Orbital Kondo effect in fractional quantum Hall systems

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 $\nu=1/3$.