Dynamical Disentanglement across a Point Contact in a Non-Abelian Quantum Hall State

TL;DR

This paper studies quasiparticle tunneling in a non-Abelian quantum Hall state at filling fraction 5/2, revealing a crossover related to the two-channel Kondo effect and analyzing entropy changes.

Contribution

It develops a bosonized theory of edge modes and identifies a physical link between tunneling behavior and the two-channel Kondo effect in a non-Abelian quantum Hall state.

Findings

Tunneling crossover from T^{-3/2} to -T^4 scaling.

Emergence of an effective spin-1/2 degree of freedom at the point contact.

Entropy change of (2\u00d72) during the flow.

Abstract

We analyze tunneling of non-Abelian quasiparticles between the edges of a quantum Hall droplet at Landau level filling fraction nu=5/2, assuming that the electrons in the first excited Landau level organize themselves in the non-Abelian Moore-Read Pfaffian state. We formulate a bosonized theory of the modes at the two edges of a Hall bar; an effective spin-1/2 degree of freedom emerges in the description of a point contact. We show how the crossover from the high-temperature regime of weak quasiparticle tunneling between the edges of the droplet, with 4-terminal R_{xx} scaling as T^{-3/2}, to the low-temperature limit, with R_{xx} - h/(10 e^2) scaling as -T^4, is closely related to the two-channel Kondo effect. We give a physical interpretation for the entropy of \ln(2\sqrt{2}) which is lost in the flow from the ultraviolet to the infrared.