Fermi Liquid Theory for the Persistent Current Past a Side-Coupled Quantum Dot

A Fermi Liquid theory is developed for the persistent current past a side coupled quantum dot yielding analytical predictions for the behavior of the first two harmonics of the persistent current as a function of applied magnetic flux. The quantum dot is assumed weakly coupled to a ring of non-interacting electrons and thus appropriately described as a Kondo impurity. The theory is valid at weak Kondo couplings in the regime where the system size, L, is much larger than the size of the Kondo screening cloud, xi_K. The predictions of the Fermi Liquid theory are compared to exact diagonalization results for the persistent current that lend support to the existence of a regime correctly described by this theory. The finite temperature conductance, at T << T_K is also calculated using Fermi liquid theory allowing the definition of a ``Wilson ratio" relating the conductance and the persistent current.