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 $\nu =1/3$.

• Received 1 March 2015

DOI:https://doi.org/10.1103/PhysRevB.92.075301