Voltage-driven quantum oscillations in graphene

We predict unusual (for non-relativistic quantum mechanics) electron states in graphene, which are localized within a finite-width potential barrier. The density of localized states in the sufficiently high and/or wide graphene barrier exhibits a number of singularities at certain values of the energy. Such singularities provide quantum oscillations of both the transport (e.g., conductivity) and thermodynamic properties of graphene - when increasing the barrier height and/or width, similarly to the well-known Shubnikov-de-Haas (SdH) oscillations of conductivity in pure metals. However, here the SdH-like oscillations are driven by an electric field instead of the usual magnetically-driven SdH-oscillations.Comment: 4 pages, 4 figure

Localized States at Zigzag Edges of Multilayer Graphene and Graphite Steps

We report the existence of zero energy surface states localized at zigzag edges of $N$-layer graphene. Working within the tight-binding approximation, and using the simplest nearest-neighbor model, we derive the analytic solution for the wavefunctions of these peculiar surface states. It is shown that zero energy edge states in multilayer graphene can be divided into three families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene; (ii) states with finite amplitude over the two last, or the two first layers of the stack, equivalent to surface states in bilayer graphene; (iii) states with finite amplitude over three consecutive layers. Multilayer graphene edge states are shown to be robust to the inclusion of the next nearest-neighbor interlayer hopping. We generalize the edge state solution to the case of graphite steps with zigzag edges, and show that edge states measured through scanning tunneling microscopy and spectroscopy of graphite steps belong to family (i) or (ii) mentioned above, depending on the way the top layer is cut.Comment: 6 pages, 4 figure

Electrostatic deposition of graphene in a gaseous environment: A deterministic route to synthesize rolled graphenes?

The synthesis of single-wall carbon nanotubes (SWCNTs) of desired diameters and chiralities is critical to the design of nanoscale electronic devices with desired properties.1-6 The existing methods are based on self-assembly, 7-16 therefore lacking the control over their diameters and chiralities. The present work reports a direct route to roll graphene. Specifically, we found that the electrostatic deposition of graphene yielded: (i) flat graphene layers under high vacuum (10-7 Torr), (ii) completely scrolled graphene under hydrogen atmosphere, (iii) partially scrolled graphene under nitrogen atmosphere, and (iv) no scrolling for helium atmospheres. Our study shows that the application of the electrostatic field facilitates the rolling of graphene sheets exposed to appropriate gases and allows the rolling of any size graphene. The technique proposed here, in conjunction with a technique that produces graphene nanoribbons (GNRs) of uniform widths, will have significant impact on the development of carbon nanotube based devices. Furthermore, the present technique may be applied to obtain tubes/scrolls of other layered materials

Symmetry Breaking in Few Layer Graphene Films

Recently, it was demonstrated that the quasiparticle dynamics, the layer-dependent charge and potential, and the c-axis screening coefficient could be extracted from measurements of the spectral function of few layer graphene films grown epitaxially on SiC using angle-resolved photoemission spectroscopy (ARPES). In this article we review these findings, and present detailed methodology for extracting such parameters from ARPES. We also present detailed arguments against the possibility of an energy gap at the Dirac crossing ED.Comment: 23 pages, 13 figures, Conference Proceedings of DPG Meeting Mar 2007 Regensburg Submitted to New Journal of Physic

Conductivity of graphene: How to distinguish between samples with short and long range scatterers

Applying a quasiclassical equation to carriers in graphene we found a way how to distinguish between samples with the domination of short and long range scatterers from the conductivity measurements. The model proposed explains recent transport experiments with chemically doped as well as suspended graphene.Comment: 6 pages, 3 figures, some references have been corrected and revise

Cyclotron motion in graphene

We investigate cyclotron motion in graphene monolayers considering both the full quantum dynamics and its semiclassical limit reached at high carrier energies. Effects of zitterbewegung due to the two dispersion branches of the spectrum dominate the irregular quantum motion at low energies and are obtained as a systematic correction to the semiclassical case. Recent experiments are shown to operate in the semiclassical regime.Comment: 6 pages, 1 figure include

Tunneling of Dirac electrons through spatial regions of finite mass

We study the tunneling of chiral electrons in graphene through a region wherethe electronic spectrum changes from the usual linear dispersion to a hyperbolic dispersion,due to the presence of a gap. It is shown that contrary to the tunneling through a potentialbarrier, the transmission of electrons is, in this case, smaller than one for normal incidence.This mechanism may be useful for designing electronic devices made of grapheneinfo:eu-repo/semantics/publishedVersio

Dirac-point engineering and topological phase transitions in honeycomb optical lattices

We study the electronic structure and the phase diagram of non-interacting fermions confined to hexagonal optical lattices. In the first part, we compare the properties of Dirac points arising in the eigenspectrum of either honeycomb or triangular lattices. Numerical results are complemented by analytical equations for weak and strong confinements. In the second part we discuss the phase diagram and the evolution of Dirac points in honeycomb lattices applying a tight-binding description with arbitrary nearest-neighbor hoppings. With increasing asymmetry between the hoppings the Dirac points approach each other. At a critical asymmetry the Dirac points merge to open an energy gap, thus changing the topology of the eigenspectrum. We analyze the trajectory of the Dirac points and study the density of states in the different phases. Manifestations of the phase transition in the temperature dependence of the specific heat and in the structure factor are discussed.Comment: Published version 10 pages, 5 figure

Dirac electrons in graphene-based quantum wires and quantum dots

In this paper we analyse the electronic properties of Dirac electrons in finite-size ribbons and in circular and hexagonal quantum dots made of graphene.Comment: Contribution for J. Phys.: Cond. Mat. special issue on graphene physic

Electronic properties of bilayer and multilayer graphene

We study the effects of site dilution disorder on the electronic properties in graphene multilayers, in particular the bilayer and the infinite stack. The simplicity of the model allows for an easy implementation of the coherent potential approximation and some analytical results. Within the model we compute the self-energies, the density of states and the spectral functions. Moreover, we obtain the frequency and temperature dependence of the conductivity as well as the DC conductivity. The c-axis response is unconventional in the sense that impurities increase the response for low enough doping. We also study the problem of impurities in the biased graphene bilayer.Comment: 36 pages, 42 figures, references adde