Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session J37: QHE: Bilayers and Graphene |
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Sponsoring Units: FIAP Chair: Herb Fertig, Indiana University Room: Morial Convention Center 229 |
Tuesday, March 11, 2008 11:15AM - 11:27AM |
J37.00001: Thin cylinder limit of Halperin bilayer quantum Hall states Alexander Seidel, Kun Yang The traditional framework to study fractional quantum Hall states is based on Laughlin type wavefunctions and Chern-Simons field theories. Recently, a new framework has been proposed that puts stronger emphasis on the one-dimensional (1d) Hilbert space structure of Landau levels. One way to obtain this framework is by observing that states describing fractional quantum Hall liquids may be adiabatically evolved into simple one-dimensional charge-density-wave (CDW) patterns when the system is deformed, e.g., into a thin torus or cylinder. Many general properties of fractional quantum Hall systems are rooted in these CDW states, such as degeneracies and fractional quantum numbers. In this talk, the thin cylinder limit of Halperin $(m,m',n)$ bilayer quantum Hall states will be discussed. The corresponding CDW patterns are quite complicated for general $(m,m',n)$, and can be worked out from a discrete version of the plasma analogy in a ''squeezed space''. The simpler cases map onto well-known spin-1/2 physics. This has some implications for a possible phase transition of the (331) state into the Moore-Read state. [Preview Abstract] |
Tuesday, March 11, 2008 11:27AM - 11:39AM |
J37.00002: Metamorphosis of quantum Hall bilayer state into a composite fermion metal B. Karmakar, V. Pellegrini, A. Pinczuk, L.N. Pfeiffer, K.W. West In the regime of strong interlayer correlation and tunneling gap $\Delta _{SAS}>$0, the quantum Hall (QH) ground state of bilayers at filling fraction $\nu _{T}$=1 can be viewed as an excitonic insulator [1]. Here it will be shown that a phase transition occurs between this excitonic state and a composite-fermion CF metal as $\Delta _{SAS}$ decreases [2,3]. The observations are based on inelastic light scattering of spin-wave (SW) mode at the Zeeman energy and spin-flip (SF$_{SAS})$ mode across $\Delta _{SAS}$. These experiments show that the SF$_{SAS}$ excitation collapses to the SW and disappears at a critical value of $\Delta _{SAS}$ while a low energy continuum of spin transitions below the SW mode appear. These transitions are interpreted as spin-flip SF$_{CF}$ excitations of the CF metal in which orientation of spin and CF Landau level index change simultaneously. Measurements of SW excitations at $\nu _{T}$=1 in the regime of $\Delta _{SAS}\approx $0 will be also shown [4]. The behavior of the SW thermal activation gap as a function of the Zeeman energy suggests a subtle competition between interlayer correlation and spin effects in the broken-symmetry QH state at $\Delta _{SAS}\approx $0. [1] S. Luin, et al., PRL. \textbf{94}, 146804 (2005); [2] S. Luin, et al., PRL. \textbf{97}, 216802 (2006); [3] B. Karmakar, et al., Solid State Comm. \textbf{143}, 504 (2007); [4] B. Karmakar, et al., work in progress. [Preview Abstract] |
Tuesday, March 11, 2008 11:39AM - 11:51AM |
J37.00003: Evidence for a finite temperature phase transition in a bilayer quantum Hall system A.R. Champagne, J.P. Eisenstein, L.N. Pfeiffer, K.W. West We study the Joshepson-like interlayer tunneling signature of the quantum Hall bilayer excitonic state at total filling factor $\nu_T = 1$ as a function of the layer separation, interlayer charge imbalance and temperature. The tunneling amplitude collapses to zero as either the temperature or interlayer spacing is increased. The interlayer tunneling amplitude dependences on the layer spacing at various temperatures are very similar, but the layer separations where the tunneling disappears scale linearly with temperature. Our results offer evidence [1] that a finite temperature phase transition separates the interlayer coherent phase from incoherent phases which lack strong interlayer correlations. The phase boundary is found to be re-entrant as a function of charge imbalance thus suggesting an intricate competition between the interlayer coherent phase and various independent layer states. This work was supported by the NSF and the DOE. \newline [1] A.R. Champagne, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, Cond-mat/0709.0718 [Preview Abstract] |
Tuesday, March 11, 2008 11:51AM - 12:03PM |
J37.00004: Area and perimeter dependence of tunneling in a bilayer 2D electron system in the \boldmath{$\nu_T=1$} quantum Hall state A.D.K. Finck, A.R. Champagne, J.P. Eisenstein, L.N. Pfeiffer, K.W. West When interlayer interactions between electrons in two parallel 2D electron systems become comparable to intralayer interactions, a quantum Hall state can occur at total filling factor $\nu_T=1$. In this state, the 2D-2D tunneling conductance at zero bias is greatly enhanced. In some theoretical models, tunneling is expected to occur primarily along the edge of the system. In large regions the tunneling conductance would therefore be proportional to the perimeter of the sample. To test this idea, we use electrostatic top gates of various sizes and shapes to locally define a $\nu_T = 1$ state. By subtracting out background tunneling originating from ungated regions of the sample, we can measure the tunneling conductance of individual gated regions. Our data show that the tunneling conductance at $\nu_T =1$ is approximately proportional to area. This implies that tunneling at $\nu_T=1$ is a bulk phenomenon in our samples. How this result is connected with the inevitable disorder in the sample will be discussed. This work is supported by the NSF under grant DMR-0552270. [Preview Abstract] |
Tuesday, March 11, 2008 12:03PM - 12:15PM |
J37.00005: Theory of Activated Transport in Bilayer Quantum Hall Systems Bahman Roostaei, Herbert Fertig, Kieran Mullen, Steven Simon We analyze the transport properties of bilayer quantum Hall systems at total filling factor $\nu = 1$ in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern- Simons theory that in drag geometries, current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment. We conclude with predictions for future experiments. [Preview Abstract] |
Tuesday, March 11, 2008 12:15PM - 12:27PM |
J37.00006: Non-perturbative approach to the quantum Hall bilayer Milica Milovanovic, Zlatko Papic We study the disordering of the superfluid phase in the quantum Hall bilayer at the filling factor one with increasing distance between the layers. We find that the possibilities for ground state wave functions that describe the superfluid at an arbitrary distance fall into two universality classes. They correspond to (1) Berezinskii-Kosterlitz-Thouless (BKT) (2D XY) model of superfluid disordering in the presence of charged impurities and (2) $\lambda$ transition (3D XY) model in a translatory invariant quantum Hall bilayer system. The BKT type of disordering likely ends with unbinding of created pairs of neutral fermionic vortices (in a transition reminiscent of the one reported in Champagne et al.). In the translatory invariant system the ensuing quantum phase transition proceeds via condensation of loops of elementary charged vortices - merons into a topological phase associated with the toric code model. [Preview Abstract] |
Tuesday, March 11, 2008 12:27PM - 12:39PM |
J37.00007: Phonon mediated resonances in bilayer magnetodrag Gokul Gopalakrishnan, Sanghun An, Dongkyun Ko, Yuko Shiroyanagi, Thomas Gramila, Loren Pfeiffer, Ken West The properties of the 2-dimensional electron gas (2DEG) have been studied extensively in the integer and fractional quantum Hall regimes. Much less is understood about the 2DEG at intermediate fields, where thermal fluctuations are comparable to the size of the Landau-level spacing. We have explored this regime by measuring frictional drag, which probes electron-electron interactions, in a bilayer system at temperatures from 1.5K to 8.5K in fields smaller than 1T. In addition to an unusual overall field dependence, we have discovered a series of oscillations in the drag resistivity which are periodic in 1/B, but are distinct from variations in the density of states, as seen in Shubnikov-de Haas oscillations. These novel magnetodrag oscillations are consistent with a phonon mediated interlayer momentum transfer mechanism. Resonances are observed when the frequency of $2k_F$ phonons matches an integer multiple of the cyclotron frequency, and they are suppressed as the densities of the two layers are mismatched. [Preview Abstract] |
Tuesday, March 11, 2008 12:39PM - 12:51PM |
J37.00008: Unusual quantum Hall Ferromagnetism in Bilayer Graphene Barlas Yafis, Rene Cote, Allan MacDonald Bilayer graphene has eight nearly degenerate Landau levels at the Dirac point compared to the four nearly degenerate levels which occur in an isolated layer. The additional degeneracy is associated with the degeneracy of $n=0$ and $n=1$ orbital Landau level states in the bilayer case and adds a Landau level pseudospin degree of freedom to the spin and valley pseudospins present in the single layer case. We predict broken symmetry states which lift the associated degeneracies with a Hunds rule which orders spin first, then valley, and finally the Landau-level pseudospin. It follows that the Landau level pseudospin orders at all odd total filling factors. We find unusual collective modes which are not gapped even though the system has uniaxial anisotropy, and a $q^{3/2}$ dispersion at small $q$ because the divergence of the pseudospin magnetization produces charges with long-range Coulomb interactions. Because of the charge carried by these collective modes, they are dipole active. We predict unusual intra-Landau-level contributions to the cyclotron resonance signal. We will also discuss unusual properties of the Skyrmions spin-textures of these quantum Hall ferromagnets. [Preview Abstract] |
Tuesday, March 11, 2008 12:51PM - 1:03PM |
J37.00009: Symmetry Broken States of Dirac Fermions in Graphene with A Partially Filled High Landau Level Hao Wang, D.N. Sheng, F.D.M. Haldane We report on numerical study of symmetry broken states of the Dirac electrons in partially filled N=3 Landau level (LL) in graphene. At half-filling, the static density-density correlation function displays sharp peaks at nonzero wavevectors. Finite-size scaling shows that the peak value grows with electron number and diverges in the thermodynamic limit, indicating an instability toward a charge density wave. A weak disorder potential plays the role of selecting a symmetry broken stripe phase as the ground state from the nearly degenerated low-energy manifold. Such a quantum phase is experimentally observable through transport measurements. Associated with the special wavefunctions of the Dirac LL, both stripe and bubble phases become possible candidates for the ground state at lower filling numbers in the N=3 LL. We have also studied the ground state evolution and quantum phase transitions of the 2D electron gas at half-filled N=1 LL under an additional repulsive three-body interaction. [Preview Abstract] |
Tuesday, March 11, 2008 1:03PM - 1:15PM |
J37.00010: Midgap states and the fractional quantum Hall regime in graphene quantum dots Igor Romanovsky, Constantine Yannouleas, Uzi Landman Graphene quantum dots (QDs) with zigzag edges exhibit midgap single-paticle states associated with such edges. At zero magnetic field ($B$), these states form a manifold of degenerate states similar to the lowest Landau level that forms in semiconductor QDs at high $B$. It has been recently suggested\footnote{B. Wunsch {\it et al.\/}, arXiv:0707.2948v2} that the midgap-state manifold in graphene dots can support correlated many-body states similar to the rotating-electron-molecule (REM) states (also referred to as rotating Wigner crystallites) that are well known in semiconductor QDs at high $B$.\footnote{C. Yannouleas and U. Landman, Rep. Prog. Phys. {\bf 70}, 2067 (2007)} Here, we will report systematic exact-diagonalization calculations (for $N=4-10$ QD electrons) describing the REM states in graphene QDs. We anticipate that the graphene REM states exhibit for all $N$ a single polygonal ring of localized electrons, in contrast to the multiple polygonal-ring configurations known from semiconductor QDs. [Preview Abstract] |
Tuesday, March 11, 2008 1:15PM - 1:27PM |
J37.00011: SO(3) theory of the integer quantum Hall effect in graphene Igor Herbut I will discuss the Hubbard model of graphene in an external magnetic field. In the continuum limit and in the Hartree-Fock approximation, the ground state energy at half filling becomes nearly symmetric under rotations of the three-component vector (N1, N2, m), with the first two components representing the Neel order parameter orthogonal to and the third component the magnetization parallel with the external magnetic field. When the symmetry breaking effects arising from the lattice, Zeeman coupling, and higher Landau levels are included the system develops a quantum critical point at which the antiferromagnetic order disappears and the magnetization has a kink. The observed incompressible states at filling factor one are argued to arise due to a finite third component of the Neel order parameter at these electron densities. Recent experiments appear consistent with N1=N2=0, and N3 finite, at the filling factors zero and one, respectively. I. F. Herbut, Phys Rev. B vol. 76, 085432 (2007); ibid. vol. 75, 165411 (2007). [Preview Abstract] |
Tuesday, March 11, 2008 1:27PM - 1:39PM |
J37.00012: Phase Diagram for Quantum Hall States in Graphene Jianhui Wang, Andrew Iyengar, Herb Fertig, Luis Brey We investigate integral and half-integral fillings (uniform and unidimensional stripe states respectively) for graphene using the Hartree-Fock approximation in the continuum limit. For fixed filling factor, the ratio between the scales of the Coulomb interaction and Landau level spacing $g=(e^{2}/ \epsilon\ell)/(\hbar v_{F}/\ell)$ is a field independent constant. However, when B decreases, the number of filled negative Landau levels increases, which surprisingly turns out to ${\it decrease}$ the amount of Landau level mixing. The resulting states at fixed filling factor $\nu$ (for $\nu$ not too big) has very little Landau level mixing even at arbitrary weak magnetic fields. This means many different phases should emanate from the origin of the phase diagram when plotted in the B v.s. density plane, in contrast to regular 2 dimensional electron gas which has a Wigner crystal state in the vicinity of the same point. The stripe amplitudes scale roughly as B, so that the density waves ``evaporate'' continuously as $B\rightarrow0$. These results will be compared to those of tight binding calculations. [Preview Abstract] |
Tuesday, March 11, 2008 1:39PM - 1:51PM |
J37.00013: Chirality Sum Rule in Graphene Multilayers Hongki Min, Allan H. MacDonald We show that the low energy electronic structure of arbitrarily stacked graphene multilayers with nearest-neighbor interlayer tunneling consists solely of chiral pseudospin doublets. Although the number of doublets in an $N$-layer system depends on the stacking sequence, the pseudospin chirality sum is always $N$. It follows that $N$-layer stacks always have $N$ distinct Landau levels at $E=0$ for each spin and valley, and that the quantized Hall conductivity $\sigma_{xy} = \pm(4 e^2/h)(N/2+n)$ where $n$ is a non-negative integer. [Preview Abstract] |
Tuesday, March 11, 2008 1:51PM - 2:03PM |
J37.00014: Valley-skyrmion and Wigner crystals in graphene Rene Cote, Jean-Francois Jobidon, Herbert A. Fertig At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime })$ about which the electronic spectra of the valence and conduction bands have a linear dispersion relation. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level $N=0$ having zero weight on the $B(A)$ sublattice for the $K(K^{\prime })$ valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of skyrmion crystals in the Hartree-Fock approximation. We show that skyrmion crystals have lower energy than Wigner crystals i.e. crystals with no pseudospin texture. The collective mode spectrum of the valley- skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and skyrmion crystals. [Preview Abstract] |
Tuesday, March 11, 2008 2:03PM - 2:15PM |
J37.00015: Lattice-Induced Double-Valley Degeneracy Lifting in Graphene by a Magnetic Field I.A. Luk`yanchuk, A.M. Bratkovsky We show that the recently discovered double-valley splitting of the low-lying Landau level(s) in the Quantum Hall Effect in graphene can be explained as a {\em perturbative} orbital interaction of intra- and inter-valley microscopic orbital currents with a magnetic field. This effect is provided by the translationally-non-invariant terms corresponding to graphene's crystallographic honeycomb symmetry but do not exist in the relativistic theory of massless Dirac Fermions in Quantum Electrodynamics. We discuss recent data in view of these results [1]. [1] I.A. Luk'yanchuk and A.M. Bratkovsky, arXiv:0707.0466 (2007) [Preview Abstract] |
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