Loss of $\pi$-junction behavior in an interacting impurity Josephson junction

Using a generalization of the noncrossing approximation which incorporates Andreev reflection, we study the properties of an infinite-$U$ Anderson impurity coupled to two superconducting leads. In the regime where $\Delta$ and $T_K$ are comparable, we find that the position of the subgap 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 behavior is lost as the position of the bound state moves above the Fermi energy.