Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session Q26: Focus Session: Graphene X: Theory |
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Sponsoring Units: DMP Chair: Tobias Stauber, University of Minho, Portugal Room: 328 |
Wednesday, March 18, 2009 11:15AM - 11:27AM |
Q26.00001: Electron-electron interactions in graphene bilayers Fan Zhang, Hongki Min, Marco Polini, Allan MacDonald Electrons in condensed matter normally form Fermi-liquid states in which e-e interactions play an inessential role. A well known exception is the case of 1D electron systems in which the Fermi-surface consists of two points and divergences associated with low-energy particle-hole excitations abound when e-e interactions are described perturbatively. Corresponding divergences normally occur in systems with higher space dimensions when Fermi lines or surfaces satisfy idealized nesting conditions. Here we discuss the role of e-e interactions in 2D graphene bilayers which behave in many ways as if they were 1D because they have point-like Fermi surfaces which satisfy the nesting condition and have two-layer chirality and because their particle-hole energies have a quadratic dispersion which compensates for the difference between 1D and 2D phase spaces. We conclude, on the basis of a perturbative RG calculation, that interaction in neutral graphene bilayers drive the system into a spontaneously broken symmetry state with layer-pseudospin ferromagnetism. [Preview Abstract] |
Wednesday, March 18, 2009 11:27AM - 11:39AM |
Q26.00002: Ferromagnetism in Graphene Stacks Dagim Tilahun, Allan MacDonald Because the density of states at the Fermi level of neutral graphene layers is proportional to external magnetic field, the ground state in strong fields is expected to have a broken symmetry - most likely ferromagnetism. In systems with stacked graphene layers this tendency competes with inter-layer hopping which favors paramagnetic ground states or perhaps other types of broken symmetries. We present a criterion for the stablility of the ferromagnetic state and discuss its application to single-layer graphene, to weakly coupled epitaxial graphene layers on SiC or other substrates, and to bulk graphite. We use the Slonczewksi-Weiss-McClure model to explain why the dominant inter-layer hopping process in Bernal (AB) stacked graphite does not compete with ferromagnetism. [Preview Abstract] |
Wednesday, March 18, 2009 11:39AM - 11:51AM |
Q26.00003: Theory of inter-edge superexchange in zigzag edge magnetism Jeil Jung, Tami Pereg-Barnea, Allan MacDonald A graphene nanoribbon with zigzag edges has a gapped magnetic ground state with an antiferromagnetic inter-edge superexchange interaction. We present a theory based on the asymptotic properties of the Dirac-model ribbon wavefunction which predicts $W^{-2}$ and $W^{-1}$ ribbon-width dependences for the superexchange interaction strength and the gap respectively. Unlike in conventional superexchange we find that both the kinetic and exchange energy contributions favor the antiferromagnetic inter-edge coupling with a dominant role of exchange several times larger in magnitude than the kinetic energy contribution. [Preview Abstract] |
Wednesday, March 18, 2009 11:51AM - 12:03PM |
Q26.00004: Numerical study on electron-electron interaction and ferromagnetic fluctuation in graphene Tianxing Ma, Feiming Hu, Zhongbing Huang, Hai-Qing Lin Within the Hubbard model on a honeycomb lattice, we investigate the effect of electron-electron interactions and ferromagnetic fluctuations in graphene numerically. We find that the system in the filling region $<$$n$$>$=1.60-1.90 shows a short-ranged ferromagnetic correlation, and the on-site Coulomb interaction tends to strengthen ferromagnetic fluctuation slightly. Furthermore, the ferromagnetic fluctuation is strengthened markedly as the next-nearest neighbor hoping energy increases, which indicate that the next-nearest neighbor hoping term plays an important role in graphene since it breaks the particle-hole symmetry. [Preview Abstract] |
Wednesday, March 18, 2009 12:03PM - 12:15PM |
Q26.00005: Gate-induced interlayer asymmetry in ABA-stacked trilayer graphene Edward McCann, Mikito Koshino We model the electronic band structure and conductivity of ABA- stacked trilayer graphene in the presence of external gates, self-consistently calculating the electric potential of the three layers. We show that a gate field perpendicular to the layers breaks mirror reflection symmetry with respect to the central layer, leading to hybridization of the linear and parabolic low-energy bands. For large gate fields, we derive an effective two-component Hamiltonian describing chiral electrons in two low-energy bands that exhibit an anti-crossing with a small hybridization gap. The magnitude of the gap is largely independent of the gate field, but the momentum at the anti- crossing and the typical band velocity both increase with it. Using the self-consistent Born approximation, we find that the density of states and the minimal conductivity in the presence of disorder generally increase as the gate field increases, in sharp contrast with bilayer graphene. [Preview Abstract] |
Wednesday, March 18, 2009 12:15PM - 12:27PM |
Q26.00006: Aharonov-Bohm-like scattering, localization, and novel electronic states in hydrogenated graphene Andrey Shytov, Dmitry Abanin, Leonid Levitov Metallic nature of transport in graphene, which is fairly robust with respect to varying amounts of disorder, changes in an unexpected way when vacancies are introduced in this material. At low energies, near the Dirac point, electron scattering on vacancies mimics scattering on Aharonov-Bohm solenoids carrying unit flux. This type of scattering results in a very narrow band of states at the Dirac point with properties resembling those of zeroth Landau level, which is positioned in the middle of a (pseudo)gap created by vacancies and resembling the cyclotron gap around zeroth Landau level. The fictitious magnetic field describing vacancies has opposite signs for the valleys K and K'. As a result of this, an externally applied magnetic field has opposite effects in the two valleys, suppressing (reinforcing) the gap in the K (K') valley. We show that this picture is in agreement with the behavior observed in a recent study [1] of electronic properties of graphene, which can be transformed from metallic state to insulating state by hydrogenation. [1] D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim, K. S. Novoselov, arXiv:0810.4706 [Preview Abstract] |
Wednesday, March 18, 2009 12:27PM - 12:39PM |
Q26.00007: Rashba spin-orbit interactions in zigzag graphene nano-ribbons Mahdi Zarea, Nancy Sandler The crystalline structure of graphene can be described in terms of a pseudo-spin degree of freedom and spinor wavefunctions. This characteristic has important physical consequences not observed in normal semiconductors. For zigzag ribbons, for instance, this translates into the existence of localized chiral edge states, with momentum coupled to pseudo-spin. In the presence of Rashba spin-orbit interactions (RSOI), this special feature makes the material a good candidate to produce localized spin polarized currents. To address this issue we investigated the role of the RSOI on the band-structure and wavefunctions of an infinite graphene plane and a zigzag nano-ribbon. We present analytic and numerical results showing that the spin profile along the edge is state-dependent. We compare these results with the profiles obtained in the presence of the intrinsic spin-orbit interaction [1]. We show that the RSOI can create average localized spin polarized currents along the edges of zigzag ribbons with appropriate applied voltages. [1] Zarea, M., Busser, C. and Sandler, N. PRL 101, 196804 (2008). [Preview Abstract] |
Wednesday, March 18, 2009 12:39PM - 12:51PM |
Q26.00008: Plasma Instabilities in Graphene Ben Yu-Kuang Hu, Antti-Pekka Jauho We discuss the possibility of the occurrence of plasma instabilities under non-equilibrium conditions in graphene. Specifically, we investigate the stability of the electronic collective modes in graphene with two counter-streaming distributions of carriers by studying the frequency-dependent dielectric function $\epsilon({\bf q},\omega)$ of the system. We find that the linear electronic dispersion of graphene results in instabilities that are qualitatively different from the standard two-stream instabilities for classical plasmas and parabolic-band systems. [Preview Abstract] |
Wednesday, March 18, 2009 12:51PM - 1:03PM |
Q26.00009: Is suspended graphene an insulator? Joaquin Drut, Timo Lahde Graphene at low energies resembles massless quantum electrodynamics in a strongly coupled regime, away from the usual perturbative region where the fine structure constant is $\alpha \simeq 1/137$. Indeed, a single sheet of graphite in vacuum presents $\alpha \sim 1$. At such strong couplings the U(4) chiral symmetry of graphene can spontaneously break, inducing a gap in the quasiparticle spectrum. The question of whether chiral symmetry is broken represents a computational challenge that lies outside the domain of analytic techniques. In this talk, we will present the results of the first Monte Carlo simulation of the low-energy effective theory of graphene in vacuum (see abstract by T.~A.~L\"ahde). We have computed the chiral condensate, which is the order parameter for the insulating charge density wave state, as a function of $\alpha$, and found a chiral phase transition that is compatible with suspended graphene being in the gapped phase. [Preview Abstract] |
Wednesday, March 18, 2009 1:03PM - 1:15PM |
Q26.00010: Many-body effects in neutral graphene bilayers Csaba Toke, Vladimir I. Falko A graphene bilayer is studied within the Hartree-Fock approximation in the tight-binding model. The exchange self-energy is studied systematically in an momentum expansion. Up to first order in the coupling constant (the effective fine structure constant) and to first order of the nonperpendicular hopping parameter we find that, for zero magnetic field, the exchange interaction with the valence band contributes with a logarithmically divergent correction to the Fermi velocity, the perpendicular inter-layer hopping, and the trigonal warping. The effective mass renormalization in the two-band effective Hamitonian is studied. For a strong perpendicular magnetic field the exciton dispersions are calculated. [Preview Abstract] |
Wednesday, March 18, 2009 1:15PM - 1:27PM |
Q26.00011: Berry phase and the role of trigonal warping in graphene systems Ivan Stanic, Karyn Le Hur In general Dirac fermions exhibit a Berry phase of $\pi$ whereas non-relativistic free-like particles have a Berry phase of $2\pi $. The two cases have been reported, both theoretically and experimentally, in single-layer and bi-layer graphene respectively. On the other hand, if one considers, for example, bi-layer graphene in more detail, its band structure shows both the Dirac-type, coming from the trigonal warping, and the parabolic, non-relativistic aspect in different energy regimes. This gives an unprecedented opportunity to investigate the \textbf{crossover between non- relativistic and Dirac fermions in a Berry phase formulation}. Here, we propose a scattering type-experiment (reflecting the Berry phase) to demonstrate this crossover. We present our theoretical results on scattering cross-sections taking into account the trigonal warping term, which confirm the jump in the Berry phase from $\pi$ to $2\pi$ as the energy of the incoming electrons is increased. This jump in the Berry phase can be understood from a general theorem relating the Berry phase and the band structure of a material. [Preview Abstract] |
Wednesday, March 18, 2009 1:27PM - 1:39PM |
Q26.00012: Trigonal Band Structure and Time-Reversal Invariance in Graphene Roland Winkler, Ulrich Zuelicke We present a symmetry analysis of the trigonal band structure in graphene. While the energy spectrum near the Fermi edge equals the spectrum of massless Dirac fermions, the transformational properties of the underlying basis functions are qualitatively different. Using group theory we develop an invariant expansion of the Hamiltonian for the electron states near the $\mathbf{K}$ points of the graphene Brillouin zone. We find that the $k$-linear dispersion near the band edge arises as an unusual consequence of time-reversal invariance. We suggest to divide the electronic properties of graphene into two categories, those that depend and those that do not depend on the transformational properties of the Bloch functions at $\mathbf{K}$. See arXiv:0807.4204. [Preview Abstract] |
Wednesday, March 18, 2009 1:39PM - 1:51PM |
Q26.00013: Two dimensional massless Dirac fermions with Coulomb interaction and random gauge potential Sen Zhou, Oskar Vafek We present a numerical study of the two dimensional massless Dirac fermions of monolayer graphene with long-range Coulomb interaction and random gauge potential. The Coulomb interaction renormalizes logarithmically the electron velocity at low energies, leading to a decrease in the density of states. While the density of states is enhanced by the random gauge potential, and has a power-law dependence in low energies, $\rho(E)\sim E^{-1+2/z}$ with $z=1+\sqrt{3}\Delta/\pi$, where $\Delta$ measures the disorder strength. The combined effect of interaction and disorder gives rise to a line of fixed points where both the interaction and disorder are finite, and the low-energy density of states is exactly linear. Results are consistent with previous renormalization group argument. [Preview Abstract] |
Wednesday, March 18, 2009 1:51PM - 2:03PM |
Q26.00014: Gap opening due to topological defects in graphene Ricardo Nunes, Joice Ara\'ujo, Helio Chacham Stone-Wales defects (SWD = two adjacent pentagon-heptagon pairs) are common low-energy defects in carbon nanotubes. Previously, Crespi et al.[{\bf PRB, 53, 1996}] have proposed a purely-carbon covalent metal sheet called ``pentaheptite,'' consisting entirely of SWDs, with a relatively low formation energy of 0.32 eV/atom, with respect to graphene. In this work, we consider three different families of periodic carbon sheets containing topological defects (TDs = pentagons and heptagons). The families differ by the density of TDs in a seed structure. In each family, we generate periodic structures in which isolated pentagons and heptagons are surrounded only by hexagons. By means of ab initio calculations, we propose that, depending on the density and distribution of TDs, these carbon sheets may behave as a semiconductor, a metal or a semimetal. In the range of TD concentrations we examine, the sheets are stable in a planar form, but, allowing for the corrugation generated by the curvature fields associated with the isolated TDs, leads to lower formation energies and to either a reduction of the density of states or to gap opening at the Fermi level. Formation energies can be very small: in particular, we obtain a semiconducting structure with a formation energy of only 92 meV/atom with respect to graphene. [Preview Abstract] |
Wednesday, March 18, 2009 2:03PM - 2:15PM |
Q26.00015: Transport of massless Dirac fermions in graphene layers in presence of electromagnetic potential barriers Sankalpa Ghosh, Manish Sharma We study the transport of massless Dirac fermions in Graphene layers through electromagnetic potential barriers. The barriers consist of periodically arranged delta function-like magnetic fields superposed with periodic electrostatic potentials. We show that such an arrangement provides a wide range of control on the electron transport through Graphene, and the associated problems can be mapped on certain classes of optical problems. We discuss the related band structure and its effect on transport over a range of magnetic field strengths and barrier widths. We also discuss the typical experimental set up where related properties can be verified. [Preview Abstract] |
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