Bulletin of the American Physical Society
APS March Meeting 2013
Volume 58, Number 1
Monday–Friday, March 18–22, 2013; Baltimore, Maryland
Session B42: Quantum Hall Effect: Edges, Interferometry, & nu = 5/2 |
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Sponsoring Units: FIAP Chair: Sriram Ganeshan, University of Maryland Room: Hilton Baltimore Holiday Ballroom 3 |
Monday, March 18, 2013 11:15AM - 11:27AM |
B42.00001: Spin and charge distribution symmetry dependence of stripe phases in two-dimensional electron systems confined to wide quantum wells Yang Liu, Dobromir Kamburov, Mansour Shayegan, Loren Pfeiffer, Ken West, Kirk Baldwin When a spin-split $N\le 2$ Landau level is half filled, the two-dimensional electron system (2DES) is expected to break the rotational symmetry by forming a unidirectional charge density wave, the so-called stripe phase. The stripes are known to rotate from the ``normal'' ([110]) direction to the ``abnormal'' ($[1\bar{1}0]$) direction when the 2DES density is raised above a critical density. We report a study of the evolution of the stripe phase orientation near Landau level filling factors $\nu = 13/2$ and 15/2 when $E_F$ lies in the two, spin-split, $N = 2$ Landau levels of the symmetric subband (the S2$\uparrow$ and S2$\downarrow$ levels) while the $N = 0$ Landau levels of the antisymmetric subband are fully occupied. We find that when $E_F$ lies in S2$\downarrow$ the stripes are always formed along the ``normal'' direction. But, when $E_F$ lies in the S2$\uparrow$ level, the orientation of the stripes can rotate to be along the ``abnormal'' direction at high densities. At a density where the stripe phase at $\nu = 13/2$ is along the ``abnormal'' direction, we can rotate it back to the normal direction by making the charge distribution asymmetric while keeping the density fixed. [Preview Abstract] |
Monday, March 18, 2013 11:27AM - 11:39AM |
B42.00002: Distinguishing Particle-Hole Conjugated Fractional Quantum Hall States Using Quantum Dot Mediated Edge Transport Hsin-Hua Lai, Kun Yang We first study the edge transport in the $\nu=1/3$ and $\nu=2/3$ Fractional Quantum Hall bars mediated by a $\nu=1$ quantum dot. We conclude that the $\nu=1/3$ and $\nu=2/3$ systems show different $1/3$-charged quasi-particle tunneling exponents. When the quantum dot becomes large, its edge states join those of the original Hall bar to reconstruct the edge state configurations. In the disorder-irrelevant phase, the two-terminal conductance of the original $\nu=1/3$ system vanishes at zero temperature, while that of the $\nu=2/3$ case is finite. In the disorder-dominated phase, the two-terminal conductance of $\nu=1/3$ system is $(1/5)e^2/h$ while that of $\nu=2/3$ system is $(1/2)e^2/h$. We further apply the same idea to the $\nu=5/2$ system which realizes either Pfaffian or anti-Pfaffian states. By engineering a central $\nu=3$ quantum dot in the $\nu=5/2$ Hall bar, we study the charged quasi-particle tunneling effects and conclude that the Pfaffian and anti-Pfaffian states show different quasi-particle tunneling exponents. If the quantum dot is large enough for its edge states joining with those of the original Hall bar, the two-terminal conductance of Pfaffian state can be $G_{Pf}\rightarrow 2 e^2/h$ while that of anti-Pfaffian state is higher, $G_{aPf} > 2 e^2/h$. [Preview Abstract] |
Monday, March 18, 2013 11:39AM - 11:51AM |
B42.00003: Intrinsic edge dipole moment of incompressible fractional quantum Hall ground states YeJe Park, F.D.M. Haldane The edges of incompressible fractional quantum Hall (FQH) fluids have a characteristic dipole moment related to their Hall viscosity, which can be split into two separate contributions: a (trivial) contribution from the Landau orbit (common to all FQH fluids in the same Landau level, and a (non-trivial) guiding-center contribution that depends on the FQH state. Using the model wave functions for (fermonic and bosonic) Laughlin states ($\nu$ = 1/2, 1/3, 1/4), and Moore-Read states ($\nu$ = 2/2, 2/4) expressed as Jack polynomials, we obtained the guiding-center occupation number distributions $n(k)$ of ``Landau-gauge" basis states with $k$ near the edge $``\nu^{-1}k_F"$ of a FQH fluid in cylindrical geometries of various circumferences, and verified the ``Luttinger" and ``edge-dipole" sum rule. The edge-dipole moments of the FQH fluids were expressed as a combination of quantized quantities: electric charge e, ``guiding center spin" s and number of fluxes per ``composite boson'' q in [F. D. M. Haldane, arXiv:0906.1854 (2009)]. Our work provides a numerical verification of the prediction. The edge dipole experiences a force due to the gradient of electric field perpendicular to the edge, and the force is balanced by stress from the ``guiding center Hall viscosity". [Preview Abstract] |
Monday, March 18, 2013 11:51AM - 12:03PM |
B42.00004: FQHE interferometer in strong tunneling regime: The role of compactness of edge fields Sriram Ganeshan, Alexander Abanov, Dmitri Averin The defining feature of quantum Hall states is the existence of topologically protected massless edge states. These states are believed to be effectively described by a theory of chiral bosons also known as the one-dimensional chiral Luttinger Liquid. The tunneling experiments provide one of the natural ways to probe these edge states. In this work, we consider multiple-point tunneling in the interferometers formed between edges of electron liquids with in general different filling factors in the regime of the Fractional Quantum Hall effect (FQHE). We derive an effective matrix Caldeira-Leggett model for the multiple tunneling contacts connecting the chiral single-mode FQHE edges. We show that the compactness of the Wen-Fr\"ohlich chiral boson fields describing the FQHE edge modes plays a crucial role in defining strong (quasiparticle) tunneling regime. We also show that the compactness condition results in electron periodicity for quasiparticle tunneling with respect to adiabatic variation of flux. [Preview Abstract] |
Monday, March 18, 2013 12:03PM - 12:15PM |
B42.00005: Edge properties of principal fractional quantum Hall states in the cylinder geometry Paul Soule, Thierry Jolicoeur We study fractional quantum Hall states in the cylinder geometry with open boundaries. We focus on principal fermionic $\nu = 1/3$ and bosonic $\nu = 1/2$ fractions in the case of hard-core interactions. The gap behavior as a function of the cylinder radius is analyzed. By adding enough orbitals to allow for edge modes, we show that it is possible to measure the Luttinger parameter of the nonchiral liquid formed by the combination of the two counterpropagating edges when we add a small confining potential. Although we measure a Luttinger exponent consistent with the chiral Luttinger theory prediction for the full hard-core interaction, the exponent remains nontrivial in the Tao-Thouless limit as well as for simple truncated states that can be constructed on the cylinder. If the radius of the cylinder is taken to infinity, the problem becomes a Tonks-Girardeau one-dimensional interacting gas in Fermi and Bose cases. Finally, we show that the Tao-Thouless and truncated states have an edge electron propagator, which decays spatially with a Fermi-liquid exponent, even if the energy spectrum can still be described by a nontrivial Luttinger parameter. [Preview Abstract] |
Monday, March 18, 2013 12:15PM - 12:27PM |
B42.00006: Edge spin excitations and reconstructions of spin-polarized and spin-unpolarized quantum Hall liquids Yuhui Zhang, Kun Yang We study the effect of electron-electron interaction on the charge and spin structures at the edge of quantum Hall liquids, under three different kinds of confining potentials. Our exact diagonalization calculation for small systems indicates that the low energy excitations of $\nu=1$ ferromagnetic state are bosonic edge spin waves. Instabilities of $\nu=1$ ferromagnetic state with altering confinement strength result from the softening of these edge spin waves, and formation of edge spin textures. In $\nu\la 2$ regime, exact diagonalization on edge electron systems indicates that compact Hartree-Fock states with different total spin always become ground states in some regions of parameter space, and the ground states appear in between two compact states are their edge spin waves. The initial $\nu=2$ instability is toward the compact state with total spin $1$. Larger systems are studied using a microscopic trial wave functions, and some quantitative predictions on the edge instabilities for a certain type of confining potential are reached in the thermodynamic limit. In fractional quantum Hall regime, $\nu= 1/3$ polarized and $\nu=2/3$, $2/5$ unpolarized states' low energy edge states are also obtained by exact diagonalization for small systems. [Preview Abstract] |
Monday, March 18, 2013 12:27PM - 12:39PM |
B42.00007: Quantum Hall Line Junctions under In-Plane Magnetic Fields P. Jiang, I. Yang, W.-H. Wang, S.-C. Yu, L.N. Pfeiffer, K.W. West, K.W. Baldwin, W. Kang Study of tunneling between two antiparallel quantum Hall edge states under the influence of in-plane magnetic field will be presented. Previously quantum Hall line junctions were shown to have highly correlated behavior consistent with formation of coupled Luttinger liquids. Power-law energy dependence observed in the tunneling conductance supports realization of the Luttinger-liquid correlation of the coupled edge states. Under the presence of in-plane magnetic field, the tunnel spectrum is found to evolve with emergence of novel features. Systematic evolution of these features are studied with in-plane fields either parallel or perpendicular to the line junction. We discuss these results in terms of the presence of additional low-excitation modes detected through momentum-resolved tunneling. [Preview Abstract] |
Monday, March 18, 2013 12:39PM - 12:51PM |
B42.00008: X-ray edge singularity in the visibility of the Aharonov-Bohm oscillations in a quantum Hall interferometer Iurii Chernii, Ivan Levkivskyi, Eugene Sukhorukov We consider a quantum dot strongly interacting with several quantum Hall edge channels. One of the channels is an arm of an electronic Mach Zender interferometer, and another one is coupled to the dot via weak tunneling. Fluctuations of the charge in the quantum dot lead to dephasing of the interfering electrons. Such processes have been studied extensively, however the effects of backaction were either not considered at all, or taken into account perturbatively in the interaction strength. We show that there are regimes where tunneling itself is mainly induced by the non-equilibrium noise in the interferometer at finite bias. Importantly, this backaction effect is non-perturbative and can not be neglected. The problem of tunneling induced by the non-equilibrium noise demonstrates equivalence to the X-Ray edge singularity problem, and the tunneling rates are found to be a power-low functions of the detuning between the dot energy level and the Fermi energy. Consequently, the visibility of the interference pattern shows a crossover between the two lorentzian-type functions with different effective temperatures at small and large energies. The two temperatures are proportional to the noise temperature with a coefficients depending on the interaction strength. [Preview Abstract] |
Monday, March 18, 2013 12:51PM - 1:03PM |
B42.00009: Backaction Dephasing Induced by a Quantum Dot Detector Toshihiro Kubo, Yasuhiro Tokura We theoretically investigate the backaction dephasing by a quantum dot detector (QDD) that couples to the quantum dot embedded in one arm of Aharonov-Bohm (AB) interferometer. We employ the nonequilibrium second-order perturbation theory and provide an analytical expression for the backaction dephasing rate, which characterizes the disturbance induced by coupling with an environment containing QDD. We show that the origin of backaction dephasing is a charge noise of QDD. In the linear transport regime through a QDD, this backaction dephasing induced by charge noise can be explained as a relaxation by an inelastic electron-electron scattering within the framework of Fermi liquid theory. In the low bias voltage regime, the increase or decrease of dephasing rate depends on the QDD energy level, the linewidth functions, and how to apply the bias voltage. Unlike quantum point contact detector, the dephasing rate would be insensitive to the bias voltage in a high bias voltage regime since the charge noise of a QDD is saturated. Moreover, such behaviors can be verified in terms of the visibility of AB oscillations by changing the bias voltage across the QDD. [Preview Abstract] |
Monday, March 18, 2013 1:03PM - 1:15PM |
B42.00010: Visibility recovery by strong interaction in an electronic Mach-Zehnder interferometer Soo-Yong Lee, Hyun-Woo Lee, Heung-Sun Sim We study the evolution of a single-electron packet of Lorentzian shape along an edge of the integer quantum Hall regime or in a Mach-Zehnder interferometer, considering a capacitive Coulomb interaction and using a bosonization approach. When the packet propagates along a chiral quantum Hall edge, we find that its electron density profile becomes more distorted from Lorentzian due to the generation of electron-hole excitations, as the interaction strength increases yet stays in a weak interaction regime. However, as the interaction strength becomes larger and enters a strong interaction regime, the distortion becomes weaker and eventually the Lorentzian packet shape is recovered. The recovery of the packet shape leads to an interesting feature of the interference visibility of the symmetric Mach-Zehnder interferometer whose two arms have the same interaction strength. As the interaction strength increases, the visibility decreases from the maximum value in the weak interaction regime, and then increases to the maximum value in the strong interaction regime. We argue that this counter-intuitive result also occurs under other types of interactions. [Preview Abstract] |
Monday, March 18, 2013 1:15PM - 1:27PM |
B42.00011: Coupling a quantum Hall droplet to a microwave transmission line Jennifer Cano, Chetan Nayak Electromagnetically coupling a quantum Hall droplet to a microwave transmission line establishes a realm of new experiments that might provide a more direct measurement of certain physical properties. Specifically, peaks in the absorption spectrum would occur at multiples of the ratio of the edge velocity to the perimeter of the droplet, potentially offering a more precise measurement of the velocity of edge modes than the few existing measurements. If the droplet is at filling fraction 5/2 and deformed to allowing tunneling between edges, additional peaks would emerge corresponding to the velocity of the neutral mode, which has never before been measured. In addition, the set-up could be used as an interferometer in fractional quantum Hall states by observing shifts in the magnitude of the absorption peak at fixed frequency as the number of quasiparticles is varied via the magnetic field. This would be complementary to existing interferometry measurements of fractional statistics. [Preview Abstract] |
Monday, March 18, 2013 1:27PM - 1:39PM |
B42.00012: Interactions in quantum Hall edge channels at filling fraction 2 Pascal Degiovanni, Erwann Bocquillon, Vincent Freulon, Charles Grenier, Jean-Marc Berroir, Bernard Pla\c{c}ais, Antonella Cavanna, Yong Jin, Gwendal F\`eve Coulomb interactions play a major role in one dimensional electronic transport. They modify the nature of the elementary excitations from Landau quasiparticles in higher dimensions to collective excitations in 1D. We report here on the direct observation of the collective neutral and charge modes of the two chiral co-propagating edge channels of opposite spins of the quantum Hall effect at filling factor $\nu=2$. Generating a charge density wave at frequency $f$ in the outer channel, we measure the current induced by inter-channel Coulomb interaction in the inner channel after a 3 microns propagation length. Varying the driving frequency from 0.7 to 11 GHz, we observe damped oscillations in the induced current that results from the phase shift between the fast charge and slow neutral eigenmodes. Measuring the dispersion relation and dissipation of the neutral mode from provides quantitative information on the scattering of quantum edge magnetoplasmons. We will then comment on the consequences of these results on quasi-particle relaxation and decoherence in the $\nu=2$ quantum Hall edge channel system. [Preview Abstract] |
Monday, March 18, 2013 1:39PM - 1:51PM |
B42.00013: Coherent Terahertz Magneto-Spectroscopy of High-Mobility Two-Dimensional Electron Gases Qi Zhang, Takashi Arikawa, Wei Pan, John Reno, John Watson, Michael Manfra, Junichiro Kono Landau-quantized high-mobility two-dimensional electron gases (2DEG) in GaAs quantum wells provide an ideal platform for studying and controlling the coherence of many-electron states. Here, we study the coherent dynamics of cyclotron resonance (CR) in a 2DEGin the terahertz range. It is well known that Kohn's theorem protects the CR frequency from the influence of electron-electron interactions, but how the coherence of CR decays via electron-electron interactions is an open question. Since the 1980s, studies have focused on CR decoherence time measurements, primarily using incoherent far-infrared spectroscopy, which fails to obtain the true CR linewidth due to the `saturation effect' in high-mobility systems. By using coherent time-domain magneto-terahertz spectroscopy, we have systematically studied the CR decoherence time in an ultrahigh-mobility 2DEG as a function of both temperature and magnetic field. These results show a clear saturation of the CR decoherence time at low temperature, which decreases monotonically with increasing magnetic field. No filling-factor-dependent oscillations of CR dephasing time have been observed. Possible CR decoherence mechanisms will be discussed in light of these new findings. [Preview Abstract] |
Monday, March 18, 2013 1:51PM - 2:03PM |
B42.00014: Influence of Device Geometry on Tunneling in $\nu$=5/2 Quantum Hall Liquid Guang Yang, Dmitri Feldman Two recent experiments [1,2] measured the temperature and voltage dependence of the tunneling current through a constriction in the $\nu$=5/2 quantum Hall liquid. The results led to conflicting conclusions about the nature of the 5/2 quantum Hall state. The results of Ref. [1] were interpreted as supporting the anti-Pfaffian non-Abelian state while the results of Ref. [2] suggested that the Abelian 331 state was more likely. Several different constriction geometries were used in Refs. [1,2]. We argue that in some of those geometries there is significant unscreened electrostatic interaction between segments of the quantum Hall edge on the different sides of the constriction. The Coulomb interaction affects the tunneling current. After the Coulomb corrections are taken into account, the results from all geometries agree and support the same 5/2 state.\\[4pt] [1] I. P. Radu, J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer, and K. W. West, Science 320, 899 (2008).\\[0pt] [2] X. Lin, C. Dillard, M. A. Kastner, L. N. Pfeiffer, and K. W. West, Phys. Rev. B 85, 165321 (2012). [Preview Abstract] |
Monday, March 18, 2013 2:03PM - 2:15PM |
B42.00015: Anomalous density dependence of the activation gap of $\nu =$5/2 fractional quantum Hall state at extremely large Landau level mixing Nodar Samkharadze, Michael Manfra, Loren Pfeiffer, Ken West, Gabor Csathy We have conducted a study of the density dependence of $\nu =$5/2 fractional quantum Hall state (FQHS) in the regime of extremely low densities, down to n$=$4.9x10\textasciicircum 10 cm\textasciicircum -2. In the density range accessed in our sample, the Landau level mixing parameter $\kappa $ spans the so far unexplored range 2.52\textless $\kappa $ \textless 2.82. Here we observe an anomalous dependence of the activation gap of $\nu =$5/2 FQHS on the carrier density. We discuss the possible origins of this unexpected behavior. N.S. and G.C. were supported by the NSF grant DMR-0907172 and DMR-1207375. K. West and L. Pfeiffer acknowledge the support of the Princeton NSF-MRSEC and the Moore Foundation. [Preview Abstract] |
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