Tunneling through an Anderson impurity between superconductors

We consider an Anderson impurity (A) weakly connected to a superconducting electrode (S) on one side and a superconducting or a normal-metal electrode (N) on the other side. A general path-integral formalism is developed and the response of SAN and SAS junctions to a constant voltage bias V is elucidated, using a combination of the Keldysh technique (to handle nonequilibrium effects) acid a dynamical mean-field approximation (to handle repulsive Hubbard interactions). An interesting physics is exposed at subgap voltages (eV < for SAN and eV<2 for SAS). For an SAN junction, Andreev reflection is strongly affected by Coulomb interaction. For superconductors with p-wave symmetry the junction conductance exhibits a remarkable peak at eV<, while for superconductors with s-wave symmetric pair potential the peak is shifted towards the gap edge eV=Delta and strongly suppressed if the Hubbard repulsive interaction increases. Electron transport in SAS junctions is determined by an interplay between multiple Andreev reflection (MAR) and Coulomb effects. For s-wave superconductors the usual peaks in the conductance that originate from MAR are shifted by interaction to larger values of V. They are also suppressed as the Hubbard interaction strength grows. For p-wave superconductors the subgap, current is much larger and the I-V characteristics reveal an interesting feature, namely, a peak in the current resulting from a midgap bound state in the junction.