Properties of Graphene: A Theoretical Perspective

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 graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic

Orbital-free density functional theory of out-of-plane charge screening in graphene.

We propose a density functional theory of Thomas-Fermi-Dirac-von Weizs\"acker type to describe the response of a single layer of graphene resting on a dielectric substrate to a point charge or a collection of charges some distance away from the layer. We formulate a variational setting in which the proposed energy functional admits minimizers, both in the case of free graphene layers and under back-gating. We further provide conditions under which those minimizers are unique and correspond to configurations consisting of inhomogeneous density profiles of charge carrier of only one type. The associated Euler-Lagrange equation for the charge density is also obtained, and uniqueness, regularity and decay of the minimizers are proved under general conditions. In addition, a bifurcation from zero to non-zero response at a finite threshold value of the external charge is proved.Comment: 38 pages, 3 figure

High-yield production of graphene by liquid-phase exfoliation of graphite

Fully exploiting the properties of graphene will require a method for the mass production of this remarkable material. Two main routes are possible: large-scale growth or large-scale exfoliation. Here, we demonstrate graphene dispersions with concentrations up to ~0.01 mg m1-1, produced by dispersion and exfoliation of graphite in organic solvents such as N-methyl-pyrrolidone. This is possible because the energy required to exfoliate graphene is balanced by the solvent -graphene interaction for solvents whose surface energies match that of graphene. We confirm the presence of individual graphene sheets by Raman spectroscopy, transmission electron microscopy and electron diffraction. Our method results in a monolayer yield of ~1 wt%, which could potentially be improved to 7–12 wt% with further processing. The absence of defects or oxides is confirmed by X-ray photoelectron, infrared and Raman spectroscopies. We are able to produce semi-transparent conducting films and conducting composites. Solution processing of graphene opens up a range of potential large-area applications, from device and sensor fabrication to liquid-phase chemistry