Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session V40: FQHE: Nu=5/2, Topological Quantum Computing |
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Sponsoring Units: FIAP Chair: Nick Bonesteel, Florida State University Room: Colorado Convention Center 503 |
Thursday, March 8, 2007 11:15AM - 11:27AM |
V40.00001: Quantum Hall effect in a quantum point contact at Landau filling fraction $\nu=\frac{5}{2}$ Jeffrey Miller, Iuliana Radu, Dominik Zumb\"uhl, Eli Levenson-Falk, Marc Kastner, Charles Marcus, Loren Pfeiffer, Ken West We study the transport properties of quantum point contacts (QPC) fabricated on a GaAs/AlGaAs two dimensional electron gas that exhibits excellent bulk fractional quantum Hall effect, including a strong plateau in the Hall resistance at Landau level filling fraction $\nu= \frac{5}{2}$. We find that the $\nu=\frac{5}{2}$ plateau is identifiable in point contacts with lithographic separations as small as 0.8 microns, but is not present in a 0.5 micron QPC. We study the temperature and dc-current-bias dependence of the $\nu=\frac{5}{2}$ plateau---as well as neighboring fractional and integer plateaus---in the QPC. We also discuss our method to study the QPC at one filling fraction while the bulk remains at a higher filling fraction. Research supported in part by Microsoft Corporation, Project Q, and HCRP at Harvard University, and ARO (W911NF-05-1-0062), the NSEC program of the NSF (PHY-0117795) and NSF (DMR-0353209) at MIT. [Preview Abstract] |
Thursday, March 8, 2007 11:27AM - 11:39AM |
V40.00002: Spin and NMR at $\nu = 5/2$ L.A. Tracy, J.P. Eisenstein, L.N. Pfeiffer, K.W. West The spin degree of freedom in a 2DES at $\nu = 5/2$ has been probed using resistively-detected NMR (RDNMR). We have measured the nuclear spin-lattice relaxation time $T_{1}$ of the host semiconductor $^{75}$As nuclei and the response of the 2DES longitudinal resistance to a NMR-induced reduction of the nuclear spin polarization. Measurements were made at temperatures ranging from 200 mK down to 75 mK, where the $\nu = 5/2$ quantum Hall state is just beginning to form. Via the hyperfine coupling, a decrease in nuclear spin polarization increases the electronic Zeeman splitting. Within this model, our RDNMR signal implies that the 2DES resistivity depends on Zeeman energy and, therefore, that the electronic spin polarization at $\nu = 5/2$ is incomplete in this temperature regime. [Preview Abstract] |
Thursday, March 8, 2007 11:39AM - 11:51AM |
V40.00003: 5/2 FQHE without assuming pairing Jainendra Jain, Csaba T\H oke We investigate the fractional quantum Hall effect at filling factor 5/2 without assuming pairing at the outset; this provides an alternative starting point to the Pfaffian wave function of Moore and Read. The model of noninteracting composite fermions produces a gapless Fermi sea at 5/2. We demonstrate that the residual interaction between composite fermions opens a gap and establishes incompressibility at this filling factor. This approach has the advantage of being amenable to systematic perturbative improvements, and produces ground as well as excited states. It also shows that the 5/2 state can be obtained from the composite-fermion Fermi sea by a slight reorganization of composite fermions near the Fermi energy. We will comment on the quantitative accuracy of this approach, as well as its relation to other approaches. [Preview Abstract] |
Thursday, March 8, 2007 11:51AM - 12:03PM |
V40.00004: Properties of a double point contact in the Moore-Read quantum Hall state. Eddy Ardonne, Eun-Ah Kim The double point contact is an ideal setup to probe the statistics properties of the 5/2 quantum Hall state. We provide quantitative predictions for such a setup at finite temperature and voltage, based on the assumption that the system is in the Moore- Read (a.k.a. pfaffian) quantum Hall state. We will focus on the non-abelian features in our predictions for current, and in particular, in the current-current correlation measurements. We find that the current-current correlations have qualitatively different frequency dependence, depending on the state of the device. Therefore, the current-current correlations provide an excellent signature of the non-abelian statistics, which should be accessible with current technology. [Preview Abstract] |
Thursday, March 8, 2007 12:03PM - 12:15PM |
V40.00005: Nature of excitations of the 5/2 fractional quantum Hall effect Nicolas Regnault, Csaba Toke, Jainendra Jain We show, with the help of exact diagonalization studies on systems with up to sixteen electrons in the presence of up to two delta function impurities, that the Pfaffian model is not accurate for the actual quasiholes and quasiparticles of the 5/2 fractional quantum Hall effect. We discuss implications for non-Abelian statistics. [Preview Abstract] |
Thursday, March 8, 2007 12:15PM - 12:27PM |
V40.00006: Explicit monodromy of Moore-Read wave functions on a torus Suk Bum Chung, Michael Stone We construct the wave functions for the Moore-Read $\nu = 5/2$ quantum Hall state on a torus in the presence of two quasiholes. These explicit wave functions allow us to compute the monodromy matrix that describes the effect of quasihole motion on the space of degenerate ground states. The result agrees with that discussed recently by Oshikawa {\it et al.} (cond-mat/067743) Our calculation provides a conformal field theory explanation of why certain transitions between ground states are forbidden. It is because taking a quasihole around a generator of the torus can change the fusion channel of the two quasiholes, and this requires a change of parity of the electron number in some of the ground states. [Preview Abstract] |
Thursday, March 8, 2007 12:27PM - 12:39PM |
V40.00007: Mapping the Braiding Properties of Non-Abelian FQHE Liquids. Emil Prodan, F. D. M. Haldane Non-Abelian FQHE (NAFQHE) states have elementary excitations that cannot be individually locally-created. When widely separated, they give rise to topological (quasi-)degeneracy of the quantum states; braiding of such non-Abelian quasiparticles (NAQP's) implements unitary transformations among the degenerate states that may be useful for ``topological quantum computing'' (TQC). We have developed a new technique for explicit computation of NAQP braiding in models exhibiting ideal NAFQHE behavior (where the topological degeneracy is exact), in particular the Moore-Read $\nu$ = 5/2 state. For systems of small numbers of NAQP's on a sphere, we have computed the non-Abelian Berry curvature and Hilbert space metric, as one NAQP is moved relative to a fixed configuration of the others, showing how the topological properties develop as the system size (NAQP separation) increases. We also studied the effect of perturbations (Coulomb interaction and substrate potentials) that lift the exact degeneracy, and become the dominant corrections when NAQP's are brought together so that quantum measurements can be made; these effects are likely to be crucial in determining whether TQC is viable in NAFQHE systems. [Preview Abstract] |
Thursday, March 8, 2007 12:39PM - 12:51PM |
V40.00008: Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement Kun Yang, Xin Wan, Edward Rezayi We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at filling fraction 5/2, with Coulomb interaction and background confining potential. We find the ground state that has the same angular momentum quantum number of, and subtantial overlap with the Moore-Read state is stable within a finite but narrow window in parameter space. The corresponding low-energy edge excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge +e/4 quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for the edge Majorana fermion mode, clearly indicating the non-Abelian nature of the quasihole. On the other hand the stabilization of a charge +e/2 quasihole does not change the characteristics of the fermionic edge excitation spectrum qualitatively. Possible edge instabilities due to the competition between Coulomb interaction and confining potential will be discussed. [Preview Abstract] |
Thursday, March 8, 2007 12:51PM - 1:03PM |
V40.00009: Spin Order and Spin Textures in Paired Quantum Hall States Ivailo Dimov, Chetan Nayak We consider quantum Hall ground states and low-lying excitations at even-denominator filling fractions, especially $\nu=5/2$, in the limit of small Zeeman energy. We show that an incompressible ground state will exhibit spontaneous ferromagnetism, which implies that it is in the universality class of the Pfaffian state. Sufficiently strong spin-orbit coupling will drive the system into the $(3,3,1)$ state. The Pfaffian state has low-energy charged excitations which are spin textures. If the Zeeman energy is below a critical value, the ferromagnetic exchange energy stabilizes a bound state of two non-Abelian quasiparticles. [Preview Abstract] |
Thursday, March 8, 2007 1:03PM - 1:15PM |
V40.00010: Interferometry Measurements of Anyonic Charge Parsa Bonderson, Johannes Slingerland, Kirill Shtengel We examine interferometric measurements of the topological charge of (possibly non-Abelian) anyons. Such measurements are essential to the implementations of topological quantum computation which have been proposed in the context of quantum Hall states. Anyons are placed in a Mach-Zehnder interferometer and their topological charge is determined from the effect it has on the interference of probe particles sent through the interferometer. We find that superpositions of distinct anyonic charges in the target collapse when the probe particles have nontrivial monodromy with the differences between the anyonic charges. [Preview Abstract] |
Thursday, March 8, 2007 1:15PM - 1:27PM |
V40.00011: Anyons in a weakly interacting system Conan Weeks, Babak Seradjeh, Marcel Franz Anyons -- particles with fractional exchange statistics -- are known to emerge as excitations in certain strongly correlated two dimensional systems such as the fractional quantum Hall liquids. Here we describe a theoretical proposal for a system whose excitations are anyons with the exchange phase $\pi/4$, but, remarkably, can be thought of as a composite of essentially noninteracting electrons. The system consists of an artificially structured type-II superconducting film adjacent to a 2D electron gas in the integer quantum Hall regime with filling fraction 1. The proposal is based on the observation that a vacancy in an otherwise periodic vortex lattice creates a bound state in 2DEG with total charge $-e/2$. [Preview Abstract] |
Thursday, March 8, 2007 1:27PM - 1:39PM |
V40.00012: Topological invariants of time-reversal-invariant band structures Joel Moore, Leon Balents The topological invariants of a time-reversal-invariant band structure in two dimensions are multiple copies of the $\boldmath{Z}_2$ invariant found by Kane and Mele. Such invariants protect the topological insulator and give rise to a spin Hall effect carried by edge states. Each pair of bands related by time reversal is described by a single $\boldmath{Z}_2$ invariant, up to one less than half the dimension of the Bloch Hamiltonians. In three dimensions, there are four such invariants per band pair. The $\boldmath{Z}_2$ invariants of a crystal determine the transitions between ordinary and topological insulators as its bands are occupied by electrons. We derive these invariants using maps from the Brillouin zone to the space of Bloch Hamiltonians and clarify the connections between $\boldmath{Z}_2$ invariants, the integer invariants that underlie the integer quantum Hall effect, and previous invariants of ${\cal T}$-invariant Fermi systems. [Preview Abstract] |
Thursday, March 8, 2007 1:39PM - 1:51PM |
V40.00013: ABSTRACT WITHDRAWN |
Thursday, March 8, 2007 1:51PM - 2:03PM |
V40.00014: Probing Non-Abelian Statistics with Quasiparticle Interferometry Johannes Slingerland, Parsa Bonderson, Kirill Shtengel We examine interferometric experiments in systems that exhibit non-Abelian braiding statistics, particularly the non-Abelian quantum Hall states that have recently been proposed as media for topologically protected quantum computation. We find a general expression for the current through a two point contact interferometer in these systems in terms of the topological S-matrix of the non-Abelian anyons. In particular, we give detailed results for the Read-Rezayi series of states, providing explicit predictions for the recently observed $nu=\frac{12}{5}$ quantum Hall plateau. [Preview Abstract] |
Thursday, March 8, 2007 2:03PM - 2:15PM |
V40.00015: Abelian and non-abelian quasi-particles as domain-wall type defects Alexander Seidel, Dung-Hai Lee The traditional framework to study fractional quantum Hall states is based on Laughlin type wavefunctions and Chern-Simons field theories. Recently, a new framework has been proposed that puts stronger emphasis on the one-dimensional (1d) Hilbert space structure of Landau levels. This formalism is based on the fact that all known many-body wavefuntions describing fractional quantum Hall liquids reduce to simple one-dimensional charge-density-wave (CDW) patterns when studied on a thin torus or cylinder. These CDW states are adiabatically connected to the bulk quantum Hall liquid states when the circumference of the cylinder or torus is increased. Many general properties of fractional quantum Hall systems are rooted in these CDW states, such as degeneracies and fractional quantum numbers. In this talk, it will be shown in particular how the properties of the $\nu=1$ bosonic Pfaffian state are encoded in the corresponding CDW-patterns. It will also be explained how even braiding statistics can be addressed in a language of adiabatically evolved 1d domain-wall states, at least in the abelian case. [Preview Abstract] |
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