Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session H28: Focus Session: Graphene I |
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Sponsoring Units: DMP Chair: Jisoon Ihm, Korean Institute of Advanced Studies Room: Colorado Convention Center 302 |
Tuesday, March 6, 2007 8:00AM - 8:36AM |
H28.00001: Theory of quantum transport in graphene and nanotubes Invited Speaker: Tsuneya Ando In graphene, electronic states are described by Weyl's equation for a massless neutrino [1,2]. The system has a topological singularity at the origin of the wave vector (${\bf k}\!=\!0$), giving rise to nontrivial Berry's phase when ${\bf k}$ is rotated around the origin [3]. The singularity causes various zero-mode anomalies such as discrete jumps in the diagonal [4], off-diagonal Hall [5], and dynamical conductivity [6] at the Fermi energy corresponding to ${\bf k}\!=\!0$. In the presence of a magnetic field, a Landau level with zero energy exists independent of the strength of the field [7], giving rise to a singular diamagnetism of graphene and the large magnetic anisotropy of the carbon nanotube [8] used extensively for the observation of the Aharonov-Bohm effect [9,10]. In the absence of a magnetic field, the system belongs to a symplectic universality class even in the presence of scatterers unless their potential range is smaller than the lattice constant. Being combined with the presence of an odd number of current carrying channels, this leads to the absence of backward scattering [11] and the presence of a perfectly conducting channel [12], making a metallic carbon nanotube a perfect conductor with ideal conductance exhibiting intriguing frequency dependence [13,14]. In the presence of scatterers with range smaller than the lattice constant, the system crossovers from the symplectic to an orthogonal class [15,16], and to a unitary class if higher order \boldmath{$k \cdot p$} terms causing trigonal warping are considered [17] or in magnetic fields [18]. These symmetry crossovers manifest themselves as strong difference in localization effects due to disorder in both graphene [18,19] and a carbon nanotube [20]. \par References: [1] J. C. Slonczewski and P. R. Weiss, Phys. Rev. {\bf 109}, 272 (1958). [2] T. Ando, J. Phys. Soc. Jpn. {\bf 74}, 777 (2005). [3] T. Ando, T. Nakanishi, and R. Saito, J. Phys. Soc. Jpn. {\bf 67}, 2857 (1998). [4] N. H. Shon and T. Ando, J. Phys. Soc. Jpn. {\bf 67}, 2421 (1998). [5] Y. Zheng and T. Ando, Phys. Rev. B {\bf 65}, 245420 (2002). [6] T. Ando, Y. Zheng, and H. Suzuura, J. Phys. Soc. Jpn. {\bf 71}, 1318 (2002). [7] J. W. McClure, Phys. Rev. {\bf 104}, 666 (1956). [8] H. Ajiki and T. Ando, J. Phys. Soc. Jpn. {\bf 62}, 2470 (1993); {\bf 63}, 4267 (1994) (Erratum). [9] H. Ajiki and T. Ando, J. Phys. Soc. Jpn. {\bf 62}, 1255 (1993). [10] S. Zaric, G. N. Ostojic, J. Kono, J. Shaver, V. C. Moore, M. S. Strano, R. H. Hauge, R. E. Smalley, and X. Wei, Science {\bf 304}, 1129 (2004). [11] T. Ando and T. Nakanishi, J. Phys. Soc. Jpn. {\bf 67}, 1704 (1998). [12] T. Ando and H. Suzuura, J. Phys. Soc. Jpn. {\bf 71}, 2753 (2002). [13] T. Ando, J. Phys. Soc. Jpn. {\bf 71}, 2505 (2002). [14] Y. Asada and T. Ando, J. Phys. Soc. Jpn. {\bf 75}, 094711 (2006). [15] H. Suzuura and T. Ando, Phys. Rev. Lett. {\bf 89}, 266603 (2002). [16] T. Ando and K. Akimoto, J. Phys. Soc. Jpn. {\bf 73}, 1895 (2004). [17] K. Akimoto and T. Ando, J. Phys. Soc. Jpn. {\bf 73}, 2194 (2004). [18] T. Ando, J. Phys. Soc. Jpn. {\bf 73}, 1273 (2004). [19] E. McCann, K. Kechedzhi, V. I. Falko, H. Suzuura, T. Ando, and B. L. Altshuler, Phys. Rev. Lett. {\bf 97}, 146805 (2006). [20] T. Ando, J. Phys. Soc. Jpn. {\bf 75}, 054701 (2006). [Preview Abstract] |
Tuesday, March 6, 2007 8:36AM - 8:48AM |
H28.00002: Charge-Tunable Electron-Phonon Coupling in Single Layer Graphene Jun Yan, Yuanbo Zhang, Philip Kim, Aron Pinczuk We report the observation of electron-phonon coupling in single layer graphene via gate-modulated Raman spectroscopy. The doubly-degenerate long-wavelength optical phonon of graphene (the G-band) is found to be very sensitive to charging of the single atomic layer by the electric-field-effect. The functional dependences of frequency and line-width on gate voltage are explained in terms of charge-tunable interactions of G-band phonons with particle-hole transitions across a vanishing band gap. The phonon dynamics uncovers, from a unique perspective, the intriguing physics of Dirac fermions residing in this two dimensional hexagonal lattice of carbon atoms. The striking symmetry manifested in the spectra offers an optical venue for the determination of the charge-neutral Dirac-point. [Preview Abstract] |
Tuesday, March 6, 2007 8:48AM - 9:00AM |
H28.00003: Electron-Phonon Interactions in Graphene and Graphene Layers Jia-An Yan, W.Y. Ruan, M.Y. Chou We have performed first-principles calculations of the phonon linewidth due to the electron-phonon coupling in one and two layers of graphene using the density-functional perturbation theory. For single-layer graphene, we find that the calculated linewidth is dominated by electron interaction with the two highest optical phonon modes near the $\Gamma$ point and by the highest optical phonon mode near the Brillouin zone boundary corners K and K$'$. A value of the mass enhancement parameter, $\lambda$= 0.3, is obtained for the one layer when we extrapolate the smearing temperature to zero. As for the case of bilayer graphene, although the phonon dispersion relations are almost identical to those of single layer, significant enhancement of electron interaction with some phonon modes is observed due to interlayer coupling, leading to distinct phonon linewidths. [Preview Abstract] |
Tuesday, March 6, 2007 9:00AM - 9:12AM |
H28.00004: Electron-phonon interaction and valley splittings in graphene W. Y. Ruan, Jia-An Yan, Li Yang, M. Y. Chou Based upon first-principles calculations, a two-valley effective mass theory has been developed for graphene in a strong magnetic field and the electron-phonon couplings calculated using density-functional perturbation theory. We showed that the electron interaction with phonons about the Brilouin zone corners can lead to valley-splittings which increases linearly with the magnetic field, in agreement with a recent experimental observation. [Preview Abstract] |
Tuesday, March 6, 2007 9:12AM - 9:24AM |
H28.00005: Electron Self-Energy Corrections to Quasiparticle Excitations in Graphene and Large Diameter Single-Walled Carbon Nanotubes Jack Deslippe, David Prendergast, Steven Louie Recent experimental measurements of the band structure and band velocity at the Dirac point in graphene highlight many novel effects due to the existence of Dirac fermions in this system. The low energy electronic states are measured to have Fermi velocity of approximately $1.1\times 10^6$ m/s, with energy dispersion obeying the 2D massless Dirac equation. Motivated by this work, we explore in detail the importance of an accurate description of the electron self-energy in determining the quasiparticle band structures of graphene, graphite, and armchair single-walled carbon nanotubes near the Fermi energy, using the GW approximation to the electron self energy. \\[1.0ex] This work was supported by National Science Foundation Grant No. DMR04-39768 and by the US DOE under Contract No. DE-AC02-05CH11231. Computational resources were provided by SDSC and NERSC. Jack Deslippe acknowledges funding from the DOE Computational Science Graduate Fellowship (CSGF). [Preview Abstract] |
Tuesday, March 6, 2007 9:24AM - 9:36AM |
H28.00006: Direct observation of Landau levels of massless and massive Dirac fermions. Guohong Li, Eva Y. Andrei The low energy quasiparticles in graphene resemble massless relativistic particles (Dirac fermions): they have a linear energy-momentum spectrum and possess internal degrees of freedom arising from the crystal symmetry of the honeycomb lattice, leading to particle anti-particle pairs. When two layers of graphene are coupled together, the quasiparticles acquire a band-mass and are transformed into chiral massive fermions. Both types of quasiparticles develop unusual Landau levels in a magnetic field which profoundly alter the magneto-transport properties. We will report the direct observation of the Landau levels associated with these quasiparticles using a low temperature STM in fields up to 12 Tesla. The experiments reveal two independent sequences of Landau levels that provide evidence for the coexistence of massless and massive Dirac fermions. The energy levels of the former exhibit a square-root dependence on both field and Landau-level index $n$, while the latter are linear in field with a Landau-level index dependence of $[n(n+1)]^{1/2}$. Both sequences exhibit a zero energy Landau level which is a unique and direct consequence of the quantum-relativistic nature of these quasiparticles. [Preview Abstract] |
Tuesday, March 6, 2007 9:36AM - 9:48AM |
H28.00007: Electron-electron and spin-orbit interactions in graphene Mehdi Zarea, Nancy Sandler Electron-electron and spin-orbit interactions in graphene nanoribbons. Narrow graphene ribbons with armchair edges exhibit insulating or metallic behavior depending on the ratio of the ribbon width to the lattice constant. Metallic behavior arises from the presence of non-degenerate localized boundary states with a linear dispersion relation.[1,2] Furthermore, in the presence of spin-orbit interactions, the edge states become spin-filtered states.[3,4] In this work, we studied a Dirac model for armchair ribbons with an effective low-energy Hamiltonian for the edge states that contains intrinsic spin-orbit and Coulomb interactions. By using the bosonization technique we obtain the phase diagram and correlation functions of the model and present a detailed comparison with results derived for armchair nanotubes. We also address the stability of the edge states in the presence of electron-electron interactions. Extensions for zigzag ribbons are discussed. [1] M.Fujita et al J.Phys.Soc.Jpn 65, 1920 (1996) [2] L. Brey and H. A. Fertig, Phys. Rev. B 73, 235411 (2006) [3] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005) [4] K. Sengupta, R. Roy, and M. Maiti, Phys. Rev. B 74, 094505 (2006) [Preview Abstract] |
Tuesday, March 6, 2007 9:48AM - 10:00AM |
H28.00008: Spin density wave formation in graphene facilitated by the in-plane magnetic field Sebastian Reyes, Alexei Tsvelik We suggest that by applying a magnetic field lying in the plane of graphene layer one may facilitate an excitonic condensation of electron-hole pairs with opposite spins and chiralities. The provided calculations yield a conservative estimate for the transition temperature $T_c \sim 0.1~ B$. [Preview Abstract] |
Tuesday, March 6, 2007 10:00AM - 10:12AM |
H28.00009: Is Graphene a Fermi Liquid? Wang-Kong Tse, Sankar Das Sarma, Euyheon Hwang In this talk, we answer the question posed in the title above by considering theoretically the electron-electron interaction induced many-body effects in undoped (`intrinsic') and doped (`extrinsic') 2D graphene layers. We find that (1) intrinsic graphene is a \textit{marginal} Fermi liquid with the imaginary part of the self-energy, $\mathrm{Im}\Sigma(\omega)$, going as linear in energy $\omega$ for small $\omega$, implying that the quasiparticle spectral weight vanishes at the Dirac point as $(\mathrm{ln}\omega)^{-1}$; and, (2) extrinsic graphene is a well-defined Fermi liquid with $\mathrm{Im}\Sigma(\omega)\sim \omega^2\mathrm{ln}\omega$ near the Fermi surface similar to 2D carrier systems with parabolic energy dispersion. We provide analytical and numerical results for quasiparticle renormalization in graphene, concluding that all experimental graphene systems are ordinary 2D Fermi liquids since any doping automatically induces generic Fermi liquid behavior. [Preview Abstract] |
Tuesday, March 6, 2007 10:12AM - 10:24AM |
H28.00010: Inelastic Coulomb scattering of 2D graphene Euyheon Hwang, B. Y. K Hu, Sankar DasSarma The inelastic quasiparticle lifetime of 2D graphene is calculated using the full dynamically screened Coulomb interaction. We calculate the imaginary part of the quasiparticle self-energy for doped (or gated) graphene, using the $G_0W$ and random phases approximations. At low energy regimes, the intraband single particle excitation (SPE) and plasmon contribute to the self energy, but the interband SPE does not contribute to the self energy due to the phase space restrictions. At higher energies ($\omega \agt E_F$) interband SPE contribution increases sharply, overwhelming the intraband SPE and plasmon contribution. The calculated inelastic quasiparticle lifetime is significantly different from semiconductors with parabolic bands because of linear energy dispersion and chiral properties of graphene. [Preview Abstract] |
Tuesday, March 6, 2007 10:24AM - 10:36AM |
H28.00011: Evidence for weak antilocalization in epitaxial graphene Xiaosong Wu, Xuebin Li, Zhimin Song, Claire Berger, Walt A. de Heer Transport in ultrathin graphite on silicon carbide is graphene-like and appears to be dominated by the electron-doped epitaxial graphene layer at the interface. Weak antilocalization in 2D samples manifests itself as a broad cusp-like depression in the longitudinal resistance for magnetic fields 10 mT $<$ B $<$ 5 T. An extremely sharp weak-localization resistance peak at B = 0 is also observed. These features quantitatively agree with recent graphene weak-localization theory. Scattering contributions from charges in the substrate and from trigonal warping due to the graphite layer are tentatively identified. The Shubnikov-de Haas oscillations show an anomalous Berry's phase. Their small amplitudes may be related to graphene scattering processes. [Preview Abstract] |
Tuesday, March 6, 2007 10:36AM - 10:48AM |
H28.00012: Spin-polarized states in zigzag-edge graphene nanostrips John W. Mintmire, Junwen Li, Daniel Gunlycke, Carter T. White Zigzag-edge graphene nanostrips (GNSs) are known to exhibit localized edge states in the vicinity of the Fermi level. It has previously been reported that these edge states are ferrimagnetic. We present a study based on first-principle DFT and Hubbard model calculations that confirm the ferrimagnetic nature of the edge states. By comparing the results, we have estimated the Hubbard U to be approximately 2.7 eV. Energy dispersions, spin polarizations, and total energies are calculated for various widths of the nanostrips. In both our approaches, we find that the ferrimagnetic states have lower energy than the spin-restricted solution. [Preview Abstract] |
Tuesday, March 6, 2007 10:48AM - 11:00AM |
H28.00013: Study of spin-polarized transport in layers of graphene W.-H. Wang, K. Pi, H. Choi, P. Wei, J. Shi, R. Kawakami Electron transport in graphene layers has drawn great attention recently due to the observation of 2D behavior and relativistic dispersion in these systems. Our attention is focused on spin-polarized transport in ferromagnet(FM)/graphene/FM devices in which the FM electrodes act as spin injectors and spin detectors. Specifically, the spin-polarized transport across graphene should be manifested as a dependence of resistance on the relative alignment of the FM electrode magnetizations (i.e. spin valve effect). Few-layer graphene (FLG) are extracted from kish graphite by sonication. FLGs are then dispersed and dried onto SiO2/Si substrate with pre-patterned electrodes. Atomic force microscopy, scanning electron microscopy and optical microscopy are used to characterize topographic properties and surface quality of FLG. FM electrodes are fabricated onto selected FLG using a combination of electron beam lithography and molecular beam epitaxy deposition in ultrahigh vacuum to ensure high quality magnetic materials and interfaces. We have performed initial electrical measurements and results from our studies will be discussed. [Preview Abstract] |
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