Primary-Filling e/3 Quasiparticle Interferometer

We report experimental realization of a quasiparticle interferometer where the entire system is in 1/3 primary fractional quantum Hall state. The interferometer consists of chiral edge channels coupled by quantum-coherent tunneling in two constrictions, thus enclosing an Aharonov-Bohm area. We observe magnetic flux and charge periods h/e and e/3, equivalent to creation of one quasielectron in the island. Quantum theory predicts a 3h/e flux period for charge e/3, integer statistics particles. Accordingly, the observed periods demonstrate the anyonic statistics of Laughlin quasiparticles

Electron interferometry in quantum Hall regime: Aharonov-Bohm effect of interacting electrons

An apparent h/fe Aharonov-Bohm flux period, where f is an integer, has been reported in coherent quantum Hall devices. Such sub-period is not expected for non-interacting electrons and thus is thought to result from interelectron Coulomb interaction. Here we report experiments in a Fabry-Perot interferometer comprised of two wide constrictions enclosing an electron island. By carefully tuning the constriction front gates, we find a regime where interference oscillations with period h/2e persist throughout the transition between the integer quantum Hall plateaus 2 and 3, including half-filling. In a large quantum Hall sample, a transition between integer plateaus occurs near half-filling, where the bulk of the sample becomes delocalized and thus dissipative bulk current flows between the counterpropagating edges ("backscattering"). In a quantum Hall constriction, where conductance is due to electron tunneling, a transition between forward- and back-scattering is expected near the half-filling. In our experiment, neither period nor amplitude of the oscillations show a discontinuity at half-filling, indicating that only one interference path exists throughout the transition. We also present experiments and an analysis of the front-gate dependence of the phase of the oscillations. The results point to a single physical mechanism of the observed conductance oscillations: Aharonov-Bohm interference of interacting electrons in quantum Hall regime.Comment: 10 pages, 4 Fig

Schwinger-Boson Mean-Field Theory of Mixed-Spin Antiferromagnet L2BaNiO5L_2BaNiO_5

The Schwinger-boson mean-field theory is used to study the three-dimensional antiferromagnetic ordering and excitations in compounds $L_2BaNiO_5$, a large family of quasi-one-dimensional mixed-spin antiferromagnet. To investigate magnetic properties of these compounds, we introduce a three-dimensional mixed-spin antiferromagnetic Heisenberg model based on experimental results for the crystal structure of $L_2BaNiO_5$. This model can explain the experimental discovery of coexistence of Haldane gap and antiferromagnetic long-range order below N\'{e}el temperature. Properties such as the low-lying excitations, magnetizations of $Ni$ and rare-earth ions, N\'{e}el temperatures of different compounds, and the behavior of Haldane gap below the N\'{e}el temperature are investigated within this model, and the results are in good agreement with neutron scattering experiments.Comment: 12 pages, 6 figure

Activation gaps for the fractional quantum Hall effect: realistic treatment of transverse thickness

The activation gaps for fractional quantum Hall states at filling fractions $\nu=n/(2n+1)$ are computed for heterojunction, square quantum well, as well as parabolic quantum well geometries, using an interaction potential calculated from a self-consistent electronic structure calculation in the local density approximation. The finite thickness is estimated to make $\sim$30% correction to the gap in the heterojunction geometry for typical parameters, which accounts for roughly half of the discrepancy between the experiment and theoretical gaps computed for a pure two dimensional system. Certain model interactions are also considered. It is found that the activation energies behave qualitatively differently depending on whether the interaction is of longer or shorter range than the Coulomb interaction; there are indications that fractional Hall states close to the Fermi sea are destabilized for the latter.Comment: 32 pages, 13 figure

Orbital magnetization in crystalline solids: Multi-band insulators, Chern insulators, and metals

We derive a multi-band formulation of the orbital magnetization in a normal periodic insulator (i.e., one in which the Chern invariant, or in 2d the Chern number, vanishes). Following the approach used recently to develop the single-band formalism [T. Thonhauser, D. Ceresoli, D. Vanderbilt, and R. Resta, Phys. Rev. Lett. {\bf 95}, 137205 (2005)], we work in the Wannier representation and find that the magnetization is comprised of two contributions, an obvious one associated with the internal circulation of bulk-like Wannier functions in the interior and an unexpected one arising from net currents carried by Wannier functions near the surface. Unlike the single-band case, where each of these contributions is separately gauge-invariant, in the multi-band formulation only the \emph{sum} of both terms is gauge-invariant. Our final expression for the orbital magnetization can be rewritten as a bulk property in terms of Bloch functions, making it simple to implement in modern code packages. The reciprocal-space expression is evaluated for 2d model systems and the results are verified by comparing to the magnetization computed for finite samples cut from the bulk. Finally, while our formal proof is limited to normal insulators, we also present a heuristic extension to Chern insulators (having nonzero Chern invariant) and to metals. The validity of this extension is again tested by comparing to the magnetization of finite samples cut from the bulk for 2d model systems. We find excellent agreement, thus providing strong empirical evidence in favor of the validity of the heuristic formula.Comment: 14 pages, 8 figures. Fixed a typo in appendix

Localized matter-waves patterns with attractive interaction in rotating potentials

We consider a two-dimensional (2D) model of a rotating attractive Bose-Einstein condensate (BEC), trapped in an external potential. First, an harmonic potential with the critical strength is considered, which generates quasi-solitons at the lowest Landau level (LLL). We describe a family of the LLL quasi-solitons using both numerical method and a variational approximation (VA), which are in good agreement with each other. We demonstrate that kicking the LLL mode or applying a ramp potential sets it in the Larmor (cyclotron) motion, that can also be accurately modeled by the VA.Comment: 13 pages, 11 figure

Entropy and Exact Matrix Product Representation of the Laughlin Wave Function

An analytical expression for the von Neumann entropy of the Laughlin wave function is obtained for any possible bipartition between the particles described by this wave function, for filling fraction nu=1. Also, for filling fraction nu=1/m, where m is an odd integer, an upper bound on this entropy is exhibited. These results yield a bound on the smallest possible size of the matrices for an exact representation of the Laughlin ansatz in terms of a matrix product state. An analytical matrix product state representation of this state is proposed in terms of representations of the Clifford algebra. For nu=1, this representation is shown to be asymptotically optimal in the limit of a large number of particles

Spin phase diagram of the nu_e=4/11 composite fermion liquid

Spin polarization of the "second generation" nu_e=4/11 fractional quantum Hall state (corresponding to an incompressible liquid in a one-third-filled composite fermion Landau level) is studied by exact diagonalization. Spin phase diagram is determined for GaAs structures of different width and electron concentration. Transition between the polarized and partially unpolarized states with distinct composite fermion correlations is predicted for realistic parameters.Comment: 5 pages, 3 figure

Transport in the Laughlin quasiparticle interferometer: Evidence for topological protection in an anyonic qubit

We report experiments on temperature and Hall voltage bias dependence of the superperiodic conductance oscillations in the novel Laughlin quasiparticle interferometer, where quasiparticles of the 1/3 fractional quantum Hall fluid execute a closed path around an island of the 2/5 fluid. The amplitude of the oscillations fits well the quantum-coherent thermal dephasing dependence predicted for a two point-contact chiral edge channel interferometer in the full experimental temperature range 10.2<T<141 mK. The temperature dependence observed in the interferometer is clearly distinct from the behavior in single-particle resonant tunneling and Coulomb blockade devices. The 5h/e flux superperiod, originating in the anyonic statistical interaction of Laughlin quasiparticles, persists to a relatively high T~140 mK. This temperature is only an order of magnitude less than the 2/5 quantum Hall gap. Such protection of quantum logic by the topological order of fractional quantum Hall fluids is expected to facilitate fault-tolerant quantum computation with anyons.Comment: 13 pages, 10 figure

Stability of the compressible quantum Hall state around the half-filled Landau level

We study the compressible states in the quantum Hall system using a mean field theory on the von Neumann lattice. In the lowest Landau level, a kinetic energy is generated dynamically from Coulomb interaction. The compressibility of the state is calculated as a function of the filling factor $\nu$ and the width $d$ of the spacer between the charge carrier layer and dopants. The compressibility becomes negative below a critical value of $d$ and the state becomes unstable at $\nu=1/2$. Within a finite range around $\nu=1/2$, the stable compressible state exists above the critical value of $d$.Comment: 4 pages, 4 Postscript figures, RevTe