Exotic resonant level models in non-Abelian quantum Hall states coupled to quantum dots

TL;DR

This paper explores the coupling of a quantum dot to non-Abelian fractional quantum Hall states, revealing how the resulting resonant level models exhibit distinct Fermi liquid and non-Fermi liquid behaviors, with implications for identifying quantum Hall states.

Contribution

It introduces a mapping between resonant level models and multichannel Kondo models in non-Abelian quantum Hall states, providing new insights into their thermodynamic and transport properties.

Findings

Differentiates Fermi liquid and non-Fermi liquid regimes based on channel symmetry.

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

Offers numerical estimates for experimental realization.

Abstract

In this paper we study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state. We assume the dot is small enough that its level spacing is large compared to both the temperature and the coupling to the spatially proximate bulk non-Abelian fractional quantum Hall state. We focus on the physics of level degeneracy with electron number on the dot. The physics of such a resonant level 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 symmetric even without fine tuning any couplings in the former state; in the latter, it is generically channel asymmetric. The two limits exhibit non-Fermi liquid and Fermi liquid properties, respectively, and therefore may be distinguished. By exploiting the mapping between the resonant level model and the multichannel Kondo model, we discuss the thermodynamic and transport properties of the system. In the special case of $k=2$, our results provide a novel venue to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction $\nu=5/2$. We present numerical estimates for realizing this scenario in experiment.