Orbital Kondo effect in fractional quantum Hall systems

We study the 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 pseudospin corresponding to an orbital Kondo impurity coupled to a chiral Luttinger liquid, while the interantidot tunneling 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 interedge tunneling. We relate the interedge conductance to the susceptibility of the Kondo impurity and calculate it analytically in various limits for both nu = 1 and nu = 1/3.