Session W29: Focus Session: Graphene V

Scanning tunneling microscopy of graphene field effect transistors

We have investigated the electronic properties of graphene field effect transistors at atomic scale using scanning tunneling microscopy. We find that photoresist, required by conventional electron beam lithography, binds to graphene and leaves residues with thickness of approximately 1 nm. We will present the procedure necessary to eliminate this residue and report our results of scanning tunneling microscopy and spectroscopy performed on graphene.   

Scanning Probe Microscopy studies of 2D and quasi-2D graphene crystal structures.

In these studies we utilize a variety of Scanning Probe techniques to observe evolution of material properties as a result of transitions from 3D to 2D crystal structures. Graphite is an ideal candidate for these studies as its stand alone 2D crystal (graphene) and quasi-2D films are conductive, stable, and chemically inert under ambient conditions. These crystals can be easily deposited on an oxidized silicon wafer, and the number of atomic layers can be precisely counted. Specific examples will be given to relate local and mesoscopic properties of these crystals as a function of the number of graphene monolayers forming the crystal. The role of the interaction between the substrate and graphene films will be considered. The finite thickness of crystals allows us to examine defects formed not only on the surface of the film but also below the topmost layer. Attenuation of corrugation in Scanning Tunneling images by overlayers of graphene is described. Compatibility of graphene films with atomic-scale electronics will be discussed.   

Imaging Electronic Interference Effects in Ultrathin Epitaxial Graphite

We have used scanning tunneling microscopy and spectroscopy at 4K to investigate local fluctuations in the electronic structure of ultrathin epitaxial graphite grown on SiC. Spectroscopic maps of the density of states for two- and three-layer films reveal spatial modulations that fluctuate with energy. These maps show short range root three by root three ordering reminiscent of Bloch wave interference observed in finite carbon nanotube segments [1]. Additional long range fluctuations have a characteristic length scale that may be related to the underlying structure of the SiC interface.\newline [1] S. G. Lemay et al., Nature 412, 617 (2001).   

Instabilities of correlated electrons on the honeycomb lattice

Motivated by the possible relevance to graphene we analyze instabilities of electrons on a honeycomb lattice, interacting by Hubbard and longer-ranged interactions. Using a functional renormalization group scheme which takes into account the wavevector-dependence of the interactions throughout the Brillouin zone, we detect the leading ordering tendencies at low temperatures. Near half band filling and for dominant onsite repulsion, a critical minimal interaction strength is required for an instability toward antiferromagnetic order, in support of a previous large-$N$ work of Herbut [Phys. Rev. Lett. 97, 146401 (2006)] which focused on the Dirac points. We also present results for longer-ranged interactions and away from half band filling.   

Fermi Liquid Theory of a Fermi Ring

We study the effect of electron-electron interactions in the electronic properties of a biased graphene bilayer. This system is a semiconductor with conduction and valence bands characterized by an unusual ``mexican-hat'' dispersion. We focus on the metallic regime where the chemical potential lies in the ``mexican-hat'' in the conduction band, leading to a topologically non-trivial Fermi surface in the shape of a ring. We show that due to the unusual topology of the Fermi surface electron-electron interactions are greatly enhanced. We discuss the possibility of an instability towards a ferromagnetic phase due to this enhancement. We compute the electronic polarization function in the random phase approximation and show that, while at low energies the system behaves as a Fermi liquid (albeit with peculiar Friedel oscillations), at high frequencies it shows a highly anomalous response when compare to ordinary metals.   

Electronic Excitations in Bilayer Graphene

The $\pi$-electronic excitations are studied for the AA- and AB-stacked bilayer graphene within the linear self-consistent-field approach. They are strongly affected by the stacking sequence, the interlayer atomic interactions, the interlayer Coulomb interactions, and the magnitude of the transferred momentum. However, they hardly depend on the direction of the transferred momentum and the temperature. There are three low-frequency plasmon modes in the AA-stacked system but not the AB-stacked system. The AA- and AB-stacked plasmons exhibit the similar $\pi$ plasmons. The first low-frequency plasmon behaves as a acoustic plasmon, and the others belong to optical plasmons. The bilayer graphene quite differ from the monolayer graphene and the AB-stacked bulk graphite, such as the low-frequency plasmons and the small-momentum $\pi$ plasmons.   

Correlation Energy of Graphene

We discuss the ground state energy of an electron gas on a honeycomb lattice (graphene), where the quasiparticle spectrum has Dirac structure, i.e. linear energy-momentum relation. The correlation energy, due to electron-electron interactions, is calculated in the two-loop approximation, which is the first correction to the Hartree-Fock energy. The possibility of inhomogeneous states is discussed.   

Electromechanical instabilities of suspended carbon nanotubes - multi mode excitations

We have theoretically investigated electromechanical instabilities of suspended carbon nanotubes when using an STM-tip to probe the suspended part of the tube. A coupling between the vibrational modes of the nanotube and tunneling electrons may lead to a pumping of energy into the mechanical subsystem, resulting in large amplitude vibrations of the CNT. This effect is related to the ''shuttle instability'' and changes the transport properties of the system. In the present study, instability of different bending modes have been investigated. We show that, with respect to the instability, different modes can be treated independently in the limit of weak electromechanical coupling. Also, we show that excitations of different modes are controlled by their vibration frequency and tunneling rates. Tunneling rates of the order of the frequency are found optimal for an instability to occur. Hence, a selective excitation of a single mode is possible. We analyze the limit cycle behavior in this case. Another scenario is simultaneous excitation of several modes, leading to a complex behavior in stationary regime.   

Electronic properties of graphene multilayers

The electronic structure, screening properties, and charge distribution in stacks of graphene layers is studied. We analyze: i) The stability of Dirac points as function of the ordering of the stack and the number of layers, ii) The existence of surface bands at the top and bottom layers for some stack orderings, iii) The appearance of gaps induced by inhomogeneous charge distributions, and iv) The charge induced by external electric fields. We find that electronic bands with linear, Dirac like, dispersion exist in stacks with the Bernal stacking and an odd number of layers, and for rhombohedral stacking. In tha last case, a dispersionless surface band is also formed. In the presence of interlayer hopping, the dielectric response of a stack with the Bernal ordering favors the formation of a charge density wave with periodicity equal to twice the interlayer spacing. In doped stacks, the charge will accumulate at the surfaces, and present an even-odd modulation.   

Local density of states of graphene with diagonal and off-diagonal disorder

We study the effect of diagonal and off-diagonal disorder in the local density of states of a graphene sheet. The exact Green's functions for graphene in the presence of a local potential and in the presence of a modification of the local hopping parameter are given. A discussion of the resonances induced by disorder in the local density of states is provided. We obtain the exact Green's function for a vacancy as a limiting procedure applied to the Green's functions with either diagonal or off-diagonal disorder. The exact Green's function in the presence of both local and off-diagonal disorder is given.   

Moire patterns in graphene bilayers: electronic structure

Moire patterns, resulting from a small angle rotation of the top layer have been observed in graphite [1]. We consider a similar situation in a graphene bilayer. We determine the angles for which the resulting structure is periodic and study its symmetries. We develop a general formalism for the calculation of the electronic properties at low energies (close to the Dirac points of the uncoupled bilayers) and for small rotation angles, based on a continuum approximation for the uncoupled layers. We discuss the resulting electronic structure and possible consequences for transport properties. [1] Z. Rong and P Kuiper, Phys. Rev B. 48, 17427, (1993)   

Experimental signatures of topological defects in graphene

We study the electronic structure of graphene with topological defects, in which some of the hexagonal plaquettes of the honeycomb lattice are replaced by pentagons or heptagons. Our tight-binding calculations show that the local electronic density of states becomes particle-hole asymmetric in the vicinity of such defects. This provides a means of experimentally distinguishing so-called ``plastic'' curvature from elastic deformation. We evaluate various analytic approaches to these defects and discuss their effects on scattering and transport.   

Direct Observation of Interface States between Single Layer Graphene and SiC*

Graphite films grown on carbon-terminated SiC exhibit coherent transport properties that suggest potential for novel nanoelectronics applications [1]. However, for films grown on silicon-terminated SiC the coherence is greatly reduced, suggesting that the interface electronic structure influences the transport [1]. We have investigated the interface structure and electronic states that form in single layer graphene grown on silicon terminated SiC, using scanning tunneling microscopy and spectroscopy measurements at 4 K. Imaging a single graphene layer reveals features of both the graphite structure and the~SiC~interface. Which structure dominates is observed to be a function of the imaging bias. Sharp peaks in the density of states were found over SiC interface features, which correspond to the onset voltages observed in topography measurements. A comparison of experimental and theoretical findings will be discussed including relevance to transport measurements. *This work is supported in part by the Office of Naval Research and NSF. [1] C. Berger et al., Science 312, 1191 (2006); J. Phys. Chem. B 108, 19912 (2004).   

Graphene-based Silica Composite Thin Films

Very thin, smooth, transparent, and electrically conductive silica films with embedded graphene-based sheets were fabricated via the sol-gel route. Individual `graphene oxide' sheets exfoliated in water were incorporated into silica sols. Composite films were formed by spin coating and rendered conductive by treatment with hydrazine, followed by curing at 400\r{ }C under nitrogen flow. The films were studied by SEM, AFM, TEM, X-ray reflectivity, XPS, UV-Vis spectroscopy, and the electrical conductivity was measured. Transparent and conductive thin silica composite films approximately 30 nm thick were fabricated on glass and silicon substrates, opening up new possibilities for making glassy materials with moderate conductivity and high optical transparency. Support from NASA ({\#}NCC-1-02037) through the University Research, Engineering and Technology Institute on Bio-inspired Materials and the NSF ({\#}CMS-0510212) is appreciated.   

Preparation and transport studies of single layer graphite oxide and graphene films

Single sheet graphite oxide films are synthesized by intercalation and exfoliation routes of graphite. Because of its layered structure, graphite can readily be intercalated using alkali metals. Such method opens up the possibility of synthesizing ultra-thin layers of graphite by reducing the graphite oxide films. The as-synthesized graphite oxide films are deposited on SiO$_{2}$/Si substrates. Ebeam lithography is used to fabricate graphite oxide Field Effect Transistors (FETs). The transport properties of these devices are studied before and after the reduction of graphite oxide films.