Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session B5: Fractional Quantum Hall Effect II 
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Sponsoring Units: FIAP DCMP Chair: Johannes Pollanen, California Institute of Technology Room: Juan Gorman Room 005 
Monday, March 2, 2015 11:15AM  11:27AM 
B5.00001: Using Composite Fermions to Probe a Wigner Solid in 2D Hole Systems Insun Jo, Yang Liu, H. Deng, M. Shayegan, L. N. Pfeiffer, K. W. West, K. W. Baldwin We have studied a GaAs doublequantumwell structure that hosts an interacting, bilayer twodimensional hole system with a large density difference between the two layers. At very low temperatures and large perpendicular magnetic field, we expect the two layers to exhibit distinct manybody states of holes: The highdensity layer develops a Fermi sea of composite fermions when its last Landau Level is halffilled, while the holes in the lowdensity layer in the same magnetic field range are at very small fillings and should condense into a Wigner crystal. Via measuring the magnetoresistance of the bilayer system, we monitor signatures of the Wigner crystallization and melting [Preview Abstract] 

B5.00002: ABSTRACT WITHDRAWN 
Monday, March 2, 2015 11:39AM  11:51AM 
B5.00003: Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect Andrey Gromov, Alexander Abanov, Gil Young Cho, Yizhi You, Eduardo Fradkin While the classical ChernSimons theory is topological, it's quantum version is not as it depends on the metric of the base manifold through the path integral measure. This phenomenon is known as the framing anomaly. It is shown that accounting for the framing anomaly of the quantum ChernSimons theory is essential to obtain the correct gravitational linear response functions of fractional quantum Hall systems (FQH). In the lowest order in gradients the effective action includes ChernSimons, WenZee and gravitational ChernSimons terms. The latter term has a contribution from the framing anomaly which fixes the value of thermal Hall conductivity and generates a ``finite size correction'' to the Hall viscosity of the FQH states on a sphere. We also discuss the effects of the framing anomaly on linear responses of nonAbelian FQH states. [Preview Abstract] 
Monday, March 2, 2015 11:51AM  12:03PM 
B5.00004: Evaluation of Quantum Scattering Time in UltraHigh Quality GaAs Quantum Wells Qi Qian, Sumit Mondal, Geoffrey C. Gardner, John D. Watson, Michael J. Manfra We present a critical analysis of the extraction of quantum scattering time from Shubnikovde Haas oscillations in ultrahigh quality GaAs quantum wells. In the regime of temperature and magnetic field study here (T{$\sim$}0.3K, B{$\leq$}0.3T) we find the canonical method for determination of quantum scattering time yields unreliable results (cf. Coleridge, Phys. Rev. B \textbf{44}, 3793). We elaborate a formalism that allows extraction of the quantum scattering time in a regime in which the normalized modulation of the density of states $\Delta g/ g_0$ is greater than unity. This approach describes well lowfield data for samples that display very large excitation gaps for fragile fractional quantum Hall states at large magnetic field. [Preview Abstract] 
Monday, March 2, 2015 12:03PM  12:15PM 
B5.00005: Quantized coefficients for the ChernSimons terms in bosonic and fermionic symmetry protected topological states in 2n$+$1D with U(1) symmetry ChaoMing Jian, Peng Ye, XiaoLiang Qi The study of symmetry protected topological (SPT) phases has led to many fruitful results. The classification of SPT states shows a big difference between bosonic systems and fermionic systems even when they share the same symmetry. In this talk, I will focus on SPT states with U(1) symmetry. In 2n$+$1 dimensions, when we gauge the U(1) symmetry, the effective actions of the gauge field contain ChernSimons term (and its generalization in higher dimensions) with quantized coefficients. The quantization of these coefficients is different between bosonic and fermionic systems. I will derive, using different methods, the quantization of coefficients for bosonic systems using general gauge invariance principle. I use Dirac fermions in 2n$+$1D coupled to U(1) gauge field to show the quantization for fermionic systems. I find that the bosonic and fermionic systems have a factor of (n$+$1)! difference in the quantization unit of the quantized coefficients.~ [Preview Abstract] 
Monday, March 2, 2015 12:15PM  12:27PM 
B5.00006: An investigation of orienting mechanisms of the quantum Hall stripe phases J. Pollanen, S. Brandsen, J.P. Eisenstein, L.N. Pfeiffer, K.W. West At high magnetic field, twodimensional electron systems (2DES) exhibit collective states possessing broken rotational symmetry. These states, known as the quantum Hall stripe phases (QHSP), are examples of electronic nematic liquid crystals. Experiments consistently show that the stripes are oriented relative to the GaAs crystal axes, but the exact nature of the native symmetrybreaking field remains unknown. We report here on an extensive study of the QHSPs in a series of high mobility single quantum well samples. These samples all have the same electron density, but differ systematically in the symmetry of the 2DES confinement potential and the distance between the 2DES and the sample surface. Tilted field magnetotransport measurements are used to observe the stripe phases and to assess the strength of the native symmetrybreaking field. We find that the stripes remain oriented in the same way in all our samples. Furthermore, our measurements show that the strength of the orienting potential does not depend on the distance to the sample surface but does exhibit an intriguing dependence on the symmetry of the 2DES confinement potential. We discuss these results in the light of recent suggestions that strain and/or spinorbit effects may determine the stripe orientation. [Preview Abstract] 
Monday, March 2, 2015 12:27PM  12:39PM 
B5.00007: Numerical characterization of nonAbelian MooreRead state in the microscopic lattice boson model Wei Zhu, Shoushu Gong, F. D. M. Haldane, D. N. Sheng Identifying the interacting systems that host the nonAbelian (NA) topological phases have attracted intense attention in physics. Theoretically, it is possible to realize the NA MooreRead (MR) state in bosonic system or doublelayer system by coupling two Abelian fractional quantum Hall (FQH) states together. Here, based on the density matrix renormalization group and exact diagonalization calculations, we study two such examples in the microscopic lattice models and investigate their NA nature. In the first example, we provide a thorough characterization of the universal properties of MR state on Haldane honeycomb lattice model, including both the edge spectrum and the bulk anyonic quasiparticle statistics. By inspecting the entanglement spectral response to the $U(1)$ flux, it is found that two of Abelian ground states can be adiabatically connected through a charge unit quasiparticle pumping from one edge to the other. In the second example, we study a doublelayer bosonic FQH system built from the $\pi$flux lattice model. Some evidences of NA nature has been identified, including the groundstate degeneracy and finite drag Hall conductance. The numerical methods we developed here provides a useful and practical way for detecting the full information of NA topological order. [Preview Abstract] 
Monday, March 2, 2015 12:39PM  12:51PM 
B5.00008: Fractional quantum Hall and nematic liquid crystal phases in a variable density twodimensional electron system S. Brandsen, J. Pollanen, J.P. Eisenstein, L.N. Pfieffer, K.W. West At high magnetic field, Coulomb interactions in a twodimensional electron system (2DES) lead to a wide variety of collective phases, including the fractional quantum Hall fluids and the nematic liquid crystals found at high Landau level occupancy. In order to examine the density dependence of these quantum states, we have developed a new sample architecture consisting of a highly doped, yet transparent, conducting cap layer grown atop a conventional modulationdoped heterojunction where the 2DES resides. Separate contacts to the 2DES and the cap layer allow the latter to function as a gate for tuning the 2DES density both before and after low temperature illumination. After illustrating the basic functioning of this structure, we will report results on the density dependence of various quantum Hall and nematic liquid crystal phases of the 2DES. [Preview Abstract] 
Monday, March 2, 2015 12:51PM  1:03PM 
B5.00009: Accessing topological order in fractionalized liquids with gapped edges Thomas Iadecola, Titus Neupert, Claudio Chamon, Christopher Mudry We consider manifestations of topological order in timereversalsymmetric fractional topological liquids (TRSFTLs), defined on planar surfaces with holes. We derive a formula for the topological ground state degeneracy of such a TRSFTL, which applies to cases where the edge modes on each boundary are fully gapped by appropriate backscattering terms. The degeneracy is exact in the limit of infinite system size, and is given by $q^{N^{\,}_{\mathrm{h}}}$, where $N^{\,}_{\mathrm{h}}$ is the number of holes and $q$ is an integer that is determined by the topological field theory. When the degeneracy is lifted by finitesize effects, the holes realize a system of $N^{\,}_{\mathrm{h}}$ coupled spinlike $q$state degrees of freedom. In particular, we provide examples where $Z^{\,}_{q}$ quantum clock models are realized on the lowenergy manifold of states. We also investigate the possibility of measuring the topological ground state degeneracy with calorimetry. [Preview Abstract] 
Monday, March 2, 2015 1:03PM  1:15PM 
B5.00010: Topology and interactions in a frustrated slab: tuning from Weyl semimetal to $C>1$ fractional Chern insulators Zhao Liu, Emil Bergholtz, Maximilian Trescher, Roderich Moessner, Masafumi Udagawa We show that a $[111]$ slab of spinorbit coupled pyrochlore lattice can become a Weyl semimetal phase with exotic surface states called as Fermi arcs, i.e., these states are localized to different surfaces depending on their quasimomentum. Remarkably, in this model, these Fermi arcs persists even when there is no Weyl point in the bulk. Considering interacting electrons in slabs of finite thickness, we find a plethora of known fractional Chern insulating phases, including a new discovered higher Chern number state which is likely a generalization of the MooreRead fermionic fractional quantum Hall state. By contrast, in the threedimensional limit, we argue for the absence of gapped states of the flat surface band due to a topologically protected coupling of the surface to gapless states in the bulk. We comment on generalizations as well as experimental perspectives in thin slabs of pyrochlore iridates. [Preview Abstract] 
Monday, March 2, 2015 1:15PM  1:27PM 
B5.00011: Detecting fractional statistics in anyon interferometry employing thermal excitation Cheolhee Han, HeungSun Sim In this work, we propose an interferometry setup of anyons, a setup slightly modified from a usual FabryPerot interferometry.\footnote{D. C. Chamon, D. E. Freed, S. A. Kivelson, S. L. Sondhi, X. G. Wen, Phys. Rev. B \textbf{55}, 2331 (1997)} In this interferometry, there appears anyon braiding between thermally excited anyons and an anyon injected from a source of the setup. This braiding process, which has unnoticed before and does not exist in bosons and fermions, results in a temperature dependent phase shift of the interference pattern of the setup. Experimental observation of the phase shift will provide a direct evidence of fractional statistics. [Preview Abstract] 
Monday, March 2, 2015 1:27PM  1:39PM 
B5.00012: Reordering Fractional Chern Insulators into Stripes of Fractional Charges Using LongRange Interactions Mengsu Chen, Vito Scarola Longrange interactions contribute to the rich phenomenology of quasiparticle collective states in the fractional quantum Hall regime. We test for analogues in models of fractional Chern insulators derived from a screened Coulomb interaction. We project the interaction to the lowest band and numerically diagonalize it. We find that the uniform fractional Chern liquid is surprisingly robust to longrange interactions but gives way to a unidirectional charge density wave of fractionally charged quasiparticles with increased screening length. Our results show that fractional Chern insulators offer a robust and important platform for studying quasiparticles collective states. [Preview Abstract] 
Monday, March 2, 2015 1:39PM  1:51PM 
B5.00013: Composite Fermions with a Warped Fermi Contour M.A. Mueed, Dobromir Kamburov, Yang Liu, Mansour Shayegan, Loren Pfeiffer, Ken West, Kirk Baldwin, Roland Winkler Composite fermions (CFs), quasiparticles formed by attaching an even number of flux quanta to each charged carrier in high perpendicular magnetic fields ($B$), capture many phenomena exhibited by an interacting system of twodimensional carriers. The flux attachment cancels out the external $B$ at a halffilled Landau level, enabling CFs to occupy a Fermi sea and possess a Fermi contour, similar to their $B$ = 0 carrier counterparts. Because the CFs are primarily a manifestation of interaction, one might argue that they should retain no memory of the $B$ = 0 particles, including their energy band properties. We will present tantalizing evidence through commensurability measurements that the composite fermions can be strongly influenced by the characteristics of the Landau level in which they are formed. In particular, the composite fermions have a warped Fermi contour when their Landau level originates from a hole band with significant warping. [Preview Abstract] 
Monday, March 2, 2015 1:51PM  2:03PM 
B5.00014: Flat Chern Bands and Edge States in the Hofstadter Model Near to Rational Flux Fenner Harper, Steven Simon, Rahul Roy We present a perturbative approach to the study of the Hofstadter model for when the amount of flux per plaquette is close to a rational fraction [Phys. Rev. B \textbf{90}, 075104 (2014)]. Within this approximation, the eigenstates of the system connect smoothly to the Landau levels of the continuum, but in general develop an additional species (or colour) degree of freedom. Using the formalism of Haldane pseudopotentials, we describe the fractional quantum Halllike wavefunctions that arise when interactions are turned on. We also discuss the form and energy spectrum of the bosonic edge excitations that would occur in the presence of a confining harmonic trap, making connections to the recent experimental realisations of the Hofstadter model using ultracold atoms. [Preview Abstract] 
Monday, March 2, 2015 2:03PM  2:15PM 
B5.00015: Topological textures and metalinsulator transition in Reentrant Integer Quantum Hall Effect: role of disorder Yuli LyandaGeller, George Simion We investigate a ground state of the twodimensional (2D) electron liquid in the presence of disorder for Landau level filling factors, for which the reentrant integer quantum Hall effect is observed. Our particular interest is the range of filling factors, which in a clean 2D system is favorable to formation of the twoelectron (2e) bubble crystal. For the smooth random potential due to charged impurities placed far away from the 2D gas, the ground state is a lightly distorted 2e bubble crystal. However, for positively or negatively charged residual impurities located approximately within about three magnetic lengths from the 2D electrons, the ground state contains charged 2e complexes formed either by positively charged impurity and 3e defect bubble, or negatively charged impurity and 2e defect bubble. In the vicinity of 1e and 3e defect bubbles, the 2e bubbles of the crystal change their shape from round to elongated forming hedgehog (for 1e defect) or vortex (for 3e defect) textures. The topological textures due to these complexes interact with vortex and hedgehog excitations, generated as temperature increases that are not bound by residual impurities. The temperature of insulator to metal transition calculated with both bound and unbound defects agrees with experiment. [Preview Abstract] 
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