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

TL;DR

This paper investigates quasiparticle tunneling in non-Abelian topological states like the nu=5/2 fractional quantum Hall state and p+ip superconductors, revealing connections to Kondo physics and providing a framework for defining tunneling Hamiltonians.

Contribution

It introduces a method to resolve the complex correlation functions of edge quasiparticles and maps tunneling problems to well-known Kondo models, advancing understanding of non-Abelian states.

Findings

Tunneling in p+ip superconductors maps to the single-channel Kondo problem.

Quasiparticle tunneling in the Moore-Read state is analogous to the two-channel Kondo effect.

Derived temperature and voltage dependence of tunneling conductivity.

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.