Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session J1: Ballistic-Diffusive Crossover in Graphene Electron Transport |
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Sponsoring Units: DCMP Chair: Sankar Das Sarma, University of Maryland Room: Spirit of Pittsburgh Ballroom A |
Tuesday, March 17, 2009 11:15AM - 11:51AM |
J1.00001: Electrical transport in suspended graphene Invited Speaker: Many quantum limit transport phenomena in graphene remain yet to be observed due to the omnipresence of carrier scattering. We report a sample preparation method that yields high quality graphene specimens and demonstrates that much of the scattering in traditional graphene-on-silica devices is not intrinsic but rather results from the interaction with the substrate underlying the graphene. We fabricate devices where electrically contacted and electrostatically gated graphene flakes are suspended over a substrate and use current-induced heating to remove the remaining impurities. The measured mobilities are found to exceed 200,000 cm$^2$/Vs in such devices, an order of magnitude improvement over the best values reported in the literature. The very high mobility of our specimens allows us to probe previously inaccessible transport regimes in graphene. At low temperatures transport is near-ballistic in a device of $\sim$2$\mu$m dimension. At large carrier density, we observe linear increase of resistivity with temperature, consistent with scattering off acoustic phonons. At near-room temperature we observe the mobility is $\sim$120,000 cm$^2$/Vs, higher than in any known semiconductor. [Preview Abstract] |
Tuesday, March 17, 2009 11:51AM - 12:27PM |
J1.00002: A self-consistent theory for graphene transport. Invited Speaker: Arguably, one of the most intriguing properties of graphene transport is the non-vanishing ``minimum conductivity'' at the Dirac point. The carrier density in these single monatomic sheets of carbon can be continuously tuned from electron-like carriers for large positive gate bias to hole-like carriers for negative bias. The physics close to zero carrier density (also called the intrinsic or Dirac region), is now understood to be dominated by the inhomogeneous situation where the local potential fluctuates around zero, breaking the landscape into puddles of electrons and holes. Here, we propose and discuss a particular hierarchy of approximations to understand graphene transport properties that includes a tight binding approximation for the low energy effective Hamiltonian, Random-Phase-Approximation to treat electron-electron interactions, the semi-classical Boltzmann transport theory to treat scattering of electrons by short and long-ranged disorder, and a self-consistent Fermi-Thomas approximation to treat impurity induced density inhomogeneity [1-2]. We find that this self-consistent theory for graphene transport is in remarkable agreement with recent experiments [3-5]. To better understand the range of validity of this theory we relax some of the assumptions and include the effects percolation [6]; calculate transport properties using an effective medium theory [7]; and examine the effects of phase-coherent quantum transport [8]. We believe that while most of the dc transport experiments on bulk graphene samples at zero magnetic field are in the parameter regime correctly captured by the semi-classical diffusive self-consistent transport theory, we demonstrate theoretically that by tuning external parameters, it is possible to access several other transport regimes.\\[4pt] References:\\[0pt] [1] Adam, Hwang, Galitski and Das Sarma, Proc. Nat. Acad. Sci. USA \textbf{104}, 18392 (2007); \\[0pt] [2] Hwang, Adam, and Das Sarma, PRL \textbf{98}, 186806 (2007); \\[0pt] [3] Tan et al. PRL\textbf{ 99}, 246803 (2007); \\[0pt] [4] Chen et al. Nature Physics \textbf{4}, 377 (2008); \\[0pt] [5] Jang et al. PRL \textbf{101},146805 (2008); \\[0pt] [6] Adam et al. PRL \textbf{101}, 046404 (2008); \\[0pt] [7] Rossi, Adam, and Das Sarma, arXiv:0809.1425v1 (2008); \\[0pt] [8] Adam, Brouwer, and Das Sarma, arXiv:0811.0609v1 (2008). [Preview Abstract] |
Tuesday, March 17, 2009 12:27PM - 1:03PM |
J1.00003: Theory of an inhomogeneous electron structure of graphene at its neutrality point Invited Speaker: Graphene is a surprisingly good conductor. Despite its direct exposure to various sources of disorder (charged impurities, non-uniformity of the substrate, etc.), graphene remains conductive even when the nominal concentration of both electron and hole carriers drops to zero - the neutrality point (NP). Theory of the minimal conductivity of graphene is an outstanding challenge because of the non-perturbative nature of disorder at the NP and the still unsettled question of which type of disorder is really dominant. Here, we report on our progress towards analytical solution of the model of graphene subject to the disorder in the form of in-plane charged impurities. Our approach is asymptotically exact for graphene in high dielectric-constant environment where Coulomb interactions of electrons with impurities and electrons with each other become weak. We show that screening of the impurity potential is nonlinear, producing a fractal structure of electron and hole puddles. Statistical properties of this density distribution as well as the charge compressibility of the system are calculated in the leading-log approximation. The minimal conductivity is shown to depend logarithmically on the dielectric constant. We compare our results with other theoretical works and current experiments. Our findings suggest that in real samples charged impurities are either not exactly coplanar with graphene, or are correlated, or are not the only source of disorder. This work is supported by the NSF. [Preview Abstract] |
Tuesday, March 17, 2009 1:03PM - 1:39PM |
J1.00004: Electronic Transport in Disordered Graphene Sheets and Nanoribbons Invited Speaker: In this talk I will present recent results of our numerical simulations of electronic transport in disordered graphene. Issues related to the scaling of the conductivity and the shot-noise Fano factor of large graphene sheets at zero and finite doping will be discussed. Our calculations are based on an efficient implementation of the recursive Green function method. I will also show how edge and bulk disorder may affect the mesoscopic conductance of graphene nanoribbons under a variety of realistic situations. We find that even for weak edge roughness, conductance steps are suppressed and a transport gap develops near the neutrality point due to strong localization. The gap inferred from our simulations is similar in magnitude to the energy gaps induced by other mechanisms, such as Coulomb blockade, many-body correlations, and lattice distortions. The effects of dephasing will also be discussed. [Preview Abstract] |
Tuesday, March 17, 2009 1:39PM - 2:15PM |
J1.00005: Electron fractionalization in two-dimensional graphenelike structures Invited Speaker: Electron fractionalization is intimately related to topology. In one-dimensional systems, such as polyacetelene, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall fluids, where time-reversal symmetry is broken by a large external magnetic field. Recently, there has been a tremendous effort in the search for examples of fractionalization in two-dimensional systems with time-reversal symmetry. Here we show that fractionally charged topological excitations exist in tight-biding systems where time-reversal symmetry is respected. These systems are described, in the continuum approximation, by the Dirac equation in two space dimensions. The topological zero-modes are mathematically similar to fractional vortices in p-wave superconductors. They correspond to a twist in the phase in the mass of the Dirac fermions, akin to cosmic strings in particle physics. The quasiparticle excitations can carry irrational charge and irrational exchange statistics. These excitations can be deconfined at zero temperature, but when they are, the charge re-rationalizes to the value 1/2. REFS.:Chang-Yu Hou, Claudio Chamon, Christopher Mudry, Phys. Rev. Lett. 98, 186809 (2007); Claudio Chamon, Chang-Yu Hou, Roman Jackiw, Christopher Mudry, So-Young Pi, Andreas P. Schnyder, Phys. Rev. Lett, 100, 110405 (2008); Claudio Chamon, Chang-Yu Hou, Roman Jackiw, Christopher Mudry, So-Young Pi, Gordon Semenoff, Phys. Rev. B 77, 235431 (2008) [Preview Abstract] |
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