Session A30: Electronic Properties of Graphene and Related Structures I

First-principles calculations of zigzag-edge graphene nanostrips with different edge species

First-principles calculations have suggested that zigzag-edge graphene nanostrips terminated with hydrogen atoms have edge states which exhibit magnetic behavior. However, it is not clear that zigzag-edge graphene nanostrips terminated with other atoms or functional groups also show similar magnetic behavior. Our local-spin-density calculations suggest that some zigzag-edge nanostrips, including oxygen-terminated nanostrips, have no magnetic edges. One reason could be that there is charge transfer at the edges which effectively dopes the pi-orbital network, causing the spin polarization to collapse.   

Hydrogenation of graphitic nanocarbons

We apply {\em ab initio} density functional calculations to study the hydrogenation of graphitic nanocarbons including fullerenes, onions and nanotubes using diethylenetriamine (DETA) as hydrogenation reagent. Our results indicate that transfer of atomic hydrogen from the amine end-group of chemisorbed DETA molecules to nanocarbons is an exothermic reaction. We explore the optimum pathway for the hydrogenation reaction and find the activation energy associated with sigmatropic rearrangement of chemisorbed hydrogen atoms to lie near 1 eV, thus facilitating formation of energetically favorable adsorbate structures by surface diffusion. Chemisorbed hydrogen assists in a local sp$^2$ to sp$^3$ bonding conversion of the graphitic nanocarbons, causing large-scale structural changes ranging from local relaxations in nanotubes to shell opening in multi-wall onions.   

Electronic Structure Study of Edge Saturated Graphene Nanoribbons

Using density functional theory and GW method, we have studied how the electronic structures of graphene nanoribbons responds to the edge saturation. The energy gaps and effective mass of the nanoribbons are highly sensitive to the edge states, as well as the nanoribbon width. This suggests a new approach to modify the electronic structure of graphene nanoribbons by tweaking the edge saturation.   

Imaging massless Dirac fermion flow in graphene nanoribbons

Since its recent experimental discovery, graphene has been the focus of intense theoretical and experimental research. Its unconventional electronic structure characterized by the linear momentum dispersion of electrons which behave as massless Dirac particles at half-filling makes graphene an ideal candidate not only for investigating fundamental physics questions, but also for constructing new nanoscale devices. Despite its importance for device applications, there are very few studies of local features of electronic transport in graphene nanoribbons (GNRs). Moreover, the application of recently advanced scanning probe techniques to imaging electronic flow in graphene is expected to lead to many interesting discoveries. Therefore, we investigate the local features of charge transport through GNRs, by employing our bond current formalism which expresses the local current fluxes flowing between neighboring sites of the hexagonal lattice in terms of nonequilibrium Green functions. We show that, while the charge density profiles for clean zigzag graphene nanoribbons (ZGNRs) close to Dirac point peak at the edges due to the zero-energy edge states, the current densities concentrate towards the nanoribbon center. The analysis of local charge current flow explains unusual transport properties of ZGNRs such as low sensitivity of current flow to edge vacancies or long-range impurities. Journal Ref: EPL {\bf 80}, 47001 (2007).   

First principles study of graphene nanoribbons and nanorectangles

We have studied the finite size effect on the electronic structure of graphene nanoribbons (GNRs) using first principles density functional techniques. In particular, we have computed the energy gap dependence on the width and length for zero-dimensional nanorectangles for both the armchair and zigzag ribbons; and compared to the one-dimensional (infinite length) cases. One-dimensional armchair ribbons are expected to be metallic if the number of carbon atoms across the ribbon is N = 3M-1, and non-metallic N $\ne $ 3M-1, where M is an integer. In addition to quantum confinement along the width of the ribbon for metallic widths, an additional finite size effect emerges along the length of ribbons only for non-metallic armchair ribbons. The origin of additional quantum confinement in these structures is explained based on the energy states near the Fermi energy. The differences between zero- and one-dimensional electronic structure properties are considered with the addition of passivating groups and their effect on the electronic properties of graphenes and their impact on nanoelectronics devices are discussed.   

Band gaps in armchair-edge graphene nanostrips

First-principles calculations have shown that all graphene nanostrips terminated with hydrogen atoms exhibit band gaps at the Fermi level. In the case of armchair-edge nanostrips, the calculations contradict a first-nearest-neighbor tight-binding prediction that one third of these nanostrips should be metallic. At the one-electron level, at least two independent causes for the band gaps in these nanostrips have been suggested, namely lattice distortion and long-range interactions. In this presentation, we present theoretical calculations of arbitrary armchair-edge nanostrips. The model, which includes distortion of edge atoms and third-nearest-neighbor interactions, leads to band gaps and band structures which are in good agreement with those obtained from our first-principles calculations.   

Study of partial oxidation of zigzag graphene 1-d ribbons

We study the effect of partial oxidation of graphene 1-d ribbons using the first principle- density functional theory. We have considered zigzag graphene, n=8 with four dangling carbon on each edge. The zigzag graphene 1-d ribbon is a zero bandgap material, when it is functionalized completely with hydrogen atoms. However, when two of these hydrogen atoms are replaced by oxygen, the band gap opens. This is due to the fact that the oxygen forms double bond with the carbon and hence disrupts the delocalization of the $\pi $ and $\pi ^{\ast }$ bond. This functionalization does not induce magnetization. On further increase of oxygen, the band decreases. When oxidation is more than 75{\%} on one side of the graphene ribbon or on either sides, the lone pair of electrons of the oxygen induces magnetization to some of the carbon atoms. Also some configurations of partially oxidized graphene show that antiferromagnetic order is the stable ordering in these systems.   

Graphene Nanoribbon(GNR) based Nanoelectronics for Interconnect Applications and Logic Devices using First Principles Calculations

We have studied electronic structures of graphene ribbon based nanoelectronics using first principles density functional techniques for interconnect applications as well as for logic devices. The conductance behaviors of them are computed based on Non-equilibrium Green's Function. For example, we have calculated the energy gap and I-V curve of Schottyky diode built by connecting two zig-zag GNRs with different passivations. All new configurations will show nonlinear I-V behavior and explicit step feature is observed in the I-V plot as well. There is also a small charge transfer at the junction area for this new configuration which is more like a traditional diode, which leads to different phenomena during the negative biasing.   

Zigzag graphene ribbons with intrinsic spin-orbit and electron-electron interactions.

The effects of intrinsic spin-orbit (I-SO) and Coulomb interactions on low-energy properties of finite width graphene zigzag ribbons are studied by means of tight-binding Hamiltonian. We derive analytic expressions for eigenstates and energies in the presence of the I-SO interaction in the hard-wall boundary limit. A detailed study of the spatial dependence of spin-filtered edge states [1] shows different edge localizations as the Dirac point is reached. Tight-binding numerical calculations reproduce exactly the analytic expression obtained for the band-structure. Coulomb interactions are included and treated within the bosonization approximation. We find that small momentum transfer scattering terms open a charge-gap in neutral ribbons, while keeping the spin sector gapless. Our numerical results suggest an exponentially vanishing gap in terms of the ribbon width for large values of the I-SO coupling constant, in clear contrast with results found for armchair ribbons [2]. [1] C.L. Kane and E.J. Mele, Phys. Rev. Lett. {\bf 95}, 226801 (2005). [2] M. Zarea and N. Sandler, Phys. Rev. Lett. Dec (2007)   

Atomic-scale studies of nanometer-sized graphene on semiconducting surfaces.

We have performed atomic level studies of graphene on semiconducting surfaces using ultrahigh vacuum scanning tunneling microscopy (UHV-STM) [1]. By mechanically exfoliating graphite and using an in-situ dry contact transfer technique [2], we observe predominantly single and double layers of atomically clean graphene with lateral dimensions of 2-20 nm. Room temperature scanning tunneling spectroscopy measurements of the 2-10 nm monolayer pieces display a size-dependent energy gap ranging from 0.1-1 eV, while monolayers with lateral dimensions of 20 nm exhibit a finite density of states at the Fermi level. [1] K.A. Ritter and J.W. Lyding, Nanotechnology, in press (http://arxiv.org/pdf/0711.0050). [2] P.M. Albrecht and J.W. Lyding, APL 83, 5029 (2003).   

Ab-initio calculation of bonding, charge redistribution and transfer of graphene on amorphous silica

We study the effects of an amorphous silica substrate on the electronic structure and electron density of graphene using Density Functional Theory. We observe that the silica substrate transfers charge to the graphene layer and the workfunction of the combined system is lower than that of an isolated graphene sheet. The inhomogeneous charge distribution of the substrate induces an inhomogeneous charge redistribution on the graphene layer, which is experimentally observed as electron and hole puddles. The binding energy between one graphene layer and the substrate is weak and reveals no sign of chemical bonding. This can also be inferred from a rigid band shift observed in the system.   

Electron states of mono- and bilayer graphene on SiC probed by STM

We present a scanning-tunneling microscopy (STM) study of a gently graphitized 6H-SiC(0001) surface in ultrahigh vaccum [1]. From an analysis of atomic scale images, we identify two different kinds of atomic scale contrasts, which we attribute to mono- and bilayer (or trilayer) graphene capping a C-rich interface. At any temperature, both terraces show quantum interferences generated by point defects. Such interferences are a fingerprint of pi-like states close to the Fermi level. We conclude that the metallic states of the first graphene layer are almost unperturbed by the underlying interface, in agreement with recent ab initio studies [2] and photoemission experiments [3]. However, a significant density of interface states is detected close to the Fermi level in the C-rich interface. [1] P. Mallet et al., Phys. Rev. B 76, 041403(R) (2007) [2] F. Varchon et al., Phys. Rev. Lett. 99, 126805 (2007) [3] A. Bostwick et al., Nat. Phys. 3, 36 (2007)   

Magnetism in graphene nanoislands and nanovoids

The rules to predict the magnetic state of both graphene nanoislands and nanovoids in otherwise perfect graphene systems are presented. We discuss how the shape of the island or void, the associated imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moment are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional calculations. The magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zigzag edges happen to be drastically different[1]. In the case of voids in semiconductor ribbons, we study the magnetism associated to a single void and the magnetic interactions developed between them[2]. [1] J. Fern\'andez-Rossier and J. J. Palacios, Phys. Rev. Lett. {\bf 99}, 177204 (2007). [2] J. J. Palacios,J. Fern\'andez-Rossier, L. Brey, in preparation.   

The electronic structure of graphene layers on SiO$_{2}$ substrate

Graphene is a single layer of carbon atoms packed in a honeycomb lattice, and its quasiparticles behave like massless Dirac fermions. Since graphene is usually supported and deposited on dielectric materials such as SiO$_{2}$ and SiC, interactions between graphene and substrate atoms can modify the electronic structure of graphene. In this work we study the structural and electronic properties of a few graphene layers on SiO$_{2}$ surfaces through first-principles calculations within the local-density-functional approximation. We examine interactions between graphene layers and Si- and O- terminated surfaces of $\alpha $-quartz and the substrate-induced doping effect. For a single graphene layer, we find that graphene strongly interacts with the O-terminated surface. A charge transfer occurs from the graphene to the surface O atoms, leading to the p-type doping. For a bilayer graphene in AB stacking, the charge transfer mostly occurs for the graphene layer right on the substrate, resulting in an asymmetric distribution of electron charges between two graphene layers and thus a gap opening at the Dirac point.   

Pair condensation in electron-hole graphene bi-layer

Using self consistent Hartree Fock calculations we show that an electron-hole graphene bi-layer exhibits spontaneous interlayer coherence when the distance between layers is sufficiently small. We describe the unique transport properties of the emergent dipolar superfluid and relate them to the nature of the underlying massless Dirac particles.