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 present a way to control both the band gap and the magnetic properties of nanoscale graphene, which might prove highly beneficial for application in nanoelectronic and spintronic devices. We have shown that chemical doping by nitrogen along a single zigzag edge lowers the symmetry from D 2h ͑pure graphene͒ to C 2v , thereby accommodating the state with antiferromagnetic spin ordering of localized states between the zigzag edges. This leads to an increase in the gap in comparison to that of pure graphene in its highest possible symmetry of D 2h and a shift of the molecular orbitals localized on the doped edge in such a way that the spin gap asymmetry, which can lead to half metallicity under certain conditions, is obtained. The doping in the middle of the graphene layer along the zigzag edge results in an impurity level between the highest occupied molecular orbital and lowest unoccupied molecular orbital of pure graphene ͑much like in semiconductor systems͒ thus decreasing the band gap and adding unpaired electrons, which can also be used to control the graphene conductivity.
We have studied the electronic and magnetic properties of graphene and their modification due to the adsorption of water and other gas molecules. Water and gas molecules adsorbed on nanoscale graphene were found to play the role of defects which facilitate the tunability of the bandgap and allow us to control the magnetic ordering of localized states at the edges. The adsorbed molecules push the wavefunctions corresponding to α-spin (up) and β-spin (down) states of graphene to the opposite (zigzag) edges. This breaks the sublattice and molecular point group symmetry that results in opening of a large bandgap. The efficiency of the wavefunction displacement depends strongly on the type of molecules adsorbed.Monolayer graphene [1] with its high electron mobility, unique magnetic phenomena [2], and unusual relativisticlike properties [3] has generated an upsurge of activities in materials science. Materials exhibiting magnetic properties are in great demand for applications in nanoscale electronics and spintronics. Most magnetic materials are metals, where ferromagnetism (which results from an imbalance between the spin-up and spin-down unpaired electrons) is often destroyed by thermal fluctuations. In carbon systems the magnetic properties are stable even at room temperatures. The nonmetalicity of carbon systems makes them biocompatible and therefore are ideal for a wide range of applications not only in nanoelectronics and spintronics [4,5,6], but also in medicine and biology. In most carbon systems the origin of magnetism is unclear, but in graphene it is expected to be the result of spin ordered states localized at the edges [7,8,9,10,11,12,13].The absence of a bandgap is however a major hindrance for graphene's application in nanoelectronics. Various mechanisms for opening a gap have been developed that involve breaking of certain symmetries in graphene by defects [11], an applied bias [4,5], and interaction with other materials [14]. Noting that the conductivity of the carbon systems [15,16] is extremely sensitive to adsorption of gas molecules due to the charge exchange between them, we assume that a more controllable way to induce interactions that break a symmetry of graphene would be gas adsorption. The charge exchange between the adsorbed molecules and graphite was found to be rather low [17], and donor or acceptor behavior is exhibited depending on the type of molecules adsorbed. However, since gas adsorption changes the electronic properties of graphene due to the charge exchange between them, we suspect that adsorption should affect the localization of electronic states along the edges and can facilitate opening of a gap.Here we study the influence of adsorption of water on the electronic and magnetic properties of graphene by molecular mechanical methods using the spin-polarized density functional theory with semilocal gradient corrected functional (UB3LYP/6-31G [18]) in the Jaguar 6.5 program [19]. The van der Waals interactions, which impact the interaction between graphene and adsorpant, are not c...
The electronic and magnetic properties of graphane with H-vacancies were investigated using the quantum-chemistry methods. The hybridization of the edges is found to be absolutely crucial in defining the size of the bandgap, which is increased from 3.04 eV to 7.51 eV when the hybridization is changed from the sp 2 to the sp 3 type. The H-vacancy defects also influence the size of the gap that depends on the number of defects and their distribution between the two sides of the graphane plane. Further, the H-vacancy defects induced on one side of the graphane plane and placed on the neighboring carbon atoms are found to be the source of ferromagnetism which is distinguished by the high stability of the state with a large spin number in comparison to that of the singlet state and is expected to persist even at room temperatures. However, the ferromagnetic ordering of the spins is obtained to be limited by the concentration of H-vacancy defects and ordering would be preserved if number of defects do not exceed eight.
The electronic properties of polycrystalline lead oxide consisting of a network of single-crystalline α-PbO platelets and the formation of the native point defects in α-PbO crystal lattice are studied using first principles calculations. The α-PbO lattice consists of coupled layers interaction between which is too low to produce high efficiency interlayer charge transfer. In practice, the polycrystalline nature of α-PbO causes the formation of lattice defects in such a high concentration that defectrelated conductivity becomes the dominant factor in the interlayer charge transition. We found that the formation energy for the O vacancies is low, such vacancies are occupied by two electrons in the zero charge state and tend to initiate the ionization interactions with the Pb vacancies. The vacancies introduce localized states in the band gap which can affect charge transport. The O vacancy forms a defect state at 1.03 eV above the valence band which can act as a deep trap for electrons, while the Pb vacancy forms a shallow trap for holes located just 0.1 eV above the valence band. Charge de-trapping from O vacancies can be accounted for the experimentally found dark current decay in ITO/PbO/Au structures.
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