Gate-induced magneto-oscillation phase anomalies in graphene bilayers

The magneto-oscillations in graphene bilayers are studied in the vicinity of the K and K' points of the Brillouin zone within the four-band continuum model ased on the simplest tight-binding approximation involving only the nearest neighbor interactions. The model is employed to construct Landau plots for a variety of carrier concentrations and bias strengths between the graphene planes. The quantum-mechanical and quasiclassical approaches are compared. We found that the quantum magneto-oscillations are only asymptotically periodic and reach the frequencies predicted quasiclassically for high indices of Landau levels. In unbiased bilayers the phase of oscillations is equal to the phase of massive fermions. Anomalous behavior of oscillation phases was found in biased bilayers with broken inversion symmetry. The oscillation frequencies again tend to quasiclassically predicted ones, which are the same for $K$ and $K'$, but the quantum approach yields the gate-tunable corrections to oscillation phases, which differ in sign for K and K'. These valley-dependent phase corrections give rise, instead of a single quasiclassical series of oscillations, to two series with the same frequency but shifted in phase.Comment: 8 pages, 8 figure

Dirac Spectrum in Piecewise Constant One-Dimensional Potentials

We study the electronic states of graphene in piecewise constant potentials using the continuum Dirac equation appropriate at low energies, and a transfer matrix method. For superlattice potentials, we identify patterns of induced Dirac points which are present throughout the band structure, and verify for the special case of a particle-hole symmetric potential their presence at zero energy. We also consider the cases of a single trench and a p-n junction embedded in neutral graphene, which are shown to support confined states. An analysis of conductance across these structures demonstrates that these confined states create quantum interference effects which evidence their presence.Comment: 10 pages, 12 figures, additional references adde

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