Session L29: Focus Session: Carbon Nanotubes and Related Materials VIII: Electronic Structure of Graphene

Electronic Structure and Morphology of Graphene Layers on SiC

Recent years have witnessed the discovery and the unique electronic properties of graphene, a sheet of carbon atoms arranged in a honeycomb lattice. The unique linear dispersion relation of charge carriers near the Fermi level (``Dirac Fermions'') lead to exciting transport properties, such as an unusual quantum Hall effect, and have aroused scientific and technological interests. On the way towards graphene-based electronics, a knowledge of the electronic band structure and the morphology of epitaxial graphene films on silicon carbide substrates is imperative. We have studied the evolution of the occupied band structure and the morphology of graphene layers on silicon carbide by systematically increasing the layer thickness. Using angle-resolved photoemission spectroscopy (ARPES), we examine this unique 2D system in its development from single layer to multilayers, by characteristic changes in the $\pi $ band, the highest occupied state, and the dispersion relation in the out-of-plane electron wave vector in particular. The evolution of the film morphology is evaluated by the combination of low-energy electron microscopy and ARPES. By exploiting the sensitivity of graphene's electronic states to the charge carrier concentration, changes in the on-site Coulomb potential leading to a change of $\pi $ and $\pi $* bands can be examined using ARPES. We demonstrate that, in a graphene bilayer, the gap between $\pi $ and $\pi $* bands can be controlled by selectively adjusting relative carrier concentrations, which suggests a possible application of the graphene bilayer for switching functions in electronic devices. This work was done in collaboration with A. Bostwick, J. L. McChesney, and E. Rotenberg at Advanced Light Source, Lawrence Berkeley National Laboratory, K. Horn at Fritz-Haber-Institut, K. V. Emtsev and Th. Seyller at Lehrstuhl f\"{u}r Technische Physik, Universit\"{a}t Erlangen-N\"{u}rnberg, and F. El Gabaly and A. K. Schmid at National Center for Electron Microscopy, Lawrence Berkeley National Laboratory.   

Tailoring electronic properties in coated graphene

Graphene is a single layer carbon material whose unique properties in transport are related to the its peculiar Fermi surface, which is made out of six points at the corners of the Brillouin zone where the conduction and valence bands touch. Due to the vanishing density of states at these points, the low energy excitations are made of massless Dirac fermions, with several anomalous properties in the transport. We propose that some of the unique properties of graphene can be tailored by the chemical adsorption of impurity atoms on its surface. If on one hand alkaline metals are good charge donors and can be used to control the number of charge carriers in graphene, transition metals have a more covalent character and can be used to induce magnetism. We show that despite pure graphene cannot be magnetized, the hybridization of the carbon p orbitals with non-magnetic d orbitals can generate strong itinerant magnetism in graphene coated with transition metal atoms. On the other hand, if an isolated impurity atom is able to form a stable localized level under hybridization with the bath of electrons in graphene, we show that the suppression of the density of states in the bath around the localized level can strongly favor the formation of a local magnetic moment at the impurity. We propose that the local magnetization of the impurity can be controlled by the application of an external gate voltage.   

Probing the Band Structure of Mono-, Bi- and Tri-layer Graphene by Infrared Absorption Spectroscopy

Absorption spectra in the infrared range (0.3 -- 1 eV) were measured for large-area, single-crystal mono-, bi- and tri-layer graphene samples produced by mechanical exfoliation of graphite. A constant absorption independent of photon energy was observed for monolayer samples. For the bi-layer, a strong absorption peak was seen at 0.37eV. The absorption spectrum of tri-layer graphene was found to be well represented by the sum of those of a mono- and a bi-layer, with the latter spectrum scaled by 2$^{1/2}$ in photon energy. These observations can be explained qualitatively within a tight-binding band structure picture and yield an accurate determination of the nearest-layer hopping constant ($\gamma _1 )$. Explicit calculations of the absorption spectra show that an optimal fit to experiment requires a shift of the Fermi energy of approximately 100 meV from the Dirac point and an empirical broadening of tens of meV.   

Electronic structure of epitaxial graphene layers on SiC

Our DFT calculations [1](VASP) demonstrate the existence of a strong interaction between the substrate and the first carbon layer in the epitaxial graphene system. This prevents any graphitic electronic properties for this layer. However, the graphitic nature of the film is recovered by the second and third absorbed layers in agreement with recent STM experiments[2]. We also present evidence of a charge transfer that depends on the interface geometry. It causes the graphene to be doped and may open a gap in agreement with ARPES experiments [3]. The effect of the complex first carbon layer structure on the ontop graphene like layer will also be discussed. Moreover we will show how a rotational disorder between two graphene sheets leads to an effective electronic decoupling of these layers and then to band structures with linear free graphene like dispersions [4]. [1] F. Varchon et al. Phys. Rev. Lett. 99, 126805 (2007) [2] P. Mallet et al., Phys. Rev. B 76, 041403(R) (2007) [3] T.Ohta et al., Science 313, 951 (2006) [4] J.Hass et al., cond-mat/0706.2134, (submitted to PRL)   

Electronic and structural properties of graphene on 6H-SiC

We present a first-principles investigation of the electronic and structural properties of one and two graphene sheets on both the Si and C-terminations of 6H-SiC. Of particular interest are properties of the interlayer states associated with the graphene sheets, their spatial and energy distribution, how they are modified by the application of external electric fields, and differences with respect to the polarity of the fields. The calculated results will be compared to the electronic and structural properties observed in scanning tunneling microscopy experiments.   

Direct Determination of the Absorption of Graphene Mono- and Multi-layers in the Visible and Near-Infrared

Single-crystal mono- and multi-layer graphene samples were prepared by mechanical exfoliation on quartz substrates. The absorption spectra of samples of 1 -- 8 monolayer thickness were measured in the optical and near-infrared range. The absorption coefficient was found to be largely independent of photon energy and linear in the number of graphene layers. Such absorption measurements can thus be used to determine the thickness of mesoscopic graphite to monolayer accuracy, as already demonstrated in the context of Rayleigh scattering [Casiraghi et al. Nano Letters 2007]. By analysis of the optical transmission problem for a thin film at the air-quartz interface, we deduced an absorption of 2.3{\%} per layer. The magnitude of the monolayer absorption agrees with the value of $\pi \alpha $, where $\alpha $ is the fine-structure constant, and corresponds the result obtained from a tight-binding model of the graphene electronic structure [Gusynin et al. PRL 2006]. The predicted (and measured) optical absorption, we note, is equivalent to a constant optical conductance of$\frac{\pi e^2}{2h}=6.09\times 10^{-5}\Omega ^{-1}$.   

Experimental Measurement of Ultrafast Carrier Dynamics in Mono- and Multi-layer Graphene Samples

The ultrafast dynamics of charge carriers in mono- and multi-layer graphene was investigated by femtosecond transient reflectivity measurements. The experiments were performed using 100-fs optical pump pulses at a wavelength of 400 nm and probe pulses at a wavelength of 800 nm. We observed a transient response on the time scale of several picoseconds. For bulk graphite, a decay time of $\sim $ 3 ps was found; for thin graphene multilayer samples, a reduced decay time was observed, dropping ultimately to $\sim $ 1 ps for a single graphene layer. The reflectivity transients can be understood in terms of coupling of the photo-generated electronic excitations to optical phonons, and the subsequent loss of energy from this sub-system. The possible role of graphene interactions with the quartz substrate and the effect of the graphene electronic specific heat on the decay rate will be discussed.   

Exposure of Epitaxial Graphene on SiC(0001) to Atomic Hydrogen

Graphene films on SiC exhibit coherent transport properties that suggest the potential for novel carbon-based nanoelectronics applications. Recent studies suggest that the role of the interface between single layer graphene and silicon-terminated SiC can strongly influence the electronic properties of the graphene overlayer. In this study, we have exposed the graphitized SiC to atomic hydrogen in an effort to passivate dangling bonds at the interface. We have used scanning tunneling microscopy to investigate the interface surface structure following exposure to atomic hydrogen for a range of sample temperatures. Initial results indicate that regions of clean SiC were successfully passivated with atomic hydrogen below 400 \r{ }C, while the underlying interface of the graphitized regions appear to be unchanged for all temperatures studied. The threshold temperature for passivating clean SiC suggest that the passivated dangling bonds are primarily from Si atoms that are present within the SiC surface reconstruction. Although the hydrogen does not appear to penetrate below the graphene layer, initial results suggest that it does adsorb to the graphene.   

Characterization of Epitaxial Graphene Oxide

Graphite oxide is a layered semiconducting material that is produced from graphite or graphene by chemical oxidation. The material is characterized by various probes such as transport, Raman spectroscopy and optical absorption spectroscopy. Here we present the properties of graphene oxide, which is chemically converted from epitaxial graphene directly on silicon carbide chips. The absorption spectrum indicates a large band gap and the Raman spectrum shows a pronounced D line while the 2D line is absent.   

Ballistic Transport of Narrow-Channeled Epitaxial Graphene

Large-area epitaxial graphene film by thermal decomposition of SiC wafer has provided the missing pathway to a viable electronics technology $^{2}$. Low temperature magneto-transport properties of narrow-channeled epitaxial graphene films with dimension of 100 nm to 500 nm, formed on the carbon face of semi-insulating 4H-SiC substrates in an Epigress VP508 SiC hot-wall chemical vapor deposition reactor, are systematically studied. Typical quasi-ballistic transport features, such as negative magnetoresistance or 1D weak localization, aperiodic magnetoresistance fluctuations, periodic magentoresistance oscillations associated with channel geometry, bend resistance and quench of Hall effect associated with nanoscale junctions, are all observed. Magneto-resistance, being independent on parallel magnetic field up to 18 T, verifies the 2D nature of epitaxial graphene. 2. C. Berger et al., \textit{Science} 312, 1191 (2006).   

Electrical conductivity of graphene oxide sheets and networks of such sheets

Electrical transport through individual flat graphene oxide sheets and through networks of crumpled graphene oxide sheets has been studied at different temperatures and strengths of the electrical field. Conductivity of individual graphene oxide sheets on silica/silicon substrate were measured with a 4-electrode configuration at room and elevated temperatures (up to 520 K) in steady state conditions and at different states of reduction and oxidation. Crumpled graphene oxide sheets in a powdered form and graphene oxide sheets dispersed inside of a dielectric matrix at different packing densities were also electrically measured in a wide temperature range (between 520 and 20 K). Possible mechanisms of an electrical charge transport through these systems and the electronic properties of graphene oxide sheets will be discussed.   

The epitaxial graphene-graphene oxide junction, a key step towards epitaxial graphene electronics

Epitaxial graphene (EG), grown by thermal decomposition of SiC, was lithographically patterned to form pairs of EG electrodes separated by narrow gaps. Graphene oxide (GO) flakes were deposited by an AC dielectrophoresis method to bridge the gaps and produce all-graphene metal-semiconductor-metal structures. Electrical measurements on these devices indicate the presence of Schottky barriers, due to the band gap in GO, at the junctions. The barrier height is found to be between 0.5 eV and 0.7 eV. It is known that annealing graphite oxide reduces the degree of oxidation; annealing these structures at 180 C reduces the barrier height, implying that the band gap can be tuned by changing the degree of oxidation. A lower limit on the mobility of GO is obtained. Recent efforts towards transistor fabrication by chemically oxidizing selected regions of patterned EG will be presented.   

Plasmons and The Spectral Function of Graphene

We report on a theoretical study of the influence of electron-electron interactions on the one-particle Green's function of a doped graphene sheet based on the random-phase-approximation and on graphene's massless Dirac equation continuum model. We find that states near the Dirac point interact strongly with plasmons with a characteristic frequency $\omega^\star_{\rm pl}$ that scales with the sheet's Fermi energy and depends on its interaction coupling constant $\alpha_{\rm gr}$, partially explaining prominent features of recent ARPES data.