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.

The time it takes to switch on and off electric current determines the rate at which signals can be processed and sampled in modern information technology. Field-effect transistors are able to control currents at frequencies of the order of or higher than 100 gigahertz, but electric interconnects may hamper progress towards reaching the terahertz (10(12) hertz) range. All-optical injection of currents through interfering photoexcitation pathways or photoconductive switching of terahertz transients has made it possible to control electric current on a subpicosecond timescale in semiconductors. Insulators have been deemed unsuitable for both methods, because of the need for either ultraviolet light or strong fields, which induce slow damage or ultrafast breakdown, respectively. Here we report the feasibility of electric signal manipulation in a dielectric. A few-cycle optical waveform reversibly increases--free from breakdown--the a.c. conductivity of amorphous silicon dioxide (fused silica) by more than 18 orders of magnitude within 1 femtosecond, allowing electric currents to be driven, directed and switched by the instantaneous light field. Our work opens the way to extending electronic signal processing and high-speed metrology into the petahertz (10(15) hertz) domain.

The control of the electric and optical properties of semiconductors with microwave fields forms the basis of modern electronics, information processing and optical communications. The extension of such control to optical frequencies calls for wideband materials such as dielectrics, which require strong electric fields to alter their physical properties. Few-cycle laser pulses permit damage-free exposure of dielectrics to electric fields of several volts per ångström and significant modifications in their electronic system. Fields of such strength and temporal confinement can turn a dielectric from an insulating state to a conducting state within the optical period. However, to extend electric signal control and processing to light frequencies depends on the feasibility of reversing these effects approximately as fast as they can be induced. Here we study the underlying electron processes with sub-femtosecond solid-state spectroscopy, which reveals the feasibility of manipulating the electronic structure and electric polarizability of a dielectric reversibly with the electric field of light. We irradiate a dielectric (fused silica) with a waveform-controlled near-infrared few-cycle light field of several volts per angström and probe changes in extreme-ultraviolet absorptivity and near-infrared reflectivity on a timescale of approximately a hundred attoseconds to a few femtoseconds. The field-induced changes follow, in a highly nonlinear fashion, the turn-on and turn-off behaviour of the driving field, in agreement with the predictions of a quantum mechanical model. The ultrafast reversibility of the effects implies that the physical properties of a dielectric can be controlled with the electric field of light, offering the potential for petahertz-bandwidth signal manipulation.

No abstract

We investigate the Fock-Darwin states of the massless chiral fermions confined in a graphitic parabolic quantum dot. In light of Klein tunneling, we analyze the condition for confinement of the Dirac fermions in a cylindrically symmetric potential. New features of the energy levels of the Dirac electrons as compared to the conventional electronic systems are discussed. We also evaluate the dipole-allowed transitions in the energy levels of the dots. We propose that in the high magnetic field limit, the band parameters can be accurately determined from the dipole-allowed transitions.

Areal density of disorder-induced resonators with a high quality factor, Q ≫ 1, in a film with fluctuating refraction index is calculated theoretically. We demonstrate that for a given kl > 1, where k is the light wave vector, and l is the transport mean free path, when on average the light propagation is diffusive, the likelihood for finding a random resonator increases dramatically with increasing the correlation radius of the disorder. Parameters of most probable resonators as functions of Q and kl are found.

No abstract

Here we show that the Pfaffian state proposed for the 5 2 fractional quantum Hall states in conventional two-dimensional electron systems can be readily realized in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ∼ 10 Tesla, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.Ever since the discovery of the quantum Hall state at the Landau level filling factor ν = 5 2 , the first evendenominator state observed in a single-layer system, it has been very aptly characterized as an "enigma" [2]. It was clear at the outset that this state must be different from the fractional quantum Hall effect (FQHE) in predominantly odd-denominator filling fractions [3,4]. Understanding this enigmatic state has been a major challenge in all these years [5]. At this half-filled first excited Landau level [6], a novel state described by a pair wave function involving a Pfaffian [7,) has been the strongest candidate. More intriguing are the elementary charged excitations at this ground state that have a charge e * = e/4 and obey 'non-abelian' statistics [10,11]. Recent observation of the e * = e/4 quasiparticle charge at ν = 5 2 quantum Hall state [12] has brought the issue to the fore [13]. It has been suggested that these non-abelian quasiparticles, besides carrying the signatures of Majorana fermions [14] in this system, might even be useful for quantum information storage and processing in an intrinsically fault-tolerant manner [15].Electrons in another recently discovered twodimensional system, graphene [16], display a range of truly remarkable behavior [17]. The dynamics of electrons in a single sheet of graphene, a hexagonal honeycombed lattice of carbon atoms is that of massless Dirac fermions with linear dispersion, chiral eigenstates, valley degeneracy, and unusual Landau levels in an external magnetic field [17]. Theoretical studies of FQHE in monolayer [18] and bilayer graphene [19] were reported earlier by us. Recent experimental observations of the ν = 1 3 FQHE in monolayer graphene [20] have provided a glimpse of the role highly correlated electrons play in graphene. Given the accute interest in studying the properties of the ν = 5 2 state in conventional twodimensional electron gas (2DEG), a natural question to ask is how does this state manifests itself in graphene.For the conventional (nonrelativistic) 2DEG the incompressible state at ν = 5 2 has been studied numerically for a finite number of electrons [13]. A relatively good (but not 100%) overlap with the Pfaffian state has been found. The overlap of the exact wave function of the finite-size systems with the Pfaffian state can be improved by varying the inter-electron potential. For example, by increasing the thickness of the two-...