Bulletin of the American Physical Society
APS March Meeting 2010
Volume 55, Number 2
Monday–Friday, March 15–19, 2010; Portland, Oregon
Session V22: Quantum Hall Effect in Graphene |
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Sponsoring Units: DCMP Chair: Dmitri Abanin, Princeton University Room: Portland Ballroom 252 |
Thursday, March 18, 2010 8:00AM - 8:12AM |
V22.00001: Collective Excitations in Graphene in a Strong Magnetic Field Andrea Fischer, Alexander Dzyubenko, Rudolf Roemer Graphene, a two-dimensional form of carbon, has become famous for its wide range of unusual properties, both fundamental and applicable. Both theory and experiment indicate the relevance of many body interactions to the magneto-optical response of graphene. Neutral collective excitations of pristine graphene in a strong perpendicular magnetic field have already been studied theoretically. In this work, we consider graphene with a low impurity density and determine the neutral magnetoplasmons, which become localised on an impurity. Two impurity types are considered: a screened Coulomb impurity and a $\delta$-function scatterer due, e.g., to a neutral foreign atom on one of the lattice sites. We assume Zeeman and valley splitting of Landau levels (LLs) $n$=0 and $n=\pm $1, so that these LLs have four sublevels; we consider various integer fillings of the zeroth LL. For both impurity types, we predict the existence of optically active bound states above and below the magnetoplasmon continuum for high enough impurity strengths [1]. Our results indicate that polarisation-resolved magneto- optical spectroscopy can be an effective tool for discriminating between different types of impurities in graphene. [1] A. M. Fischer, A. B. Dzyubenko, and R. A. R\"{o} mer, PRB \textbf{80}, 165410 (2009) [Preview Abstract] |
Thursday, March 18, 2010 8:12AM - 8:24AM |
V22.00002: Landau Level Collapse in Gated Graphene Structures Nan Gu, Mark Rudner, Leonid Levitov, Andrea Young, Philip Kim Electron cyclotron motion in solids can be changed in a variety of interesting ways by applying an external electric field. This talk will describe a new regime of magnetotransport, recently observed in measurements performed on lateral heterojunctions in graphene. The Landau levels, formed on top of a potential barrier imposed by external gates, are shown to undergo an abrupt collapse when the strength of magnetic field is reduced below a certain critical value. The threshold for collapse is determined by the competition between magnetic confinement and the strength of the barrier. Semiclassical analysis of the transformation of closed cyclotron orbits into open deconfined orbits is presented and is shown to agree well with experimental results. [Preview Abstract] |
Thursday, March 18, 2010 8:24AM - 8:36AM |
V22.00003: Temperature, Magnetic field, and Gate Bias Dependence of the Infrared Hall Effect in Graphene C.T. Ellis, A.V. Stier, A. Stabile, M.-H. Kim, G. Sambandamurthy, J. Cerne, S. Banerjee In our study we probe the infrared Hall conductivity ($\sigma_ {xy}$) for single and bilayer graphene in the 120-1000 meV range as a function of gate bias at temperatures down to 7K and magnetic fields up to 7T using Faraday measurements. Unlike the longitudinal conductivity ($\sigma_{xx}$), which measures the sum of the optical responses for left and right circularly polarized light, $\sigma_ {xy}$ measures the difference and therefore is sensitive to small changes in symmetry. While $\sigma_{xx}$ and the DC Hall effect have revealed extraordinary properties of graphene (Zhang, Nature 2005; Novoselov, Nature 2005; Jiang, PRL 2007; etc...) recent calculations (Morimoto, PRL 2009) predict remarkable step-like features in the infrared $\sigma_{xy}$. We also probe the chiral response of graphene due to spatial inversion symmetry breaking. Our graphene samples are prepared using several methods, including anodically bonding graphite to pyrex, which can produce a high yield of large single layer graphene flakes ($>$100 $\mu$m) (Shukla et al., Solid State Comm. 2009), normal mechanical exfoliation of kish graphite, and grown chemical vapor deposition techniques. [Preview Abstract] |
Thursday, March 18, 2010 8:36AM - 8:48AM |
V22.00004: Real Space Imaging of the Quantum Hall Effect and Valley Polarization in Graphene David Miller, Kevin Kubista, Ming Ruan, Walt De Heer, Phillip First, Gregory Rutter, Joseph Stroscio When a perpendicular magnetic field is applied to a graphene sheet, the resulting eigenenergies (Landau Levels or LLs) have a nonlinear energy distribution that includes a four-fold degenerate zero-energy state ($LL_{0}$). Maps of the energy-resolved local density of states (LDOS) acquired via cryogenic scanning tunneling spectroscopy (STS) provide atomic-scale images of the LL spatial distribution. Focusing on $LL_{0}$, we use STS maps to show the distribution of ``drift states'' and find unexpected atomic-scale spatial variations of the LDOS above a critical field of $B_{*} = 4 T$. We resolve an energy gap in $LL_{0}$ and show how it depends on the local A-B lattice symmetry and magnetic field. The gap is observed only within patches of at least a few magnetic lengths in size, which forces the splitting to ``turn off'' below the critical field. We attribute this behavior to a breaking of the local sublattice symmetry imposed by moire layer stacking. [Preview Abstract] |
Thursday, March 18, 2010 8:48AM - 9:00AM |
V22.00005: Electromagnetic absorption in the quantum Hall ferromagnetic states of bilayer graphene Ren\'e C\^ot\'e, Jules Lambert, Yafis Barlas, Allan H. MacDonald In a quantizing magnetic field, the Landau level orbitals $n=0$ and $n=1$ of a graphene bilayer in the Bernal stacking have zero kinetic energy. An electron in the $N=0$ Landau level must then be described by three quantum numbers: its spin, its valley index $K$ or $K'$ and an orbital quantum number $n=0,1$. It was recently shown [1] that, in the Hartree- Fockapproximation, the ground states of the graphene bilayer at integer filling factors $\nu \in [-3,4]$ can be described as different kinds of quantum Hall ferromagnets (QHF's) with finite interlayer or inter-orbital coherence. In this talk, we discuss the new ground states introduced by adding a finite interlayer voltage, $\Delta_{B}$ to the bilayer. We study the dispersion relation of the pseudospin waves in these phases and compute the electromagnetic absorption due to these collective modes. We show that the different ground states give rise to different signatures in the absorption spectrum. \\[4pt] [1] Yafis Barlas, R. C\^ot\'e, K. Nomura, and A. H. MacDonald, Phys. Rev. Lett.,$\bf 101$, 097601 (2008). [Preview Abstract] |
Thursday, March 18, 2010 9:00AM - 9:12AM |
V22.00006: Corbino Measurement of Graphene in Quantum Hall States Yue Zhao, Paul Cadden-Zimansky, Philip Kim The origin and the nature of zero energy quantum Hall (QH) state at the charge neutrality point of graphene are still under debate. In conventional Hall bar geometry of graphene device, direct access of bulk conduction in QH regime has been complicated due to the presence of edge state channel in the device. We employ Corbino device geometry in graphene and measure the bulk conduction between inner and outer electrode without edge state channel connection. We observe $\nu=0$ state is independent of in-plane magnetic field, indicating that its origin is not of spin-related. [Preview Abstract] |
Thursday, March 18, 2010 9:12AM - 9:24AM |
V22.00007: Quantum Hall states in graphene with correlated hopping disorder Caio Lewenkopf, Ana L. C. Pereira, Eduardo R. Mucciolo Ripples are believed to be one of the important sources of long-range disorder in graphene. Observed both in suspended, as well as in graphene deposited on substrates, smooth ripples can be modeled in the tight-binding Hamiltonian by locally changing the hopping term. We investigate the density of states and the participation ration (PR) of a graphene single-layer sheet with correlated hopping disorder in the quantum Hall regime. We find that for hopping correlation lengths $\lambda$ larger than the lattice parameter, the width of the $n$th Landau Level (LL) increases with $n$. The $n=0$ LL splits into two peaks, but as $\lambda$ increases their widths are dramatically reduced. We observe that this width reduction becomes particularly pronounced when $\lambda$ is of the order or higher than the magnetic length. The analysis of the PR suggests that, with increasing $\lambda$, the localization length decreases for the states from the $n>0$ LLs, while it increases for the $n=0$ Landau level. [Preview Abstract] |
Thursday, March 18, 2010 9:24AM - 9:36AM |
V22.00008: Quantum Hall effect in suspended graphene: two-lead versus Hall bar geometry I. Skachko, F. Duerr, A. Luican, E.Y. Andrei, X. Du, D. Abanin Following our observation of the Fractional Quantum Hall effect in suspended graphene [1], we investigate why the Quantum Hall effect in this system can be observed in a two-lead geometry but not in a Hall bar geometry. By comparing magnetotransport data obtained from nonsuspended graphene Hall bar samples having various distances between voltage and current leads, we conclude that the Hall voltage is shorted out when the corresponding voltage leads are in the so called hot spot region in the immediate vicinity of current leads. We evaluate the distribution of electric field lines in the device and estimate the extent of the hot spots. We argue that due to the small size of suspended graphene devices imposed by the requirement of mechanical stability, the voltage leads are affected by the hot spots, limiting the usefulness of the Hall bar geometry. We will discuss ways to circumvent hot-spot related shorting of the Hall voltage in samples with various geometries. \\[4pt] [1] X. Du, I. Skachko, F. Duerr, A. Luican and E.Y. Andrei, Nature \textbf{462}, 192-194 (2009). [Preview Abstract] |
Thursday, March 18, 2010 9:36AM - 9:48AM |
V22.00009: Theory of the magnetic-field-induced insulator in graphene Jeil Jung, Allan MacDonald Recent experiments have demonstrated that neutral graphene sheets become insulators when placed in an external magnetic field. This anomalous behavior is related to the unusual four-fold degenerate quantization of $n=0$ Landau levels near the Dirac point which causes interaction physics to become important at quite weak magnetic fields. The ground state of a neutral system in a magnetic field is a bulk 2D insulator. Zeeman splitting favors a spin polarized state in which the two majority spin $n=0$ levels are occupied. This solution supports edge states with non-trivial conducting properties. Under certain conditions these edge states can be very poor conductor, consistent with the large measured resistances. In our work we suggest an alternate explanation based on $\pi$-band tight-binding-model Hartree-Fock calculations which conveniently accounts for Landau level mixing between states near the Dirac point with other states more remote in energy. We find that when Landau level mixing is included the ground state is a density-wave state, related with the fact that $n=0$ Landau levels in different valleys occupy different honeycomb sublattices. The density wave solutions do not support edge states and are immediately consistent with the very large measured resistance of the field-induced insulator state. [Preview Abstract] |
Thursday, March 18, 2010 9:48AM - 10:00AM |
V22.00010: Quantum Anomalous Hall Effect in Graphene Zhenhua Qiao, Shengyuan Yang, Yugui Yao, Jian Wang, Qian Niu The anomalous Hall-effect (AHE) in graphene is investigated using the Landauer-Buttiker formula and tight-binding method in the presence of Rashba spin-orbit interaction and exchange field M. We found that the anomalous Hall conductance could be exactly quantized to one in the unit of e(2)/h by tuning the controllabe substrate-induced spin-orbit interaction and M. [Preview Abstract] |
Thursday, March 18, 2010 10:00AM - 10:12AM |
V22.00011: Local Compressibility Measurements of Broken-Symmetry States in Suspended Bilayer Graphene Jens Martin, Ben Feldman, Thomas Weitz, Monica Allen, Amir Yacoby We have performed local compressibility measurements of a suspended bilayer graphene flake using a scanning single electron transistor. In addition to the expected energy gaps at filling factors \textit{$\nu $} = $\pm $4 and $\pm $8, we observe Landau levels corresponding to broken-symmetry states at \textit{$\nu $} = 0 and $\pm $2. The width of the incompressible region at each filling factor is independent of magnetic field $B$, and is on the order of 10$^{10}$ cm$^{-2}$, indicative of the low disorder in suspended devices. Remarkably, the \textit{$\nu $} = $\pm $4 gaps even persist below 50 mT. The measured energy gap between each Landau levels scales linearly with $B,$ with a magnitude of approximately 4 meV/T for \textit{$\nu $} = $\pm $4 and approximately 1 meV/T for the broken-symmetry states. In addition, the flakes exhibit decreased compressibility near the charge neutrality point at $B$ = 0. Scanning the tip position reveals density variations consistent with estimates from transport and from the width of the incompressible regions around each Landau level. [Preview Abstract] |
Thursday, March 18, 2010 10:12AM - 10:24AM |
V22.00012: Bilayer Graphene: Interaction-Induced Quantum Hall States and Unusual Excitations Shivaji Sondhi, D.A. Abanin, S.A. Parameswaran Recently, new interaction-induced quantum Hall (QH) states were observed\footnote{B. Feldman et al., Nature Physics, doi:10.1038/nphys1406 (2009); Y. Zhao et al., arXiv:0910.0217 (2009).} in bilayer graphene (BG). In this talk we address the nature of these QH states, as well as their properties\footnote{D. Abanin et al., Phys. Rev. Lett. 103, 076802 (2009), and to be published.}. We focus on the ferromagnetic (FM) states at even filling factors, which, in the leading approximation, result from the spontaneous breaking of valley/spin $SU(4)$ symmetry. Calculating microscopic anisotropies of the QHFM, we find the order in which Landau level (LL) degeneracies are lifted. Furthermore, we discuss the phase diagram of the system as a function of perpendicular electric field and parallel magnetic field, and find that they can be used to drive transitions between different QH states. We show that, as a result of unusual LL structure of BG, some of the QHFM states support new type of excitations -- spin/valley textures (skyrmions) that carry charge two, which provides a unique example of pairing of charges in a system with purely repulsive interactions. We propose several experiments to test our findings. [Preview Abstract] |
Thursday, March 18, 2010 10:24AM - 10:36AM |
V22.00013: Quantum Hall effect in multi-terminal suspended graphene devices Fereshte Ghahari, Yue Zhao, Kirill Bolotin, Philip Kim The integer and fractional quantum hall effects have been already observed in two terminal suspended graphene devices. However in this two probe device geometry, mixing between magnetoresistance $\rho_{xx}$ and Hall resistance $\rho_{xy}$ for incompletely developed quantum Hall states leads to substantial deviation of conductance plateaus values. In this talk, we present the experimental results from four terminal suspended graphene devices. The quality of quantum Hall effect will be discussed in muti-terminal device geometry in conjunction with the current-induced annealing process to improve the quality of graphene samples. [Preview Abstract] |
Thursday, March 18, 2010 10:36AM - 10:48AM |
V22.00014: Magnetoresistance in Graphite: Do Dirac Fermions play a role? Hridis Pal, Dmitrii Maslov We calculate the dependence of basal transverse magnetoresistance in graphite (H parallel to the c axis) on magnetic field and find a regime where this dependence is linear in field. The linearity is attributed to the presence of extremely light carriers near the H points of the Brillouin zone. We also explore theoretically quantum oscillations in conductivity and examine if the presence of Dirac fermions near the H points can have any signature in these oscillations. [Preview Abstract] |
Thursday, March 18, 2010 10:48AM - 11:00AM |
V22.00015: Optical Hall conductivity for the graphene QHE in the honeycomb lattice model Takahiro Morimoto, Yasuhiro Hatsugai, Hideo Aoki We have previously revealed from a numerical study that the Hall plateaus are retained in the optical Hall conductivity $\sigma_{xy}(\omega)$ in the ac ($\sim$ THz) regime in both of the ordinary two-dimensional electron gas and the massless Dirac model in the quantum Hall regime, although the plateau height in ac deviates from the quantized values. The effect remains unexpectedly robust against a significant strength of disorder, which we attribute to an effect of localization [1]. Here we extend the calculation to graphene, for which we should go back to the honeycomb tight-binding model rather than the Dirac model. We have found that, when the disorder is chiral-symmetric as in bond disorder and random magnetic flux which should represent the effect of ripples, the step structure in the optical Hall conductivity is anomalously sharp for the N=0 Landau level. We expect the structure to be observable in clean, suspended graphene samples through the Faraday rotation of the order of the fine-structure constant $\alpha$. \\[4pt] [1] T. Morimoto et al., PRL {\bf 103}, 116803 (2009). [Preview Abstract] |
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