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

Sparse Gamma Rhythms Arising through Clustering in Adapting Neuronal Networks

Gamma rhythms (30–100 Hz) are an extensively studied synchronous brain state responsible for a number of sensory, memory, and motor processes. Experimental evidence suggests that fast-spiking interneurons are responsible for carrying the high frequency components of the rhythm, while regular-spiking pyramidal neurons fire sparsely. We propose that a combination of spike frequency adaptation and global inhibition may be responsible for this behavior. Excitatory neurons form several clusters that fire every few cycles of the fast oscillation. This is first shown in a detailed biophysical network model and then analyzed thoroughly in an idealized model. We exploit the fact that the timescale of adaptation is much slower than that of the other variables. Singular perturbation theory is used to derive an approximate periodic solution for a single spiking unit. This is then used to predict the relationship between the number of clusters arising spontaneously in the network as it relates to the adaptation time constant. We compare this to a complementary analysis that employs a weak coupling assumption to predict the first Fourier mode to destabilize from the incoherent state of an associated phase model as the external noise is reduced. Both approaches predict the same scaling of cluster number with respect to the adaptation time constant, which is corroborated in numerical simulations of the full system. Thus, we develop several testable predictions regarding the formation and characteristics of gamma rhythms with sparsely firing excitatory neurons

Resonance-driven random lasing

4 pages, 4 figures.-- Supplementary material available at http://dx.doi.org/10.1038/nphoton.2008.102: Fig. 1: Ohm's law fit for photonic glass, Fig. 2: Two dyes photonic glass reference sample.A random laser is a system formed by a random assembly of elastic scatterers dispersed into an optical gain medium. The multiple light scattering replaces the standard optical cavity of traditional lasers and the interplay between gain and scattering determines the lasing properties. All random lasers studied to date have consisted of irregularly shaped or polydisperse scatterers, with a certain average scattering strength that was constant over the frequency window of the laser. In this letter we consider the case where the scattering is resonant. We demonstrate that randomly assembled monodisperse spheres can sustain scattering resonances over the gain frequency window, and that the lasing wavelength can therefore be controlled by means of the diameter and refractive index of the spheres. The system is therefore a random laser with an a priori designed lasing peak within the gain curve.The work was financially supported by the European Commission (EC) (LENS) under contract number RII3-CT-2003-506350, by the European Union (EU) through the Network of Excellence IST-2-511616-NOE (PHOREMOST), CICyT NAN2004-08843-C05, MAT2006-09062, the Spanish MEC Consolider-QOIT CSD2006-0019 and the Comunidad de Madrid S-0505/ESP-0200.Peer reviewe