Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session P46: FQHE |
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Sponsoring Units: FIAP Chair: Dmitri Feldman, Brown University Room: Baltimore Convention Center 349 |
Wednesday, March 15, 2006 11:15AM - 11:27AM |
P46.00001: Measuring Exchange Interactions by Tunneling Deep Into the Quantum Hall Liquid O.E. Dial, R.C. Ashoori, L.N. Pfieffer, K.W. West We present measurements of the tunneling density of states of a two dimensional electron gas (2DEG) in GaAs at energies up to 10 meV above and below the Fermi energy. Using time domain capacitance spectroscopy (TDCS), we determine the current-voltage (IV) characteristics for tunneling perpendicularly between a gated 2DEG and a 3D electron continuum separated by a thin tunneling barrier. In TDCS, sharp pulses are applied to the sample while measuring displacement currents from electrons entering or leaving the 2DEG, allowing tunneling IV measurements without direct electrical contact to the 2DEG. We observe changes in the Landau level structure far from the Fermi surface as we fill and empty individual Landau levels by varying the electron density and magnetic field. This provides a unique measurement of the exchange enhanced spin splitting of empty and filled Landau levels. [Preview Abstract] |
Wednesday, March 15, 2006 11:27AM - 11:39AM |
P46.00002: Thermal Dephasing in the Laughlin Quasiparticle Interferometer F.E. Camino, Wei Zhou, V.J. Goldman We report experiments on thermal dephasing of the Aharonov-Bohm oscillations in the novel Laughlin quasiparticle (LQP) interferometer, [1] where quasiparticles of the 1/3 FQH fluid execute a closed path around an island of the 2/5 fluid. In the $10.2 \leq T \leq 141$ mK temperature range, qualitatively, the experimental results follow a thermal dephasing dependence expected for an electron interferometer, and show clear distinction from the activated behavior observed in resonant tunneling and Coulomb blockade devices, both in the chiral Luttinger liquid ($\chi$LL) and the Fermi liquid regimes. The data fit very well the $\chi$LL dependence predicted for a $g=1/3$ two point-contact LQP interferometer. [2] The fit yields a value of the chiral edge excitation velocity, $u=1.4\times 10^4$ m/s obtained for the first time for a continuous FQH edge excitation spectrum. The small deviation from the zero-bias theory seen below 20 mK indicates yet unrecognized source of experimental decoherence, not included in theory. \newline \noindent [1] F. E. Camino et al., Phys. Rev. B $\bf 72$, 075342 (2005). \newline \noindent [2] C. de C. Chamon et al., Phys. Rev. B $\bf 55$, 2331 (1997). [Preview Abstract] |
Wednesday, March 15, 2006 11:39AM - 11:51AM |
P46.00003: Flux Period Scaling in the Laughlin Quasiparticle Interferometer Wei Zhou, F.E. Camino, V.J. Goldman Aharonov-Bohm superperiod was rececently reported for electron interferometer devices in the quantum Hall regime, where electron paths circle a 2D electron island. The electron island main confinement is produced by etch trenches, into which front gate metal is deposited. We determine experimentally the A-B period $\Delta_B$ at several front gate voltages $V$ for electrons ($f =1$) and Laughlin quasiparticles (2/5 embedded in 1/3). For moderate $|V| \leq 300 $ mV, on each QH plateau, we find linear dependence of $\Delta_B$ on $V$. For $f=1$, the electron A-B path area $S$ can be found from $\Delta_B$ using flux quantization condition $\Delta_\Phi =S\Delta_B =h/e$ for the flux period $\Delta_\Phi$. The A-B area enclosed by the $f=1/3$ edge channel (the 2/5 island area) is not known independently if the FQH flux period is not known a priory. The front gate voltage dependence of $\Delta_B$ provides such independent determination of the 2/5 island area. The directly measured values of $\Delta_B$ and its slope $d\Delta_B /dV$ can be combined to derive the voltage $V (1e)$ attracting a unit charge to the area of the A-B path, assuming $S$ is known. For a many-electron ($\sim$2000) 2D disc of radius $r$, the product $rV(1e)$ should be approximately constant, independent of the QH filling or the area. Thus the $f=2/5$ island area can be determined directly with a $\sim$10\% accuracy, which is quite sufficient to distinguish the physically reasonable possibilities of the flux periods $5h/e$, $5h/2e$, $1h/e$, and $h/2e$. [Preview Abstract] |
Wednesday, March 15, 2006 11:51AM - 12:03PM |
P46.00004: Extracting fractional statistics from superperiodic Aharonov-Bohm oscillations Eun-Ah Kim, Steven Kivelson We consider a quantum Hall interferometer in which the quasiparticles of a fractional quantum Hall (FQH) liquid with filling factor $\nu_1=1/3$ propagate around a large ring of radius $r_1$, which is encircles an island with a smaller radius $r_2$ occupied by FQH liquid with filling factor $\nu_2=2/5$. We study the conductance oscillations that result from the incompressibility of the FQH liquid occupying the island and the constructive interference condition for the quasiparticles encircling the outer ring. Since the constructive interference condition depends on both the magnetic flux enclosed by the encircling path and the statistical phase gained by the encircling quasiparticle due to the presence of quasiparticles in the island, such conductance oscillations can be used to detect signatures of fractional statistics. We find that oscillatory period depends on both radii, $r_1$ and $r_2$. We discuss the relation between our results and the recent experiments by F.E.Camino, W. Zhou and V.J. Goldman in the context of our model. [Preview Abstract] |
Wednesday, March 15, 2006 12:03PM - 12:15PM |
P46.00005: Resonant tunneling in fractional Hall effect Chuntai Shi, Jainendra Jain We study theoretically the possible transitions of a fractional quantum Hall island surrounded by another fractional quantum Hall state, induced by either the variation of the magnetic field or a backgate voltage, and find a rich set of possibilities in addition to the one considered previously[1],The elementary transitions correspond to the addition or removal of a composite fermion from the edge or the interior of the island; combinations of elementary transitions may occur simultaneously due to electrostatic constraints. Relevance to a recent experiment[2] is considered, which measures the resonant tunneling of composite fermions through their quasi-bound states around such a 2/5 island surrounded by the 1/3 sea. It is shown that the results are consistent with the notion of fractional braiding statistics, but can be explained on the basis of fractional charge alone. We also perform calculations based on microscopic composite fermion wavefunctions of finite systems to test the theoretical considerations. [1]J.K.Jain, S.A.Kivelson, and D.J.Thouless, Phys.Rev.Lett.\textbf{71}, 3003(1993). [2]F.E.Camino, W.Zhou, and V.J.Goldman, Phys.Rev.B \textbf {72}, 075342(2005). [Preview Abstract] |
Wednesday, March 15, 2006 12:15PM - 12:27PM |
P46.00006: Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics Kam Tuen Law, Dima Feldman, Yuval Gefen We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the Aharonov-Bohm flux and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. [Preview Abstract] |
Wednesday, March 15, 2006 12:27PM - 12:39PM |
P46.00007: Pauli-like principle for Abelian and non-Abelian FQHE quasiparticles F. D. M. Haldane A general formulation of condensed matter physics describes the Hamiltonian as $H_0 + H_1$, where $H_0$ is a positive ``topological'' Hamiltonian with a highly-degenerate zero-energy ground state (extensive $T=0$ entropy) and $H_1$ is the ``physical'' Hamiltonian that splits this huge multiplet. Usually, $H_0$ is a non-interacting Hamiltonian, with zero modes that form a simple Fock space spanned by Wannier orbitals of low-energy electron bands, or a Landau level, etc. Systems of Laughlin FQHE quasiholes are described by a more general $H_0$ that removes low-relative-angular momentum two-particle states from the zero-mode spectrum, and the non-Abelian Moore-Read and Read-Rezayi quasihole systems involve removal of $n > 2$ particle states. The latter are candidates systems for topological quantum computation. The zero-modes count has been previously obtained by counting the number of linearly-independent polynomials of various types. I give a simpler Pauli-principle-like formulation that transparently gives the counting rules, and allows the creation of subsets of lowest-Landau-level Slater determinant states from which the zero-mode states can be constructed. This aids numerical diagonalization of $P_0H_1P_0$, where $P_0$ is the projection into the zero-modes space of $H_0$, for exact-diagonalization simulations of the manipulations of non-Abelian quasiparticles proposed for topological quantum computations. [Preview Abstract] |
Wednesday, March 15, 2006 12:39PM - 12:51PM |
P46.00008: Quantitative study of the non-Abelian statistics of quasiholes and quasiparticles in the nu=5/2 paired Hall state Csaba Toke, Jainendra Jain We analyze quantitatively various properties of a collection of quasihole and quasiparticle excitations of the paired composite fermion state, described by a Pfaffian wave function proposed by Moore and Read (Nucl.Phys.B 360, 362, 1991), which are relevant to the validity of the notion of non-abelian braiding statistics. Working in the spherical geometry, we study the coupling of two quasiholes as a function of their distance by evaluating both the density profile and the interaction energy of a quasihole pair. Further, we perform a numerical study to check whether the $2^{n-1}$ independent states of $2n$ quasiholes are almost degenerate, i.e.\ the coupling between these states is exponentially suppressed as a function of their separation, which will be crucial for any practical realization of non-Abelian statistics. We also compare the exact diagonalization spectra of the Coulomb interaction in the second Landau level and the model three-body contact interaction for which the Pfaffian state and its quasihole variants are known to be exact. Based on the connection between Halperin's 331 state and the Pfaffian state (Greiter, Wen, and Wilczek, PRL 66, 3205, 1991) we construct a class of quasiparticle wave functions, which we study with respect to both the three- body contact interaction and the Coulomb interaction to test their accuracy. [Preview Abstract] |
Wednesday, March 15, 2006 12:51PM - 1:03PM |
P46.00009: Probing Non-Abelian Statistics in the $\nu=5/2$ Fractional Quantum Hall State Parsa Bonderson, Alexei Kitaev, Kirill Shtengel We analyse an interferometric experiment to detect non-Abelian quasiparticle statistics -- one of the hallmark characteristics of the Moore-Read state expected to describe the observed FQHE plateau at $\nu= 5/2$. The implications for using this state for constructing a topologically protected qubit as has been recently proposed by Das Sarma, Freedman and Nayak are also addressed. [Preview Abstract] |
Wednesday, March 15, 2006 1:03PM - 1:15PM |
P46.00010: Composite fermions and conformal field theory Susanne Viefers, Hans Hansson, Jainendra Jain, Chiachen Chang, Jon Magne Leinaas We show how Quantum Hall quasiparticle wave functions similar to those in the composite fermion theory are related to correlators of certain nonlocal operators in a conformal field theory. Charge and statistics are determined using both analytical and numerical methods. [Preview Abstract] |
Wednesday, March 15, 2006 1:15PM - 1:27PM |
P46.00011: An Exact Solution for the Half-filled Lowest Landau Level Emil Bergholtz, Anders Karlhede We present an exact solution for the interacting electron gas in the half-filled lowest Landau level on a thin torus. The low energy sector consists of non-interacting, one-dimensional, neutral fermions (dipoles). The ground state, which is homogeneous, is the Fermi sea obtained by filling the negative energy states and the excited states are the gapless neutral excitations out of this one-dimensional sea. We identify this ground state as a version of the Rezayi-Read state, and find that it develops continuously, as the circumference grows, into the Rezayi-Read state that is believed to describe the observed metallic phase in the two-dimensional system. This suggests a Luttinger liquid description of the half-filled Landau level. [Preview Abstract] |
Wednesday, March 15, 2006 1:27PM - 1:39PM |
P46.00012: One-Dimensional Theory of the Quantum Hall System Anders Karlhede, Emil J. Bergholtz We consider the lowest Landau level on a torus as a function of its circumference $L_1$. When $L_1\rightarrow 0$, the ground state at general rational filling fraction is a crystal with a gap---a Tao-Thouless state. For filling fractions $\nu=p/(2pm+1)$, these states are the limits of Laughlin's or Jain's wave functions describing the gapped quantum Hall states when $L_1\rightarrow \infty$. For the half-filled Landau level, there is a transition to a Fermi sea of non-interacting neutral dipoles, or rather to a Luttinger liquid modification thereof, at $L_1\sim5$ magnetic lengths. This state is a version of the Rezayi-Read state, and develops continuously into the state that is believed to describe the observed metallic phase as $L_1\rightarrow \infty$. Furthermore, the effective Landau level structure that emerges within the lowest Landau level follows from the magnetic symmetries. [Preview Abstract] |
Wednesday, March 15, 2006 1:39PM - 1:51PM |
P46.00013: Competing liquid and solid orders at $\nu=1/5$ Chia-Chen Chang, Csaba Toke, Gun Sang Jeon, Jainendra K. Jain The lowest Landau level states at very low filling factors are accurately understood as topological quantum crystals of composite fermions. At higher fillings (but still in the lowest Landau level), on the other hand, the system forms an incompressible composite- fermion liquid. However at $\nu=1/5$, both descriptions fail to give an accurate account to the true ground state. Our numerical calculations show that for small systems the crystal has lower energy than the liquid, and only for $N\ge 10$ does the liquid become the ground state. We find that a linear combination of the CF liquid and the CF crystal wave functions provides an excellent account of the actual state for small systems. These results indicate that the $1/5$ fractional Hall state is highly susceptible to the formation of composite fermion crystallites in it. We will discuss the relevance of these results to experiment, and also the possibility of inducing a liquid-solid transition at $1/5$ by tuning the interaction. [Preview Abstract] |
Wednesday, March 15, 2006 1:51PM - 2:03PM |
P46.00014: Electric field effects in the Hall conductivity Alejandro Kunold, Manuel Torres We study the Hall conductivity as a topological invariant under the influence of an intense electric field. We consider a model of a 2DEG in a two-dimensional lattice in the presence of an applied in-plain electric field and perpendicular magnetic field. The Hall conductivity is determined from quasiclassical calculations. In the presence of an electric field the longitudinal quasi-momentum is quantized leading to the appearance of a ‘‘magnetic Stark ladder’’, in which the bands of the Hofstadter butterfly are replaced by a series of quasi discreet levels. We show that the transverse conductivity of this levels is an integer topological invariant independent of the intensity of the electric field thus leading to an integer Hall conductivity. [Preview Abstract] |
Wednesday, March 15, 2006 2:03PM - 2:15PM |
P46.00015: Measurement of Spin Excitations in the Fractional Quantum Hall Regime of 1/2$<\nu<$1 Jun Yan, Yann Gallais, Aron Pinczuk, Loren Pfeiffer, Ken West We use inelastic light scattering methods to investigate quasiparticle excitations of the fractional quantum Hall liquid in the filling factor range 1/2$<\nu<$1. The long wavelength spin wave mode at the Zeeman energy shows intriguing behavior. The mode is observed at the filling factors nu=1, 2/3 and 3/5 of the quantized Hall states but its intensity collapses for filling factors away from these states. In the filling factor range 1/2$<\nu<$2/3 spin excitations are observed below the Zeeman energy. These modes are interpreted as spin flips where the composite fermion Landau level quantum number and spin orientation change. The spectral lineshapes of spin flip excitations suggest a spin polarization transition between $\nu$=3/5 and $\nu$=2/3 [1]. [1] Irene Dujovne et al, PRL 95, 056808 (2005) [Preview Abstract] |
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