The Interacting Impurity Josephson Junction: Variational Wavefunctions   and Slave Boson Mean Field Theory
  We investigate the Josephson coupling between two superconductors mediated through an infinite U Anderson impurity, adapting a variational wavefunction approach which has proved successful for the Kondo model. Unlike the Kondo problem, however, a crossing of singlet and doublet state energies may be produced by varying the ratio of Kondo energy to superconducting gap, in agreement with recent work of Clerk and Ambegaokar. We construct the phase diagram for the junction and discuss properties of different phases. In addition, we find the singlet and doublet state energies within a slave boson mean field approach. We find the slave boson mean field treatment is unable to account for the level crossing. 
A. V. Rozhkov and Daniel P. Arovas