Waheb Bishara

Interferometric signature of non-Abelian anyons

Department of Physics, California Institute of Technology, Pasadena, California 91125, USA Microsoft Research, Station Q, Elings Hall, University of California, Santa Barbara, CA 93106, USA Department of Physics, University of California, Santa Barbara, CA 93106, USA Department of Physics and Astronomy, University of California at Riverside, Riverside, CA 92507 Institute for Quantum Information, California Institute of Technology, Pasadena, California 91125, USA Dublin Institute for Advanced Studies, School of Theoretical Physics, 10 Burlington Rd, Dublin, Ireland Department of Mathematical Physics, National University of Ireland, Maynooth, Ireland (Dated: September 18, 2009)

Edge states and interferometers in the Pfaffian and anti-Pfaffian states of the nu=(5/2) quantum Hall system

We compute the tunneling current in a double point contact geometry of a quantum Hall system at filling fraction nu=(5/2), as a function of voltage and temperature, in the weak tunneling regime. We quantitatively compare two possible candidates for the state at nu=(5/2): the Moore-Read Pfaffian state, and its particle-hole conjugate, the anti-Pfaffian. We find that both possibilities exhibit the same qualitative behavior, and both have an even-odd effect that reflects their non-Abelian nature, but differ quantitatively in their voltage and temperature dependence.

Effect of Landau level mixing on the effective interaction between electrons in the fractional quantum Hall regime

We compute the effect of Landau-level mixing on the effective two-body and three-body pseudopotentials for electrons in the lowest and second Landau levels. We find that the resulting effective three-body interaction is attractive in the lowest relative angular momentum channel. The renormalization of the two-body pseudopotentials also shows interesting structure. We comment on the implications for the v = 5/2 fractional quantum Hall state.

Odd-even crossover in a non-Abelian ν=5/2 interferometer

We compute the backscattered current in a double point-contact geometry of a quantum-Hall system at filling fraction ν=5/2 as a function of bias voltage in the weak backscattering regime. We assume that the system is in the universality class of either the Pfaffian or anti-Pfaffian state. When the number of charge e/4 quasiparticles in the interferometer is odd, there is no interference pattern. However, the coupling between a charge e/4 quasiparticle and the edge causes it to be absorbed by the edge at low energies. Consequently, an interference pattern appears at low bias voltages and temperatures, as if there were an even number of quasiparticles in the interferometer. We relate this problem to that of a semi-infinite Ising model with a boundary magnetic field. Using the methods of perturbed boundary conformal field theory, we give an exact expression for this crossover of the interferometer as a function of bias voltage. Finally, we comment on the possible relevance of our results to recent interference experiments.

Multichannel Kondo Models in Non-Abelian Quantum Hall Droplets

We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state which is spatially separated from it by an integer quantum Hall state. Near a resonance, the physics at energy scales below the level spacing of the edge states of the dot is governed by a k-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction nu=2+k/(k+2) or its particle-hole conjugate at nu=2+2/(k+2). The k-channel Kondo model is channel isotropic even without fine-tuning in the former state; in the latter, it is generically channel anisotropic. In the special case of k=2, our results provide a new venue, realized in a mesoscopic context, to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction nu=5/2.

Quantum Hall states at nu=(2/(k + 2)): Analysis of the particle-hole conjugates of the general level-k Read-Rezayi states

We study the ν = 2 k+2 quantum Hall states which are particle-hole conjugates of the ν = k k+2 Read-Rezayi states. We find that equilibration between the different modes at the edge of such a state leads to an emergent SU(2)k algebra in the counter-propagating neutral sector. Heat flow along the edges of these states will be in the opposite direction of charge flow. In the k = 3 case, which may be relevant to ν = 2 + 2 5 , the thermal Hall conductance and the exponents associated with quasiparticle and electron tunneling distinguish this state from competing states such as the hierarchy/Jain state.

Non-Abelian Anyon Superconductivity

Non-Abelian anyons exist in certain spin models and may exist in quantum Hall systems at certain filling fractions. In this work, we studied the ground state of dynamical SU(2) level-kappa Chern-Simons non-Abelian anyons at finite density and no external magnetic field. We find that, in the large-kappa limit, the topological interaction induces a pairing instability and the ground state is a superconductor with d+id gap symmetry. We also develop a picture of pairing for the special value kappa=2 and argue that the ground state is a superfluid of pairs for all values of kappa.

Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots

In this paper, we study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state. We assume the dot is small enough that its level spacing is large compared to both the temperature and the coupling to the spatially proximate bulk non-Abelian fractional quantum Hall state. We focus on the physics of level degeneracy with electron number on the dot. The physics of such a resonant level is governed by a k-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction ν=2+k/(k+2) or its particle-hole conjugate at ν=2+2/(k+2). The k-channel Kondo model is channel symmetric even without fine tuning any couplings in the former state; in the latter, it is generically channel asymmetric. The two limits exhibit non-Fermi-liquid and Fermi-liquid properties, respectively, and therefore may be distinguished. By exploiting the mapping between the resonant level model and the multichannel Kondo model, we discuss the thermodynamic and transport properties of the system. In the special case of k=2, our results provide a distinct venue to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction ν=5/2. We present numerical estimates for realizing this scenario in experiment.

Sagnac interference in carbon nanotubes

The Sagnac interference mode arises when two interfering counterpropogating beams traverse a loop, but with their velocities detuned by a small amount 2u, with vR/L=vF±u. In this paper we perform a perturbative nonequilibrium calculation of Sagnac interference in single-channel wires as well as armchair nanotube loops. We study the dependence of the Sagnac conductance oscillations on temperature and interactions. We find that the Sagnac interference is not destroyed by strong interactions, but becomes weakly dependent on the velocity detuning u. In armchairs nanotubes with typical interaction strength, 0.25<=g<=0.5, we find that the necessary temperature for observing the interference effect, TSAG is also only weakly dependent on the interaction, and is enhanced by a factor of 8 relative to the temperature necessary for observing Fabry-Perot interference in the same system, TFP.