Session U29: Focus Session: Carbon Nanotubes and Related Materials XII: Graphene Transport

Scanning Tunneling Microscopy and Spectroscopy of Rotated Phases on C-Face Epitaxial Graphene

Diffraction data have shown that multilayer graphene grown on the (000-1) polar face of SiC forms with a high density of rotational stacking faults [1]. We present STM evidence of these rotated phases along with rationale for the particular angles observed. Topographic images show flat, micron scale domains with surface modulation periods corresponding to moir\'{e} patterns generated by rotational stacking faults near the surface. The modulation periods are in agreement with surface x-ray diffraction and low energy electron diffraction data. STS data will be presented and the effects of the observed rotated domains on the electronic structure of C-face multilayer graphene films will be discussed. [1] J. Hass, F.Varchon, J. E. Mill\'{a}n-Otoya, M. Sprinkle, W.A. de Heer, C. Berger, P.N. First, L. Magaud, E.H. Conrad (\textit{to be published}), http://arxiv.org/abs/0706.2134   

Gate-tunable Graphene Flakes Probed by Scanning Tunneling Spectroscopy at Atomic Scale

The nanometer scale electronic properties of mechanically cleaved graphene flake devices having tunable back-gates are resolved using scanning tunneling microscopy and spectroscopy. We observe an energy gap feature in the graphene tunneling spectrum that is unexpectedly pinned to the Fermi level ($E_{F}$ ) for different gate-induced electron densities. The Dirac point, on the other hand, is shifted by the back-gate by an amount prescribed by the graphene linear band structure. This energy gap is found to arise from a suppression of elastic electronic tunneling to graphene states near $E_{F}$ and a significant enhancement of tunneling (seen as a more than factor of 10 increase in the conductance) at higher energies due to a phonon-mediated inelastic channel. This work reveals important new tunneling processes in gate-tunable graphitic layers.   

Local Variations of Graphene Electronic Structure Probed by STM.

Transport measurements on devices made from exfoliated graphene sheets have shown that graphene has a high mobility and long mean free path. However, the role that disorder plays in these measurements remains unknown, as does the source of the disorder. In order to better understand the causes of disorder on the local scale, we have performed scanning tunneling spectroscopy measurements on gated graphene flakes at 4.2K in an UHV environment. Our spectroscopy measurements show local variations in graphene electronic properties at different length scales. These variations are analyzed in terms of graphene 2D electronic structure.   

Probing Chiral Quasiparticles using Local-Density-of-States Measurements in Graphene

We show that STM local-density-of-states (LDOS) measurements in weakly disordered graphene sheets probe the pseudospin chirality of states near Dirac points. The Fourier transformed LDOS $N({q},\omega)$ has both intravalley contributions centered near reciprocal lattice vectors and intervalley contributions displaced by the wavevector $Q$ which connects graphene's two distinct Dirac points. We explain the qualitative differences between these two features in $N(q,\omega)$ on the basis of analytic calculations starting from graphene's continuum model Dirac equation, and comment on the sensitivity of both $N(q,\omega)$ features to the mix of atomic length scale and smooth disorder sources. For on-site disorder, the LDOS $N(q,\omega)$ measured on A sites due to an A site potential has the periodicity of the Brillouin zone, whereas the pattern produced by a B site potential is periodic with a primitive cell three times larger.   

Mesoscopic valley-Hall effect in graphene

An intriguing property of graphene is the existence of a degree of freedom associated with the two inequivalent valleys in the Brillouin zone. A controlled manipulation of this degree of freedom may potentially be used in novel electronic devices. We study the mesoscopic valley-Hall effect that may provide a route toward the desired control. The effect appears when the inversion symmetry of the crystal is broken, and it can generate a transverse valley current in response to an applied electric field. We look at a few sample setups and discuss the dependence on the geometry and the appearance of valley-Hall edge states. We also compare and contrast our results with those obtained from linear response theory in bulk samples.   

Electronic screening in graphite

Nonlocal screening in highly-oriented pyrolitic graphite was investigated with inelastic x-ray scattering. Measurements were performed over a sufficiently broad range of momentum and energy to permit complete inversion of the loss function, $-Im [1/\epsilon(k,\omega)]$, allowing real-time, microscopic imaging of the induced electron density around a charged impurity. In addition, we found evidence for a sign change in the zero-frequency dielectric function, $\epsilon(k,0)$, over a sizeable range of momentum. This ``antiscreening" should cause the Coulomb interaction to be attractive, perhaps assisting superconductivity in this system.   

Band Structure of K(2x2) on graphene

The electronic structure of K(2x2) on graphene, the same stochiometry as bulk KC$_{8}$, was studied using angle-resolved photoemission spectroscopy (ARPES). In addition to bands derived from the graphene $\pi $ states an intercalant induced ``interlayer band'' is observed centered at $\Gamma $. Of these two bands, the dominant mass renormalization occurs in the $\pi $-derived bands, as determined by characterization of the ``kinks'' in the dispersion measured by ARPES. This suggests that the superconductivity in bulk KC$_{8}$ has a more important role than the interlayer band.   

Coulomb scattering and transport in graphene

The exact transport cross-section off a Coulomb impurity in graphene [1] is proportional to the carrier wavelength. Unexpectedly, the relativistic Coulomb scattering also exhibits a pronounced attraction-repulsion asymmetry [1,2]: Massless carriers are scattered more strongly when they are attracted to a charged impurity than when they are repelled from it. This finding, confirmed recently [3], can be used to separately determine the surface density of donors and acceptors in a graphene monolayer [2]. I will outline quantitative and qualitative differences between the exact result [1] and the commonly used Born approximation for charged impurity scattering. [1] D. S. Novikov, arXiv:0706.1391, Phys. Rev. B (in press); [2] D. S. Novikov, Appl. Phys. Lett. 91, 102102 (2007); [3] J. H. Chen, C. Jang, M. S. Fuhrer, E. D. Williams, M. Ishigami, arXiv:0708.2408v2.   

Resonance Raman investigation of monolayer and bilayer graphene

The Raman spectra of graphene samples exhibit a band around 2700 cm$^{-1}$, the so called G$'$ band, that is ascribed to a double resonance Raman process involving electrons and phonons in the vicinity of the Dirac point. A dispersive behavior in the position and shape of this band is observed when we change the laser energy used in the Raman experiment, showing that it can be used to probe experimentally the dispersion of electrons and phonons near the Dirac point of graphene. We will present a resonance Raman investigation of monolayer and bilayer graphene using many different laser lines in the visible and near IR range. By the analysis of the dispersive behavior of the G$'$ band we can obtain information about the electronic structure of monolayer and bilayer graphene, such as the intralayer and interlayer tight-binding parameters. Our results reveals a significant asymmetry between the electronic dispersion in the valence and conduction bands of bilayer graphene. We are also able to obtain experimental values for the velocity of the TO and LA phonons near the Dirac point of graphene.   

Effect of contact induced states on minimum conductivity in graphene

Recent experiments show that the conductivity of graphene tends to a minimum value in the range of $\sim $2-12${e^2} \mathord{\left/ {\vphantom {{e^2} h}} \right. \kern-\nulldelimiterspace} h$ as the Fermi energy $E_{f}$ approaches the charge neutral Dirac points ($E=0)$. We point out that contact induced states can help explain the structure dependence of the minimum conductivity observed experimentally even if the samples were purely ballistic. Contact induced states are similar to the well-known metal induced gap states (MIGS) in metal-semiconductor Schottky junctions, which typically penetrate only a few atomic lengths into the semiconductor, while the depth of penetration decreases with increasing band gap. However, in graphene we find that these states penetrate a much longer distance of the order of the width of the contacts. As a result, ballistic graphene samples with a length less than their width can exhibit a resistance proportional to length that is not `Ohmic' in origin, but arises from a reduced role of contact-induced states. While actual samples are probably not ballistic and involve scattering processes, our results show that these contact induced effects need to be taken into account in interpreting experiments and minimum conductivity depends strongly on the structure and configuration (two- vs. four-terminal).   

Theory of superconductivity by the edge states in graphene

Superconductivity in graphite intercalation compound and carbon nanotubes has been attracting much attention due to its high superconducting transition temperature above 10 K. However, the density of states (DOS) near the Fermi energy of graphene is not sufficient to explain the observed high transition temperature. Thus, the mechanism of the superconductivity is an important issue. The STS measurements (Kobayashi et al., PRB73,125415, Niimi et al., PRB73,085421) show an anomalous DOS near the Fermi level of graphene which is relevant to localized edge states. The edge states significantly enhance the local DOS near the zigzag edge. Thus, it is valuable to examine the effect of the edge states on the superconductivity. Using the Eliashberg equation, we obtain an appreciable transition temperature for the edge states. We found that the effects of the Coulomb interaction and Fermi energy position are sensitive to the formation of superconducting gap. We will discuss the condition for observing the edge state superconductivity. (Sasaki et al., J. Phys. Soc. Jpn. 76, 033702 (2007))   

Ground-state carrier density in graphene

We calculate the carrier density spatial distribution for the ground state of a single layer graphene sheet in presence of randomly distributed charged impurities. In our calculation we include the effects due to the exchange and correlation energy. We carefully study how the distance $d$ of the charge impurities from the graphene layer and an external bias affect the spatial distribution of the carrier density. At zero bias we find that the carrier density is characterized by the presence of electron and hole puddles with equal probability and that, for $d\approx 1$, the typical size of the puddles is of the order of $30\;{\rm nm}$ in agreement with recent experiments \footnote{J. Martin {\em et al.}, Nature Physics (2007)}. With the same approach we study the situation when a tunable barrier potential is applied locally and a bipolar junction within the graphene sheet is formed. This work is supported by NRI-NSF.