Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session B37: FQHE in Higher Landau Levels |
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Sponsoring Units: FIAP Chair: Chetan Nayak, Microsoft Station Q Room: Morial Convention Center 229 |
Monday, March 10, 2008 11:15AM - 11:27AM |
B37.00001: Evolution of the Fractional Quantum Hall States in the Second Landau Level H.C. Choi, W. Kang, S. Das Sarma, L.N. Pfeiffer, K.W. West Study of the energy gap of the fractional quantum Hall effect (FQHE) in the second Landau level will be presented. Two symmetrically doped GaAs/AlGaAs quantum well samples with densities $n = 3.2 \times10^{11}$cm$^{-2}$ and $n = 2.8\times10^{11}$cm$^{-2}$ with respective mobilities of $\mu = 28.3\times10^6 $cm$^2$/Vs and $\mu = 10.5\times 10^6$cm$^2$/Vs were studied. In the higher mobility sample, clear FQHE states are observed at filling factor $\nu = $ 5/2, 7/3, 8/3, 14/5, 11/5, 12/5, 16/7, and 19/7. Some of the higher order FQHE states disappear in the lower mobility sample, and clear FQHE states are observed at $\nu = $ 5/2, 7/3, 8/3, 14/5, and 11/5. The energy gaps of the FQHE states at $\nu = $ 5/2, 7/3 and 8/3 in the higher mobility sample are found to exceed 500mK. The energy gaps of the $\nu = $ 5/2, 7/3 and 8/3 states in the lower mobility sample are typically reduced by more than 50\% in comparison. Our measured gap for $\nu=$5/2 state, which is less than 1/5 of the theoretical gap, can be understood when the finite width correction and disorder broadening are factored in. Evolution of the energy gap with mobility shows that the even-denominator FQHE state at $ \nu = $ 5/2 is the most robust FQHE state in the second Landau level. In addition, the $\nu = $ 7/3 and 8/3 states are unlikely to be the second Landau level analog of the Laughlin states at $\nu = $ 1/3 and 2/3 in the lowest Landau level. [Preview Abstract] |
Monday, March 10, 2008 11:27AM - 11:39AM |
B37.00002: Fractional Quantum Hall Effect and Electron Correlations in Partially Filled First Excited Landau Level George Simion, John J. Quinn The possibility of using non-Abelian quasiparticle excitations in quantum computing has led to a revival of interest in the fractional quantum Hall (FQH) states of excited Landau levels.We present a quantitative study of most prominent incompressible quantum Hall states in the partially filled first excited Landau level (LL1) which have been recently studied experimentally by Choi et al.(cond-mat:0707.0236v2). The pseudopotential describing the electron- electron interaction in LL1 is harmonic at short range. It produces a series of incompressible states which is different from its LL0 counterpart. The numerical data indicate that the most prominent states $\nu=\frac{5}{2}$, $\frac{7}{3}$, and $\frac{8} {3}$ are not produced by Laughlin correlated electrons, but result from a tendency of electrons to form pairs or larger clusters which eventually become Laughlin correlated. States with smaller gaps at filling factors $\frac{14}{5}$, $\frac{16} {7}$, $\frac{11}{5}$, $\frac{19}{7}$ are Laughlin correlated electrons or holes and fit Jain's sequence of filled $\rm{CF}^4 $ levels. [Preview Abstract] |
Monday, March 10, 2008 11:39AM - 11:51AM |
B37.00003: Fractional quantum Hall effect in higher Landau levels Michael R. Peterson, S. Das Sarma The fractional quantum Hall effect in the second Landau level (LL), particularly at filling factor 5/2, has seen a resurgence of research activity since its possible use in fault tolerant topological quantum computation was pointed out[1]. We do not, however, have a complete understanding of the FQHE in the second LL(SLL) compared with the corresponding lowest LL situation. For instance, while the Moore-Read Pfaffian state is the leading candidate for the 5/2 FQHE, it has only a moderate overlap ($\sim$0.9) with the exact wavefunction for finite size systems of electrons interacting through the Coulomb interaction. In this work we consider the finite thickness of the electrically polarized quasi-2D quantum confinement in three models: Zhang-Das Sarma, infinite square-well, and Fang-Howard potentials, respectively. We calculate overlap between the Laughlin(fillings 1/3 and 1/5) or Pfaffian(filling 1/2) and the corresponding exact state, obtained by exact diagonalization, in the lowest, second, and third LLs as a function of the layer thickness. We find that the Pfaffian state becomes a nearly exact description of the physics at filling factor 1/2 in the SLL for a finite value of thickness. We also show the comparative trends in the ground state energy and the excitation gap as a function of layer thickness, comparing among the first, second, and the third LLs. We acknowledge support from Microsoft Q Project. [1] Das Sarma et al. PRL 94, 166802(2005) [Preview Abstract] |
Monday, March 10, 2008 11:51AM - 12:03PM |
B37.00004: Spin Order in Paired Quantum Hall States Ivailo Dimov, Bertrand Halperin, Chetan Nayak We consider quantum Hall states at even-denominator filling fractions, especially $\nu=5/2$, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at $\nu = 5/2$ an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau theory for the spin degrees of freedom of paired Hall states is a perturbed CP$^2$ model. We compute the coefficients in the Ginzburg-Landau theory by a BCS-Stoner mean field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state. [Preview Abstract] |
Monday, March 10, 2008 12:03PM - 12:15PM |
B37.00005: Confinement of fractional quantum Hall states in the first excited Landau level Michael Manfra, Robert Willett, Loren Pfeiffer, Kenneth West The quasiparticles of certain exotic quantum Hall states in the first excited Landau level including $\nu $=5/2 and $\nu $=12/5 are believed to obey non-Abelian statistics. Manipulation of such quasiparticles is crucial to recent proposals of topologically protected quantum computation. Most schemes to determine the statistics of the quantum Hall quasiparticles rely on the manipulation of the correlated state in confined geometries. As a preliminary step in this direction, we report on the magnetic field and temperature dependences of transport through quantum point contacts (qpc's) in the regime where the first excited Landau level is partially occupied in the confined region. Our high density (n$\sim $4x10$^{11}$cm$^{-2})$ and high mobility GaAs samples are of sufficient quality such that well-defined quantum Hall states are resolved at $\nu $=8/3, 5/2, and 7/3 in the bulk at low temperature. In particular, we have studied the impact of confining geometry design and the size of the qpc opening on the stability of higher order fractional states in the qpc. [Preview Abstract] |
Monday, March 10, 2008 12:15PM - 12:27PM |
B37.00006: Confinement of Fractional Quantum Hall States Robert Willett, Michael Manfra, Ken West, Loren Pfeiffer Confinement of small-gapped fractional quantum Hall states facilitates quasiparticle manipulation and is an important step towards quasiparticle interference measurements. Demonstrated here is conduction through top gate defined, narrow channels in high density, ultra-high mobility heterostructures. Transport evidence for the persistence of a correlated state at filling fraction 5/3 is shown in channels of 2$\mu $m length but gated to near 0.3$\mu $m in width. The methods employed to achieve this confinement hold promise for interference devices proposed for studying potential non-Abelian statistics at filling fraction 5/2. R.L. Willett, M.J. Manfra, L.N. Pfeiffer, K.W. West, Appl. Phys. Lett. \textbf{91}, 052105 (2007). [Preview Abstract] |
Monday, March 10, 2008 12:27PM - 12:39PM |
B37.00007: Fractional Quantum Hall Hierarchy and the Second Landau Level Parsa Bonderson, J.K. Slingerland We generalize the Haldane-Halperin hierarchy picture to apply to non-Abelian fractional quantum Hall states, and propose trial wave functions to describe the observed Hall conductance plateaus in the second Landau level. These hierarchy states are constructed over the Moore-Read state, the expected description of the $\nu = 5/2$ plateau, and thus all have electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising model $\sigma$-vortex type. [Preview Abstract] |
Monday, March 10, 2008 12:39PM - 12:51PM |
B37.00008: Edge States and Interferometers in the Pfaffian and anti-Pfaffian States Waheb Bishara, Chetan Nayak In this work we use two theoretical candidates for describing the $\nu=5/2$ Quantum Hall state, the Moore-Read Pfaffian and its particle-hole conjugate, to calculate the conductance of a two point contact interferometer in the weak tunneling regime. We invoke the appropriate edge theory and calculate the conductance as a function of temperature and voltage, and we establish the connection to the underlying bulk topological theory. [Preview Abstract] |
Monday, March 10, 2008 12:51PM - 1:03PM |
B37.00009: Spectrum of Quantum Entanglement in Fractional Quantum Hall States Hui Li, F.D.M. Haldane We present numerical studies of the bipartite entanglement in fractional quantum Hall (FQH) states. We partitioned the (spherical geometry) Landau-level orbitals into two hemispheres: the entanglement spectrum derives from the Schmidt decomposition $|\psi\rangle = {\sum}_{i}\exp(-{\beta_{i}}/{2}) |\psi_{A}^{i}\rangle\otimes|\psi_{B}^{i}\rangle$, where $|\psi_{A}^{i}\rangle$ (or $|\psi_{B}^{i}\rangle$) are orthonormal. The $\beta_{i}$ are ``energy levels'' of a system with thermodynamic entropy at ``temperature'' $k_{B}T =1$ equivalent to the entanglement entropy. The \textit{entanglement spectrum}, \textit{i.e.}, the relation between the $\beta_i$ and the quantum numbers that classify $|\psi_{A}^{i}\rangle$ (or $|\psi_{B}^{i}\rangle$), serves as a ``fingerprint'' of the topological phase of the FQH state, and reveals much more information than just the entanglement entropy, a single number. The spectrum of, \textit{e.g.}, the $1/3$ Laughlin state has far fewer levels than expected for a generic wavefunction, and its low-energy spectrum corresponds to that of a conformal field theory (CFT). We studied the wavefunctions that interpolate between the Laughlin state and the ground state of a realistic Coulomb interaction potential at $\nu = 1/3$: the generic number of levels is restored, but the low-lying CFT structure remains essentially unchanged. We also describe the interpolation between the Moore-Read state and the Coulomb interaction ground state at $\nu = 5/2$. [Preview Abstract] |
Monday, March 10, 2008 1:03PM - 1:15PM |
B37.00010: Model Wavefunctions For Non-Abelian Quasiparticles B. Andrei Bernevig, F.D.M. Haldane We present model wavefunctions for quasiparticle (as opposed to quasihole)excitations of the $Z_k$ parafermion sequence (Laughlin/Moore-Read/Read-Rezayi) of Fractional Quantum Hall states. These states satisfy two generalized clustering conditions: they vanish when either a cluster of $k+2$ electrons is put together, or when two clusters of $k+1$ electrons are formed at different positions. For Abelian Fractional Quantum Hall states ($k=1$), our construction reproduces the Jain quasielectron wavefunction, and elucidates the difference between the Jain and Laughlin quasiparticle constructions. For two (or more) quasiparticles, our states differ from those constructed using Jain's method. By adding our quasiparticles to the Laughlin state, we obtain a hierarchy scheme which gives rise to a non-abelian $\nu=\frac{2} {5}$ FQH state. [Preview Abstract] |
Monday, March 10, 2008 1:15PM - 1:27PM |
B37.00011: Jack Polynomials, Exclusion Statistics, and non-Abelian FQHE States at $\nu$ = $k/(km+r)$ F. D. M. Haldane, B. Andrei Bernevig We describe a general family of non-Abelian FQHE states at
$\nu$ = $k/(km+r)$ with polynomial wavefunctions
$\prod_{i |
Monday, March 10, 2008 1:27PM - 1:39PM |
B37.00012: Searching for anyons in a realistic model of fractional quantum Hall liquids Zi-Xiang Hu, Xin Wan, Peter Schmitteckert We study quasihole/particle excitations in a microscopic model of fractional quantum Hall liquids with long-range Coulomb interaction and an edge confining potential. We find with a local trapping potential quasihole/particle states can emerge from the Laughlin and the Moore-Read states. The presence of Abelian and non-Abelian quasiholes has a distinct effect on the corresponding edge spectra. The stability of quasiholes/particles depends on the detail of the confining potential and the trapping potential. We discuss the relevance of the calculation to the high-accuracy generation and control of individual anyons in potential experiments, in particular, in the context of topological quantum computing. [Preview Abstract] |
Monday, March 10, 2008 1:39PM - 1:51PM |
B37.00013: Probing Non-Abelian Statistics in $\nu=12/5$ Quantum Hall State Kam Tuen Law The tunneling current and shot noise between two Fractional Quantum Hall edges in $ \nu=12/5 $ state in electronic Mach- Zehnder Interferometer with two quantum point contacts (QPCs) is studied. We show that the tunneling current and shot noise can be used to probe the existence of non-Abelian statistics in the $ k=3 $ Read-Rezayi state. More specifically, the dependence of the current on the Aharonov-Bohm flux in the Read- Rezayi state is asymmetric under the change of the sign of the applied voltage. This property is absent in the Laughlin states. Moreover the Fano factor can exceed 12.7 electron charges in the $k=3 $ Read-Rezayi state. This number is much greater than the maximum possible Fano factor in all Laughlin states and the Moore-Read state which was shown previously to be $ e $ and $ 3.2 e $ respectively. [Preview Abstract] |
Monday, March 10, 2008 1:51PM - 2:03PM |
B37.00014: Effect of Landau Level Mixing on Braiding Statistics Steven H. Simon We examine the effect of Landau level mixing on the braiding statistics of quasiparticles of abelian and nonabelian quantum Hall states. While path dependent geometric phases can perturb the abelian part of the statistics, we find that the nonabelian properties remain unchanged to an accuracy that is exponentially small in the distance between quasiparticles. [Preview Abstract] |
Monday, March 10, 2008 2:03PM - 2:15PM |
B37.00015: Studying topological order in quantum Hall states using entanglement entropy calculations. Masud Haque, Oleksandr Zozulya, Kareljan Schoutens, Ed Rezayi, Nicolas Regnault We present calculations of the entanglement entropy in fractional quantum Hall (FQH) states. Calculating the entanglement entropy between spatially separated regions allows us to probe the topological order in Laughlin and Moore-Read states. The entanglement entropy is also found to be a sensitive indicator of quantum phase transitions between FQH and non-FQH states. [Preview Abstract] |
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