The bands of graphite are extremely sensitive to topological defects which modify the electronic structure. In this paper we found non-dispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene as a signature of a transition from a parabolic dispersion of bilayer graphene to the characteristic linear dispersion of graphene. This transition occurs for relative rotation angles of layers around 1.5 o and is related to a process of layer decoupling. We have performed ab-initio calculations to develop a tight binding model with an interaction Hamiltonian between layers that includes the π orbitals of all atoms and takes into account interactions up to third nearest-neighbors within a layer.Graphene is a sheet of carbon atoms arranged on a honeycomb lattice recently obtained by micro-mechanical cleavage of graphite 1 . This two-dimensional lattice has a singular linear band dispersion 2 which makes the charge carriers behave as massless Dirac fermions with a speed of v F ≈ 10 6 m/s, travelling large distances without interaction. These properties change drastically in the presence of a second layer. A Bernal or AB stacked bilayer graphene (BLG) is a stack of two carbon sheets in such a way that an atom of one of the layers is in the center of the other layer's hexagon. Like single layer graphene, BLG is also a semimetal but its dispersion relation is quadratic and its charge carriers have a non-zero effective mass.Few layers of graphene grown epitaxially on different surfaces show a variety of defects including rotations of the top layer, for instance in graphene layers prepared by chemical vapor deposition (CVD) 3 . Moiré patterns are very often observed in Scanning Tunneling Microscopy (STM) measurements when a relative rotation between top layers is present 4,5 . Graphite is also extremely sensitive to topological defects which can modify its electronic structure. Extended defects like lattice dislocations lead to the presence of localized states at the Fermi energy 6,7 as is the case of graphene ribbons with zigzag edges 8 . These localized states can also be found as a result of local defects such as in graphene antidot lattices 9 . They were predicted in superstructures with honeycomb symmetry by N. Shima et al. 10 , who suggest the occurrence of ferromagnetism when electron correlation is turned on.In addition one of the mechanisms proposed to explain high-T c superconductivity is associated with the presence of extended Van Hove Singularities (VHS) near the Fermi energy 11-13 . This kind of VHS arising from a nearly dispersionless band has been observed in high-T c cuprates by angle-resolved photoemission 14,15 . The superconductivity in graphene when the fermi level is close to a VHS has been also explored theoretically 16 . Recently Guohong Li et al.17 reported the observation of two symmetric low-energy VHSs in the density of states, measured by scanning tunneling spectroscopy, in twisted graphene layers. They showed that the position of these singularities can b...

We investigate the electronic transport properties of a bilayer graphene flake contacted by two monolayer nanoribbons. Such a finite-size bilayer flake can be built by overlapping two semiinfinite ribbons or by depositing a monolayer flake onto an infinite nanoribbon. These two structures have a complementary behavior, that we study and analyze by means of a tight-binding method and a continuum Dirac model. We have found that for certain energy ranges and geometries, the conductance of these systems oscillates markedly between zero and the maximum value of the conductance, allowing for the design of electromechanical switches. Our understanding of the electronic transmission through bilayer flakes may provide a way to measure the interlayer hopping in bilayer graphene.Comment: 11 pages, 8 figure

We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer graphene spectrum shows two parabolic Bernal-like bands and a twisted-like Dirac cone. For small twist angles, the parabolic bands present a gap that increases for decreasing rotation angle. There is also a shift in the twisted-like Dirac cone with a similar angle dependence. We correlate the gap in the trilayer with the shift of the Dirac cone in an isolated twisted bilayer, which is due to the loss of electron-hole symmetry caused by sublattice mixing in the rotated geometry. Using a tight-binding and a continuum model, we derive an effective Hamiltonian which accounts for the relevant low-energy properties of this system.

The electronic transport of a noninteracting quantum ring side-coupled to a quantum wire is studied via a single-band tunneling tight-binding Hamiltonian. We found that the system develops an oscillating band with antiresonances and resonances arising from the hybridization of the quasibound levels of the ring and the coupling to the quantum wire. The positions of the antiresonances correspond exactly to the electronic spectrum of the isolated ring. Moreover, for a uniform quantum ring the conductance and the persistent current density were found to exhibit a particular odd-even parity related with the ring-order. The effects of an in-plane electric field was also studied. This field shifts the electronic spectrum and damps the amplitude of the persistent current density. These features may be used to control externally the energy spectra and the amplitude of the persistent current.

The existence of bound states in the continuum was predicted at the dawn of quantum mechanics by von Neumann and Wigner. In this work we discuss the mechanism of formation of these exotic states and the feasibility to observe them experimentally in symmetrical heterostructures composed by segments of graphene ribbons with different widths forming a graphene quantum dot. We identify the existence of bound states in the continuum in these graphene quantum dot systems by means of local density of states and electronic conductance calculations.

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In this work we address the effects on the conductance of graphene nanoribbons (GNRs) of organic molecules adsorbed at the ribbon edge. We studied the case of armchair and zigzag GNRs with quasi-one-dimensional side-attached molecules, such as linear poly-aromatic hydrocarbons and poly(para-phenylene). These nanostructures are described using a single-band tight-binding Hamiltonian and their electronic conductance and density of states are calculated within the Green's function formalism based on real-space renormalization techniques. We found that the conductance exhibits an even-odd parity effect as a function of the length of the attached molecules. Furthermore, the corresponding energy spectrum of the molecules can be obtained as a series of Fano antiresonances in the conductance of the system. The latter result suggests that GNRs can be used as a spectrograph sensor device.