Edge states and tunneling of non-Abelian quasiparticles in the nu=5/2 quantum Hall state and p+ip superconductors

Abstract

We study quasiparticle tunneling between the edges of a non-Abelian topological state. The simplest examples are a p+ip superconductor and the Moore-Read Pfaffian non-Abelian fractional quantum Hall state; the latter state may have been observed at Landau-level filling fraction nu=5/2. Formulating the problem is conceptually and technically non-trivial: edge quasiparticle correlation functions are elements of a vector space, and transform into each other as the quasiparticle coordinates are braided. We show in general how to resolve this difficulty and uniquely define the quasiparticle tunneling Hamiltonian. The tunneling operators in the simplest examples can then be rewritten in terms of a free boson. One key consequence of this bosonization is an emergent spin-1/2 degree of freedom. We show that vortex tunneling across a p+ip superconductor is equivalent to the single-channel Kondo problem, while quasiparticle tunneling across the Moore-Read state is analogous to the two-channel Kondo effect. Temperature and voltage dependences of the tunneling conductivity are given in the low- and high-temperature limits.

24 pages, 7 figures

References in corpus (13)

• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-Abelian braiding statistics of vortex matter in a $p_x+i{p}_y$ superconductor
• Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
• Quantum phase transitions across p-wave Feshbach resonance
• Fusion rules and vortices in $p_x+i{p}_y$ superconductors
• Towards Universal Topological Quantum Computation in the $\nu =5/2$ Fractional Quantum Hall State
• Dynamical Disentanglement across a Point Contact in a Non-Abelian Quantum Hall State
• The effects of non-abelian statistics on two-terminal shot noise in a quantum Hall liquid in the Pfaffian state
• "Wormhole" geometry for entrapping topologically-protected qubits in non-Abelian quantum Hall states and probing them with voltage and noise measurements
• Aharonov-Bohm effect in the non-Abelian quantum Hall fluid

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