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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 noninteracting 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, K. The predictions of the Fermi-liquid theory for this model 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 TTK, is also calculated using Fermi-liquid theory allowing the definition of a “Wilson ratio” relating the conductance and the persistent current.