Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session H1: Electronic Structure of Disordered Graphene |
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Sponsoring Units: DCMP Chair: Allan MacDonald, University of Texas at Austin Room: Spirit of Pittsburgh Ballroom A |
Tuesday, March 17, 2009 8:00AM - 8:36AM |
H1.00001: Scanning Single Electron Transistor Microscopy on Graphene Invited Speaker: Jens Martin We use a scanning single electron transistor to map the local density of states of graphene and the carrier density landscape in the vicinity of the neutrality point. At zero magnetic field our results confirm the existence of electron-hole puddles. These puddles could explain graphene's anomalous non-zero minimal conductivity at zero average carrier density. Moreover, we find that, unlike non-relativistic particles the density of states can be quantitatively accounted for by considering non-interacting electrons and holes. At high magnetic field we investigate the appearance of localized states. Particle localization is an essential ingredient in quantum Hall physics. In conventional high mobility two-dimensional electron systems Coulomb interactions were shown to compete with disorder and to play a central role in particle localization. Surprisingly, despite the stronger disorder in graphene compared to the standard two-dimensional systems, our findings indicate that localization in graphene is also dominated by Coulomb interactions and not single particle physics. [Preview Abstract] |
Tuesday, March 17, 2009 8:36AM - 9:12AM |
H1.00002: Magnetic Oscillations and Landau Quantization in Decoupled Epitaxial Graphene Multilayers* Invited Speaker: Joseph A. Stroscio A fundamental challenge to the development of a new electronics based on single atomic sheets of carbon, known as graphene, is to realize a large-area production platform that can produce a carbon system with the same intrinsic properties as a single sheet of graphene. Multi-layer epitaxial graphene (MEG) grown on SiC substrates has been proposed as a possible platform to this end [1]. The central question is, Can MEG \textit{behave} as single layer graphene with the same intrinsic electrical characteristics? In this talk we show that MEG graphene on SiC exhibits single layer graphene properties through new tunneling magnetic measurements. The circular motion of electrons in a magnetic field has historically been a powerful probe of the Fermi surface properties of materials. Oscillations in many measureable properties, such as magnetization, thermal conductivity, and resistance, all reflect the Landau quantization of the electron energy levels. In this talk we show the ability to observe tunneling magneto-conductance oscillations (TMCOs) in the tunneling differential conductance as a function of both magnetic field and electron energy. The TMCO arise from \textit{intense} Dirac quantization of the 2-dimensional Dirac electron and hole quasiparticles in MEG grown on SiC substrates. Spatial profiles of the Landau quantization demonstrate the high quality of MEG on SiC with carrier concentrations that vary less than 10{\%} over hundreds of nm. The single layer quantization observed in these multi-layer samples is attributed to observed rotational stacking domains that effectively decouple the carbon layers in MEG on SiC, thereby yielding single layer graphene properties in a large area carbon production method. *In collaboration with Lee Miller, Kevin Kubista, Gregory M. Rutter, Ming Ruan, Mike Sprinkle, Claire Berger, Walt A. de Heer, and Phillip N. First, Georgia Institute of Technology [1] W.A. de Heer et. al., Solid State Comm. \textbf{143}, 92 (2007). [Preview Abstract] |
Tuesday, March 17, 2009 9:12AM - 9:48AM |
H1.00003: Effect of potential barriers on transport in graphene Invited Speaker: B. Huard The energy of graphene charge carriers grows linearly with their momentum. This zero-mass behavior, associated with an absence of a forbidden region between electrons and holes, deeply modifies transport properties of electrons across potential steps and barriers. We perform transport measurements in graphene monolayers where the potential profile is tuned by a set of local gates [1,2]. By varying the height and width of potential barriers and the energy of charge carriers, we can test the predictions on the transmissions of the conduction channels across a potential step in graphene. Besides, we observe the effect of disorder and of screening of an external field in graphene. These experiments have a direct consequence in any transport measurement in graphene. We indeed showed that such potential steps naturally develop at the interface between graphene and a metallic electrode [3]. We discuss the effects of these steps in various geometries [4]. In collaboration with N. Stander, J.A. Sulpizio, Physics Department, Stanford University, Stanford, CA 94025, USA; and J. Cayssol, D. Goldhaber-Gordon, CPMOH, UMR5798, Universit\'e de Bordeaux, 33405 Talence, France. \\[4pt] [1] B. Huard, J.A. Sulpizio, N. Stander, K. Todd, B. Yang, D. Goldhaber-Gordon, Phys. Rev. Lett. \textbf{98}, 236803 (2007)\\[0pt] [2] N. Stander, B. Huard, D. Goldhaber-Gordon, condmat/0806.2319\\[0pt] [3] B. Huard, N. Stander, J.A. Sulpizio, D. Goldhaber-Gordon, \textbf{Phys. Rev. B}, \textbf{78}, 121402 (R) (2008)\\[0pt] [4] J. Cayssol, B. Huard, D. Goldhaber-Gordon, (to appear soon) [Preview Abstract] |
Tuesday, March 17, 2009 9:48AM - 10:24AM |
H1.00004: Ground-state Properties of Inhomogeneous Graphene Sheets Invited Speaker: Marco Polini When inter-valley scattering is weak and gauge fields due to {\it e.g.} ripples are neglected, doped and gated graphene sheets can be described using an envelope-function Hamiltonian with a new sublattice pseudospin degree-of freedom, an ultrarelativistic massless-Dirac free-fermion term, a pseudospin {\it scalar} disorder potential, and a non-relativistic instantaneous Coulombic interaction term. There is considerable evidence from experiment that this simplified description of a honeycomb lattice of Carbon atoms is usually a valid starting point for theories of those observables that depend solely on the electronic properties of $\pi$-electrons near the graphene Dirac point [1]. Although the use of this model simplifies the physics considerably it still leaves us with a many-body problem without translational invariance, which we do not know how to solve. In this talk we present a Kohn-Sham-Dirac density-functional-theory (DFT) scheme for graphene sheets that treats slowly-varying inhomogeneous scalar external potentials and electron-electron interactions on an equal footing [2]. The theory is able to account for the unusual property that the exchange-correlation contribution to chemical potential increases with carrier density in graphene [3,4]. Consequences of this property, and advantages and disadvantages of using the DFT approach to describe it, are discussed. The approach is illustrated by solving the Kohn-Sham-Dirac equations self-consistently for a model random potential describing charged point-like impurities located close to the graphene plane. The influence of electron-electron interactions on these non-linear screening calculations is discussed at length, in the light of recent experiments [5,6] reporting evidence for the presence of electron-hole puddles in nearly-neutral graphene sheets. \\[4pt] [1] A.K. Geim and K.S. Novoselov, Nature Mater. {\bf 6}, 183 (2007); A.K. Geim and A.H. MacDonald, Phys. Today {\bf 60}, 35 (2007); A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, arXiv:0709.1163v2 (2007).\\[0pt] [2] M. Polini, A. Tomadin, R. Asgari, and A.H. MacDonald, Phys. Rev. B {\bf 78}, 115426 (2008).\\[0pt] [3] Y. Barlas, T. Pereg-Barnea, M. Polini, R. Asgari, and A.H. MacDonald, Phys. Rev. Lett. {\bf 98}, 236601 (2007); M. Polini, R. Asgari, Y. Barlas, T. Pereg-Barnea, and A.H. MacDonald, Solid State Commun. {\bf 143}, 58 (2007). \\[0pt] [4] E.H. Hwang, B.Y.-K. Hu, and S. Das Sarma, Phys. Rev. Lett. {\bf 99}, 226801 (2007).\\[0pt] [5] J. Martin, N. Akerman, G. Ulbricht, T. Lohmann, J.H. Smet, K. von Klitzing, and A. Yacoby, Nature Phys. {\bf 4}, 144 (2008).\\[0pt] [6] V.W. Brar, Y. Zhang, C. Girit, F. Wang, A. Zettl, and M. Crommie, Bull. Am. Phys. Soc. {\bf 53} (2), 443 (2008). [Preview Abstract] |
Tuesday, March 17, 2009 10:24AM - 11:00AM |
H1.00005: Ground-state of Two-dimensional Graphene in the Presence of Random Charged Impurities Invited Speaker: Enrico Rossi The low energy electronic excitations of graphene are described by a massless Dirac fermion model. In clean isolated graphene the Fermi energy lies exactly at the Dirac point where the linear chiral electron and hole bands cross each other. Close to the Dirac point the average carrier density vanishes and the density fluctuations are expected to dominate the physics of graphene. In current experiment the fluctuations are mostly due to quenched disorder. In this talk I present the Thomas-Fermi-Dirac (TFD) theory [1] to calculate the carrier density of graphene in presence of disorder. The TFD theory includes the effects of non-linear screening, exchange and correlation. The approach is independent of the disorder source and very efficient allowing the calculation of disorder-averaged quantities that can be directly compared with experiments. Recent transport results strongly suggest that in current graphene samples charge impurities are the main source of disorder. I then present the results of the TFD theory for this case. I show that close to the Dirac point the carrier density breaks-up in electron-hole puddles and is characterized by two types of inhomogeneities: wide regions of low density and sparse narrow regions of high density and a typical correlation length of ~10 nm. I present detailed results that show how the disordered averaged quantities characterizing the carrier density profile depend on the experimental parameters. I show that at finite voltages the density probability distribution has a bimodal character providing direct evidence for the existence of puddles over a finite range of gate voltages. In graphene the exchange-correlation term increases with density contrary to parabolic-band electron liquids and because of this it tends to suppress density inhomogeneities. I show that this effect becomes very important close to the Dirac point, especially at low impurity densities. [Preview Abstract] |
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