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# Measurements of quasiparticle tunneling in the υ= 5/2 fractional quantum Hall state

Department of Physics, Massachusetts Institute of Technology, 02139, Cambridge, Massachusetts, USA
(Impact Factor: 3.66). 04/2012; 85(16). DOI: 10.1103/PhysRevB.85.165321

ABSTRACT Some models of the 5/2 fractional quantum Hall state predict that the quasiparticles, which carry the charge, have non-Abelian statistics: exchange of two quasiparticles changes the wave function more dramatically than just the usual change of phase factor. Such non-Abelian statistics would make the system less sensitive to decoherence, making it a candidate for implementation of topological quantum computation. We measure quasiparticle tunneling as a function of temperature and dc bias between counterpropagating edge states. Fits to theory give e*, the quasiparticle effective charge, close to the expected value of e/4 and g, the strength of the interaction between quasiparticles, close to 3/8. Fits corresponding to the various proposed wave functions, along with qualitative features of the data, strongly favor the Abelian 331 state.

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##### Article: Probing the $\nu=\frac{5}{2}$ quantum Hall state with electronic Mach-Zehnder interferometry
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ABSTRACT: It was recently pointed out that Halperin's 113 topological order explains the transport experiments in the quantum Hall liquid at filling factor $\nu=5/2$. The 113 order, however, cannot be easily distinguished from other likely topological orders at $\nu=5/2$ such as the non-Abelian Pfaffian and anti-Pfaffian states and the Abelian Halperin 331 state in Fabry-Perot interferometry. In this paper, we show that an electronic Mach-Zehnder interferometer provides an unambiguous identification of these candidate $\nu=5/2$ states. Specifically, the $I$-$V$ curve for the tunneling current through the interferometer is more asymmetric in the 113 state than in other $\nu=5/2$ states. Moreover, the Fano factor for the shot noise in the interferometer can reach 13.6 in the 113 state, much greater than the maximum Fano factors 3.2 in the Pfaffian and anti-Pfaffian states and 2.3 in the 331 state.
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##### Article: Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
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ABSTRACT: The phenomenon of fractional quantum Hall effect (FQHE) was first experimentally observed 33 years ago. FQHE involves strong Coulomb interactions and correlations among the electrons, which leads to quasiparticles with fractional elementary charge. Three decades later, the field of FQHE is still active with new discoveries and new technical developments. A significant portion of attention in FQHE has been dedicated to filling factor 5/2 state, for its unusual even denominator and possible application in topological quantum computation. Traditionally FQHE has been observed in high mobility GaAs heterostructure, but new materials such as graphene also open up a new area for FQHE. This review focuses on recent progress of FQHE at 5/2 state and FQHE in graphene.
12/2014; 1(4). DOI:10.1093/nsr/nwu071
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##### Article: Theoretical investigation of edge reconstruction in the ν=5/2 and 7/3 fractional quantum Hall states
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ABSTRACT: The edge physics of the ν=5/2 fractional quantum Hall state is of relevance to several recent experiments that use it as a probe to gain insight into the nature of the bulk state. We perform calculations in a semirealistic setup with positive background charge at a distance d, by exact diagonalization both in the full Hilbert space (neglecting Landau level mixing) and in the restricted Pfaffian basis of edge excitations. Our principal finding is that the 5/2 edge is unstable to a reconstruction except for very small d. In addition, the interactions between the electrons in the second Landau level and the lowest Landau level enhance the tendency toward edge reconstruction. We identify the bosonic and fermionic modes of edge excitations and obtain their dispersions by back-calculating from the energy spectra as well as directly from appropriate trial wave functions. We find that the edge reconstruction is driven by an instability in the fermionic sector for setback distances close to the critical ones. We also study the edge of the ν=7/3 state and find that edge reconstruction occurs here more readily than for the ν=1/3 state. Our study indicates that the ν=5/2 and 7/3 edge states are reconstructed for all experimental systems investigated so far and, thus, must be taken into account when analyzing experimental results. We also consider an effective field theory to gain insight into how edge reconstruction might influence various observable quantities.
Physical Review B 10/2014; 90:165104. DOI:10.1103/PhysRevB.90.165104 · 3.66 Impact Factor