Bulletin of the American Physical Society
APS March Meeting 2015
Volume 60, Number 1
Monday–Friday, March 2–6, 2015; San Antonio, Texas
Session F5: Fractional Quantum Hall Effect IV |
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Sponsoring Units: FIAP Chair: Yang-Le Wu, University of Maryland Room: Juan Gorman Room 005 |
Tuesday, March 3, 2015 8:00AM - 8:12AM |
F5.00001: Entanglement and dispersion of single-mode excitations in fractional quantum Hall effect Yang-Le Wu, N. Regnault, B. Andrei Bernevig Low-lying excitations above the topological ground state of a fractional quantum Hall system can be captured by the single mode approximation. We revisit this problem using the recently developed matrix product states (MPS) for quantum Hall model wave functions. We will show how to extend the MPS construction for the ground state to the single-mode excitations. This alternative representation reveals the entanglement structure of these excited states. We will also discuss the link between the dispersion of these excitations and the spectral properties of the MPS transfer matrix. [Preview Abstract] |
Tuesday, March 3, 2015 8:12AM - 8:24AM |
F5.00002: Theory of Nematic Fractional Filled Landau Levels Yizhi You, Gil Young Cho, Eduardo Fradkin We present a theory of nematic phase transition in fractional quantum Hall fluids where nematicity acts as a dynamical metric degree of freedom which interplays with the underlying topological phase. The nematic FQH states of a 2DEG arise as an instability triggered by attractive quadrupolar interaction. The effective field theory for the isotropic-nematic phase transition in FQHE has z = 2 dynamical exponent. This is due to a Berry phase term of the nematic order parameter, which is related (but not equal) to the non-dissipative Hall viscosity. The spectrum of collective excitation indicates that the mass gap of GMP mode collapses at the nematic phase transition.The leading coupling between the nematicity and gauge fields has a similar form of Wen-Zee term. A disclination of the nematic order parameter carries a non-quantized electric charge and has non-quantized fractional statistics. We also present similar nematic theory in a half-filled Landau levels. Considering the Chern-Simons gauge fluctuation, the effective mass of the fermion has infrared divergence. Consequently, the effective theory also has a parity-odd Berry phase term which is akin to non-dissipative response. The interplay between the nematic vortex current and Chern-Simons gauge would be displayed. [Preview Abstract] |
Tuesday, March 3, 2015 8:24AM - 8:36AM |
F5.00003: Anatomy of protected edges without symmetry Michael Levin, Sriram Ganeshan In this talk, we consider the $\nu = 2/3$ fractional quantum Hall state which has been shown to have protected gapless edge modes even if all symmetries are broken, including charge conservation. Since the edge protection for the 2/3 state exists even when charge conservation is broken, one might expect that there is something fundamentally anomalous about the $\nu = 2/3$ edge beyond the usual U(1) chiral anomaly. In this talk we investigate the anomalous structure of the 2/3-edge state by testing its non-perturbative robustness to a particular type of defect. The defects we consider break charge conservation symmetry and thereby provide insight into the anomalous nature of the 2/3 edge going beyond the U(1) chiral anomaly. [Preview Abstract] |
Tuesday, March 3, 2015 8:36AM - 8:48AM |
F5.00004: Role of the continuum states in the thermodynamics of the $\nu = 1/3$ fractional quantum Hall effect Peter Raum, Vito Scarola The high energy excitations of fractional quantum Hall states dictate thermodynamics at experimentally accessible temperatures. We construct a microscopic formalism for the thermodynamics of the $\nu=1/3$ Laughlin state as generated by a hard core repulsive model. We use exact diagonalization of the hardcore repulsive model for small system sizes to gather statistics for the excitations. These results are extrapolated to the thermodynamic limit using an ansatz partition function that captures the ground state, low-energy excitations, and high energy continuum states. The continuum states are found to play an important role at low temperatures, even below the characteristic gap. [Preview Abstract] |
Tuesday, March 3, 2015 8:48AM - 9:00AM |
F5.00005: Anisotropic gapped excitation modes in the SLL from Light Scattering Aron Pinczuk, Ursula Wurstbauer, Antonio L. Levy, John Watson, Geoff C. Gardner, Michael J. Manfra, Ken West, Loren Pfeiffer The fascinating interaction physics in the SLL supports the emergence of exotic quantum phases and unconventional FQHE states as e.g. anisotropic, possibly nematic, FQHE states at $\nu = 5/2$ [1] and $\nu = 7/3$ [2]. We explore the fascinating physics of these states by studying low-lying collective excitation spectrum from resonant inelastic light scattering (RILS) experiments. Here, we focus on the filling factor range $5/2 > \nu > 2$. We observe clear signatures from gapped modes that weaken with increasing temperature for several filling factors that are known from transport to be incompressible FQHE states like $\nu$ = 2+2/5, 2+3/8 and 2+1/3. These modes exhibit a clear dependence on filling factor, unambiguously uncovering incompressible quantum states. The lowest mode exhibits a remarkably strong polarization dependence that can be interpreted as fingerprint for the lack of rotational symmetry of the ground state. This interpretation of the observed RILS mode would support nematic FQHE states in the SLL. \\[4pt] [1] Y. Liu et al., Phys. Rev. B 88, 035307 (2013).\\[0pt] [2] J. Xia et al., Nature Phys. 7, 845-848 (2011). [Preview Abstract] |
Tuesday, March 3, 2015 9:00AM - 9:12AM |
F5.00006: Orbital Kondo Effect in Fractional Quantum Hall Systems Yashar Komijani, Pascal Simon, Ian Affleck We study transport properties of a charge qubit embedded in series between two chiral Luttinger liquids. This is realized for example by a double anti-dot placed between the edge states of the integer $\nu=1$ or fractional $\nu=1/3$ quantum Hall systems. We show that in the limit of a large capacitive coupling between the anti-dots, their quasi-particle occupancy behaves as a pseudo-spin which realizes an orbital Kondo impurity embedded in a Luttinger liquid, while the inter anti-dot tunnelling acts like an impurity magnetic field. The latter tends to destabilize the Kondo fixed point at $\nu=1/3$ and produce an effective inter-edge scattering, as in quasi-particle tunnelling in quantum point contacts. We relate the backscattered conductance to the spin relaxation of the Kondo impurity, i.e. the imaginary part of pseudo-spin susceptibility and calculate it in various limits for both $\nu=1$ and $\nu=1/3$. [Preview Abstract] |
Tuesday, March 3, 2015 9:12AM - 9:24AM |
F5.00007: Fractional Chern Insulator of Hard-Core Bosons in Topological Flat Bands Cheng-Chien Chen, Hong-Chen Jiang, Hong Yao We study a two-dimensional lattice model of hard-core bosons by density matrix renormalization group and exact diagonalization methods. At low filling $\nu=1/2$, Abelian fractional quantum Hall (FQH) states emerge with signatures of a two-fold ground-state degeneracy on a torus and a nonzero topological entanglement entropy (TEE) $\gamma=-\ln{\sqrt{2}}$. At filling $\nu=2/3$, more exotic non-Abelian FQH states may emerge with a three-fold ground-state degeneracy and a TEE $\gamma=-\ln{2}$. The ($C$+1)-fold degenerate ground states are found to exhibit a nonzero Chern number $C$ at filling $\nu=C/(C+1)$. The system is topologically trivial at filling $\nu=1$, characterized by a symmetry-breaking density-wave order in the thermodynamic limit. [Preview Abstract] |
Tuesday, March 3, 2015 9:24AM - 9:36AM |
F5.00008: Characterization of Quasiholes in Fractional Chern Insulators Ravindra Bhatt, Zhao Liu, Nicolas Regnault We provide a detailed study of the Abelian quasiholes of $\nu=1/2$ bosonic and $\nu=1/3$ fermionic fractional quantum Hall (FQH) states on the torus geometry and in fractional Chern insulators (FCIs). We establish the correspondence between the density distribution of a quasihole in a FCI and that of the corresponding FQH state by defining an effective magnetic length on the lattice. This effective magnetic length only depends on the lattice model that hosts the FCI. In this way, the quasihole size in a FCI can be predicted for any lattice model once the quasihole size of the corresponding FQH state is known. We discuss the effect of the lattice embedding on the quasihole size. We find that an optimal embedding exists that can support the quasihole correspondence between FCIs and FQH states. We also perform the braiding of FCI quasiholes to probe the fractional statistics of these excitations. The numerical values of the braiding phases accurately match the theoretical predictions. [Preview Abstract] |
Tuesday, March 3, 2015 9:36AM - 9:48AM |
F5.00009: Composite Fermions waltz to the tune of a Wigner crystal Hao Deng, Yang Liu, Mansour Shayegan, Loren Pfeiffer, Ken West, Kirk Baldwin We present a new technique and experimental results that directly probe the magnetic-field-induced Wigner crystal (WC) in a 2D electron system. We measure the magneto-resistance of a bilayer electron system with unequal layer densities at high magnetic fields. One layer has a very low density and is in the WC regime ($\nu \ll 1$), while the other (``probe'') layer is near $\nu$ = 1/2 and hosts a sea of composite fermions, quasi-particles formed by attaching two flux-quanta to each interacting electron. The composite fermions feel the periodic electric potential of the WC in the other layer and exhibit magneto-resistance maxima whenever their cyclotron orbit encircles certain integer number (up to 37) of the WC lattice points. The positions of the maxima reveal that the WC has a triangular lattice and yield a direct measure of its lattice constant. Our results provide a striking example of how one can probe an exotic many-body state of 2D electrons using equally exotic quasi-particles of another many-body state. [Preview Abstract] |
Tuesday, March 3, 2015 9:48AM - 10:00AM |
F5.00010: Spontaneous valley ordering in SnTe (001) surface states Ming Xie, Xiao Li, Fan Zhang, Allan MacDonald In this work we study the spontaneous valley ordering in SnTe surface states. SnTe is a topological mirror insulator in which the bulk mirror symmetry allows robust surface states to appear on certain surfaces like (001), (111) and (110). These surface states provide a new platform to study multi-flavor Landau level physics in the quantum Hall regime. Attention has been drawn to the (001) surface by a recent experimental observation of a four-fold degenerate Landau level formed at zero energy [Science 341, 1496 (2013)]. This degeneracy arises because the single-particle bandstructure at low energies consists of four surface Dirac cones. In the presence of electron-electron interactions, however, this four-fold degeneracy is expected to be lifted. In this work we construct a theory to show that at all integer filling factors between -2 and $+$2 the ground state is a gapped quantum Hall state. We further demonstrate that these ground states are valley nematic phases, and discuss some experimental consequences. [Preview Abstract] |
Tuesday, March 3, 2015 10:00AM - 10:12AM |
F5.00011: Transmission Measurements in a Low Density Two --Dimensional Electron Gas in an Array of Antidots Chi Zhang, Jian Mi, Loren Pfeiffer, Ken West Under high magnetic fields, the microwave conductivity of a two-dimensional electron system containing an antidot array with factional Landau filling was discovered [1]. On the other hand, at low temperature T$=$0.3 K, we have measured the transmission in the low density (n$=$0.6x10$^{\mathrm{11}}$ cm$^{\mathrm{-2}})$ , ultraclean GaAs/AlGaAs sample with an array of anitidots. In our measurements, we observed an interesting feature around the $\nu =$1, 2, which may be related to the charged edge mode in the integer quantum Hall regime. [1] P. D. Ye, L. W. Engel, D. C. Tsui, J. A. Simmons, J. R. Wendt, G. A. Vawter, and J. L. Reno, Phys. Rev. B, 65, 121305 (2002). [Preview Abstract] |
Tuesday, March 3, 2015 10:12AM - 10:24AM |
F5.00012: Critical exponent in a projected lattice model for integer quantum Hall plateau transitions Qiong Zhu, Xin Wan, R.N. Bhatt Motivated by the recent numerical studies on the Chalker-Coddington network model with a larger-than-expected localization length critical exponent, we revisited the exponent calculation in the disordered Hofstadter model. We project the Hamiltonian into the lowest subband, which is the lattice analog of the lowest Landau level, and calculate the Chern number for individual eigenstates to analyze their localization properties. We compare the finite-size scaling of the total number of the conducting states, the width of the distribution of the conducting states, and the Hall conductance. We confirm that earlier calculations on the lattice model have also underestimated the localization length critical exponent and discuss the manifestation of the leading irrelevant scaling field. [Preview Abstract] |
Tuesday, March 3, 2015 10:24AM - 10:36AM |
F5.00013: Quantum Hall plateau transitions in the bulk entanglement spectrum Xin Wan, Qiong Zhu, Guang-Ming Zhang We discuss an alternative route to access the quantum Hall transitions via studying the so-called bulk entanglement spectrum. By partitioning the pure integer quantum Hall ground state in a checkerboard fashion we show the emergence of a quantum network with bulk gapless excitations at the Brillouin zone center without fine tuning. The emergent critical theories have a one-to-one correspondence to the Chern number characterization of the original ground states [arXiv:1409.4916]. For example, the resulting critical theory for the $\nu = 1$ state is the (2+1)-dimensional relativistic quantum field theory characterized by a single Dirac cone spectrum and a pair of fractionalized zero-energy states. For the $\nu = 2$ state the critical theory exhibits a quadratic band crossing. The effect of disorder on the transitions will be presented. [Preview Abstract] |
Tuesday, March 3, 2015 10:36AM - 10:48AM |
F5.00014: Microwave Absorption of Edge States in Quantum Hall Droplets Jie Zhang, Lingjie Du, Ruiyuan Liu, RuiRui Du, Loren Pfeiffer, Ken West Microwave absorption spectroscopy has been proposed as a unique tool in studies of edge physics of quantum Hall droplets (Cano et al., Phys. Rev. B 88, 165305 (2013). In our ongoing experiment we pattern co-planar waveguide (CPW) and micrometer-size discs on the same chip of a high-mobility GaAs/AlGaAs two-dimensional electron gas. The CPW is placed inside a broad-band sample holder, which is fitted with millimeter wave coax cables. The whole setup is top-loaded into a 300 mK helium3 cryostat equipped with a superconducting solenoid. In this talk the construction of the spectrometer, preliminary data, and discussions will be presented. [Preview Abstract] |
Tuesday, March 3, 2015 10:48AM - 11:00AM |
F5.00015: Thermal Hall Effect and Geometry with Torsion Alexander Abanov, Andrey Gromov We formulate a geometric framework that allows to study momentum and energy transport in non-relativistic systems. We show how momentum and energy current can be computed as responses to variations in geometry. It turns out that in the absence of Lorentz invariance the appropriate geometry is not Riemannian, but the Newton-Cartan geometry with temporal torsion. Our approach generalizes the classic Luttinger's formulation of thermal transport. In particular, we clarify the geometric meaning of the fields conjugate to energy and energy current. These fields describe the geometric background with non-vanishing temporal torsion. We use the developed formalism to construct the equilibrium partition function of a non-relativistic system coupled to the NC geometry in 2+1 dimensions and to derive various thermodynamic relations. As a by-product we argue that the bulk thermal Hall conductance is not topologically protected. [Preview Abstract] |
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