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

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.

18 pages, 2 figures. Clarified final discussion

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• Charging of a quantum dot coupled to Luttinger liquid leads
• Measuring Luttinger Liquid Correlations from Charge Fluctuations in a Nanoscale Structure
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Cited by in corpus (11)

• Multi-channel Kondo impurity dynamics in a Majorana device
• Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime
• Detection of Majorana edge states in topological superconductors through the non-Fermi-liquid effects induced in an interacting quantum dot
• Capacitance of a resonant level coupled to Luttinger liquids
• Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires
• Coulomb blockade with neutral modes
• Density of states of a dissipative quantum dot coupled to a quantum wire
• Driven quantum dot coupled to a fractional quantum Hall edge
• Orbital Kondo effect in fractional quantum Hall systems
• Identification of the Fractional quantum Hall edge modes by density oscillations
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States