Multi-channel Kondo Models in non-Abelian Quantum Hall Droplets

TL;DR

This paper explores how a quantum dot coupled to non-Abelian fractional quantum Hall states can be described by multi-channel Kondo models, offering a way to distinguish between different quantum Hall states at filling fraction 5/2.

Contribution

It establishes a connection between quantum Hall edge states and multi-channel Kondo models, revealing channel isotropy or anisotropy depending on the state, and proposes a method to differentiate Pfaffian and anti-Pfaffian states.

Findings

For Read-Rezayi states, the model is channel isotropic without fine tuning.

For particle-hole conjugates, the model is generally channel anisotropic.

Provides a mesoscopic approach to distinguish Pfaffian and anti-Pfaffian states at ν=5/2.

Abstract

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 $\nu=5/2$.