Loss of Pi-Junction Behaviour in an Interacting Impurity Josephson Junction

Using a generalization of the non-crossing approximation which incorporates Andreev reflection, we study the properties of an infinite-U Anderson impurity coupled to two superconducting leads. In the regime where $\mathrm{\Delta }$ and $T_K$ are comparable, we find that the position of the sub-gap resonance in the impurity spectral function develops a strong anomalous phase dependence-- its energy is a minimum when the phase difference between the superconductors is equal to $\pi$. Calculating the Josephson current through the impurity, we find that $\pi$-junction behaviour is lost as the position of the bound-state moves above the Fermi energy.