation in the lattice structure -invariably present in all real samples -affects the formation of the condensate via the induced charge inhomogeneity. In the former case, we use a numerical Thomas-Fermi-Dirac theory to describe the local fluctuations in the electronic density in double layer graphene devices and estimate the effect these realistic fluctuations have on the formation of the condensate. To make this estimate, we calculate the critical temperature for the interlayer excitonic superfluid transition within the mean-field BCS theory for both optimistic (unscreened) and conservative (statically screened) approximations for the screening of the interlayer Coulomb interaction. We also estimate the effect of allowing dynamic contributions to the interlayer screening. We then conduct similar calculations for double quadratic bilayer graphene, showing that the quadratic nature of the low-energy bands produces pairing with critical temperature of the same order of magnitude as the linear bands of double monolayer graphene.

No abstract