Orbital Kondo effect in fractional quantum Hall systems

TL;DR

This paper investigates the orbital Kondo effect in fractional quantum Hall systems by analyzing transport properties of a charge qubit coupled to chiral Luttinger liquids, revealing how inter-antidot tunneling influences the Kondo fixed point.

Contribution

It introduces a model linking charge qubit behavior to orbital Kondo physics in fractional quantum Hall edges, providing analytical insights into conductance and impurity susceptibility.

Findings

Kondo impurity behavior varies between integer and fractional quantum Hall states.

Inter-antidot tunneling can destabilize the Kondo fixed point in fractional states.

Analytical expressions for conductance and susceptibility are derived.

Abstract

We study transport properties of a charge qubit coupling two chiral Luttinger liquids, realized by two antidots placed between the edges of an integer $\nu=1$ or fractional $\nu=1/3$ quantum Hall bar. We show that in the limit of a large capacitive coupling between the antidots, their quasiparticle occupancy behaves as a pseudo-spin corresponding to an orbital Kondo impurity coupled to a chiral Luttinger liquid, while the inter antidot tunnelling acts as an impurity magnetic field. The latter tends to destabilize the Kondo fixed point for the $\nu=1/3$ fractional Hall state, producing an effective inter-edge tunnelling. We relate the inter-edge conductance to the susceptibility of the Kondo impurity and calculate it analytically in various limits for both $\nu=1$ and $\nu=1/3$.