Bulletin of the American Physical Society
APS March Meeting 2017
Volume 62, Number 4
Monday–Friday, March 13–17, 2017; New Orleans, Louisiana
Session A27: Fractional Quantum Hall Effect I. |
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Sponsoring Units: FIAP Room: 290 |
Monday, March 13, 2017 8:00AM - 8:12AM |
A27.00001: Universal DC Hall conductivity of Jain's state $\nu=\frac{N}{2N\pm1}$ Dung Nguyen, Dam Son We present the Fermi-liquid theory of the fractional quantum Hall effect to describe Jain's states with filling fraction $\nu=\frac{N}{2N\pm1}$, that are near half filling. We derive the DC Hall conductivity $\sigma^H(\mathbf{k})$ in closed form within the validity of our model. The results show that, without long range interaction, DC Hall conductivity has the universal form which doesn't depend on the detail of short range Landau's parameters $F_n$. When long range interaction is included, DC Hall conductivity depends on both long range interaction and Landau's parameters. We also analyze the relation between DC Hall conductivity and static structure factor. [Preview Abstract] |
Monday, March 13, 2017 8:12AM - 8:24AM |
A27.00002: Modular Transformations of Fermionic Fractional Quantum Hall Phases Alan Tran, Parsa Bonderson, Meng Cheng The universal properties (fusion and braiding) of quasiparticles in bosonic topologically ordered phases can be described by unitary modular tensor categoreis (UMTCs). The modular transformations of such systems on surfaces, such as a torus, are directly related to the mutual and self statistics of the quasiparticles. Fermionic topologically ordered phases similarly have associated UMTCs, which describe the universal properties of not just their quasiparticles, but also their fermionic vortices. We explain the relation of the fermionic modular (spin-modular) transformations to the corresponding UMTC data. We validate this prescription for a variety of fractional quantum Hall states by explicitly computing the fermionic modular transformations on the FQH wavefunctions. [Preview Abstract] |
Monday, March 13, 2017 8:24AM - 8:36AM |
A27.00003: Central Charge from Adiabatic Transport of Cusp Singularities in the Quantum Hall Effect Tankut Can We identify the central charge of fractional quantum Hall (FQH) states by studying adiabatic evolution in the parameter space of singular surfaces. In particular, we study FQH states on a punctured sphere and compute the Berry curvature under adiabatic motion of cusp singularities at the punctures. The Berry curvature is finite in the large N limit and completely controlled by the central charge, a robust geometric response coefficient. [Preview Abstract] |
Monday, March 13, 2017 8:36AM - 8:48AM |
A27.00004: Coulomb anomaly in the tunneling between compressible quantum Hall bilayers: the role of partial spin polarization Patrick Lee, Debanjan Chowdhury, Brian Skinner Tunneling of electrons into a two-dimensional electron system is known to exhibit a "Coulomb anomaly", in which the tunneling conductance vanishes at low energy due to a many-body interaction effect. In this way, measurement of the Coulomb anomaly can be used as a probe of many-body correlations. Here we discuss the tunneling conductance between two identical copies of the half-filled Landau level, for which the Coulomb anomaly arises from many-body correlations between composite Fermions. We focus in particular on the dependence of the conductance on the spin polarization in the electron system and on the layer separation, and we compare with recent experiments [1]. [1] J. Eisenstein et al., PRB 94, 125409 (2016). [Preview Abstract] |
Monday, March 13, 2017 8:48AM - 9:00AM |
A27.00005: Collective mode excitations of the $\nu=0$ QH state in graphene Yafis Barlas In high magnetic fields, graphene at the charge neutrality point ($\nu=0$) becomes an insulator. This is due to valley-dependent interactions within the zeroth Landau level (LL) that result in canted anti-ferromagnetic (CAF) spin ordering. As the Zeeman energy is increased, the CAF state transitions to a quantum Hall ferromagnetic state, with symmetry protected counter-propagating edge modes. This non-local signal has been verified in tilted-fields. Using a microscopic model with valley-dependent interactions in the zeroth LL, we derive an effective $SU(4)$ spin model Hamiltonian for $\nu=0$ QH state. We use this model to calculate the collective valley and spin excitations in the $\nu =0$ QH state. In the long wavelength limit, the collective spin and valley excitation energies scale as $\omega \sim v q $, in the $\nu =0 $ CAF state. We also calculate the energy of the neutral topological spin and valley Skyrmions in the $\nu =0$ QH state. The role of the collective mode excitation on the spin and valley transport in the $\nu=0$ insulating QH state will be addressed. [Preview Abstract] |
Monday, March 13, 2017 9:00AM - 9:12AM |
A27.00006: Lattice Monte Carlo Study of Composite Fermion Liquid (CFL) State Berry Phase on Torus Jie Wang, Scott Geraedts, E. H. Rezayi, F. D. M. Haldane The CFL state is a gapless state that can occur at Landau-level filling $1/m$ when $m$ is even, and an emergent Fermi surface for composite fermions forms. The Berry phase associated with moving one composite fermion around Fermi surface is predicted from the theory of the anomalous quantum Hall effect in two-dimensional metals to determine the Hall conductivity. We examine this quantity in the CFL state using a model wavefunction (on the torus) that explicitly exhibits a Fermi surface, and has been show to give very good agreement with states found in exact diagonalization (ED) studies. We have implemented a many-body analog of the k-space Berry curvature formalism that generalized the one-body form based on the periodic part of a single-particle Bloch wavefunction. This model wavefunction is studied by the Monte Carlo method for much larger sizes than can be studied using ED, based on a new mathematically-exact discretized formulation of holomorphic states on the torus which greatly simplifies the Monte-Carlo studies. [Preview Abstract] |
Monday, March 13, 2017 9:12AM - 9:24AM |
A27.00007: Quantitative Theory of Tunneling in a Bilayer System in a Strong Magnetic Field Yuhe Zhang, Jainendra K. Jain, J. P. Eisenstein Tunnel transport in a bilayer system provides valuable insight into the strongly correlated non-Fermi liquid nature of the composite fermion Fermi sea and FQH states. We identify the peak current with a ``hard" interlayer exciton, in which the tunneling electron is uncorrelated, modulo the Pauli avoidance, with the background state. This identification is supported by an accurate quantitative agreement of the calculated energy of the hard exciton with the experimentally measured value. The dependence of this energy on an additional parallel magnetic field is also quantitatively explained in terms of a lateral offset in the positions of the electron and hole of the exciton. We further estimate the critical Zeeman energy where transition occurs from a fully spin polarized composite fermion Fermi sea to a partially spin polarized one, carefully incorporating corrections due to finite width and Landau level mixing, and find it to be in very good agreement with the Zeeman energy where a qualitative change has been observed at small bias voltage in a recent experiment [Eisenstein {\em et al.}, Phys. Rev. B {\bf 94}, 125409 (2016)]. [Preview Abstract] |
Monday, March 13, 2017 9:24AM - 9:36AM |
A27.00008: Magnetic Field Induced Interlayer Charge Transfer in Interacting Electron Bilayer Systems Hao Deng, Yang Liu, Loren N. Pfeiffer, Kenneth W. West, Kirk W. Baldwin, Mansour Shayegan We report that the layer densities of an asymmetric electron bilayer system change with the sweeping of perpendicular magnetic field. By monitoring each layer's density independently, we observe oscillations of layer densities as a function of magnetic field. The interlayer charge transfer can be partially explained by the alignment of Landau levels in different layers. A simple calculation based on this mechanism qualitatively explains the experimental results; the discrepancy, however, points to the role of many-body interaction in bilayer systems. This interlayer charge transfer provides a means to study the interlayer interaction in the presence of high magnetic fields. Work supported by the NSF (Grants DMR-1305691, ECCS-1508925, and MRSEC DMR-1420541), the DOE Basic Energy Sciences (Grant DE-FG02-00-ER45841), the Gordon and Betty Moore Foundation (Grant GBMF4420), and the Keck Foundation. [Preview Abstract] |
Monday, March 13, 2017 9:36AM - 9:48AM |
A27.00009: Design rules for modulation doped AlAs quantum wells Yoon Jang Chung, K. W. Baldwin, K. W. West, D. Kamburov, M. Shayegan, L. N. Pfeiffer AlxGa1-xAs/AlAs/AlxGa1-xAs quantum wells were grown with various barrier compositions ranging from x$=$0.26 to x$=$0.8. We investigate the modulation doping characteristics of the samples by magneto-transport measurements. The carrier concentration in the well peaks near the barrier alloy fraction of x$=$0.26 in the dark and near x$=$0.38 after illumination with a red LED. This behavior is consistent with the results in a separate study for AlxGa1-xAs/GaAs/AlxGa1-xAs quantum wells in the range of x$=$0.26 to x$=$1.0. We show from a charge transfer model that the calculated energy difference between the conduction band offset at the well interface and the donor energy level, $\Delta $EC-ED, coincides for the two types of wells. This implies that, despite the differing positions of the conduction band minimum for the GaAs and AlAs wells, the doping of either well is governed by the electronic properties of the barrier. Based on this knowledge we designed high quality AlAs quantum wells with low (1 x 10$^{11}$ cm$^{-2})$ and high (3 x 10$^{11}$ cm$^{-2})$ density, and the magneto-transport data show clear signals of the fractional quantum Hall effect (2/3, 3/5, 4/7 for low density and 5/3, 8/5 for high density). [Preview Abstract] |
Monday, March 13, 2017 9:48AM - 10:00AM |
A27.00010: Abstract Withdrawn
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Monday, March 13, 2017 10:00AM - 10:12AM |
A27.00011: On the effective theory of quantum Hall edge Jimmy Hutasoit, Oleksandr Gamayun, Vadim Cheianov The edge of a quantum Hall state can be described by a chiral conformal field theory (CFT). As this is an effective theory, one must also consider deformations to the chiral CFT. I will revisit the formulation of perturbation theory in the presence of such deformations by considering two examples that exhibit exact solution. An ubiquitous feature of such an effective edge theory is that it exhibits emergent symmetries that were not parts of the underlying Hamiltonian. As a result, electron operators constructed out of the effective degrees of freedom form multiplets transforming under the emergent symmetry. Even though the deformations mentioned above can break the emergent symmetry, it is interesting to explicitly construct edge theories with exactly one electron operator. This is related to an open problem in classifying non-trivial CFT simple current with trivial tensor structure. [Preview Abstract] |
Monday, March 13, 2017 10:12AM - 10:24AM |
A27.00012: Pairing of particle-hole symmetric composite fermions in half-filled Landau level Zhiqiang Wang, Sudip Chakravarty In a recent proposal of the half-filled Landau level, the composite fermions are taken to be Dirac particles and particle-hole symmetric. Cooper pairing of these composite fermions in different angular momentum channels, $\ell$, can give rise to different kinds of Pfaffian states. In addition to the well-known Moore-Read Pfaffian and anti-Pfaffian states, a new putative particle-hole symmetric Pfaffian state, corresponding to the $s-$wave pairing channel, was also proposed. However, the possible underlying pairing mechanism is not clear at all. In this work we provide a specific pairing mechanism for realizing some of these Pfaffian states. We show that there can be nonzero pairing in angular momentum channels $|\ell|\ge 1$ depending on the magnitude of a coupling constant. There is a quantum phase transition from the Dirac composite Fermi-liquid state to Cooper pairing states in angular momentum channels $|\ell|\ge 1$ as the coupling constant is tuned across its critical point value. Surprisingly the particle-hole symmetric $\ell=0$ channel pairing turns out to be impossible irrespective of the size of the coupling constant. [Preview Abstract] |
Monday, March 13, 2017 10:24AM - 10:36AM |
A27.00013: Bosonic Analogue of Dirac Composite Fermi Liquid David Mross, Jason Alicea, Olexei Motrunich The status of particle-hole symmetry has long posed a challenge to the theory of the quantum Hall effect. It is expected to be present in the half-filled Landau level, but is absent in the conventional field theory, i.e., the composite Fermi liquid. Recently, Son proposed an alternative, explicitly particle-hole symmetric theory which features composite fermions that exhibit a Dirac dispersion. In my talk, I will introduce an analogous particle-hole-symmetric metallic state of bosons at odd-integer filling. This state hosts composite fermions whose energy dispersion features a quadratic band touching and corresponding $2π$ Berry flux, protected by particle-hole and discrete rotation symmetries. As in the Dirac composite Fermi liquid introduced by Son, breaking particle-hole symmetry recovers the familiar Chern-Simons theory. I will discuss realizations of this phase both in 2D and on bosonic topological insulator surfaces, as well as its signatures in experiments and simulations. [Preview Abstract] |
Monday, March 13, 2017 10:36AM - 10:48AM |
A27.00014: Quasiparticles Charge in Hole-States of the FQHE Moty Heiblum, Mitali Banerjee, Vladimir Umansky Current and energy flow in fractional hole-states of the first Landau level; namely, with filling $\nu $in the range 1/2\textless $\nu $\textless 1, is much more complicated than in the particle-states (Laughlin's, 1/2\textgreater $\nu $\textgreater 0). In the hole-states topological counter-propagating charge and/or neutral edge-modes coexist, moving charge and energy downstream as well as upstream. While their thermal conductance [1] and the proliferation of upstream neutral modes were recently reported [2,3], their partitioned quasiparticle charge was studied only in $\nu =$2/3 [3]. Studying the main hole-states $\nu \quad =$2/3, 3/5, and 4/7, we found a universal behavior. The `apparent partitioned charge' (by a QPC) was always $e^{\ast }=\nu e$, as deduced from shot-noise measurements. The surprising part was that the Fano factor was not due to charge partitioning; but was directly related to the fragmentation of upstream neutral modes to particle-hole pairs. The fragmentation led to current fluctuations with the observed, quantized, Fano factor [3]. [1] M. Banerjee et al., To be published. [2] H. Inoue et al., Nat. Comm. 5, 4067 (2014). [3] R. Sabo et al., arXiv:1603.06908. [Preview Abstract] |
Monday, March 13, 2017 10:48AM - 11:00AM |
A27.00015: Fluid dynamics with Hall viscosity: variational approach Alexander Abanov, Gustavo Monteiro Hall (odd) viscosity is a non-dissipative part of fluid stress tensor allowed in isotropic two-dimensional fluids with broken parity. In this work we formulate the variational principle for hydrodynamics of compressible fluids with Hall viscosity in arbitrary geometric and electromagnetic background fields as well as study the responses of such fluids to external perturbations. Using the developed variational approach we consider various constraints on fluid dynamics. Motivated by dynamics of quantum Hall droplets, we impose for example a constraint relating fluid vorticity to its density as suggested in [1]. We also consider various boundary conditions and applications of variational principle in studies of fluids with Hall viscosity. [1] M. Stone. Superfluid dynamics of the fractional quantum Hall state. Phys. Rev. B, 42, 212–217 (1990). [Preview Abstract] |
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